1 Load data

2 Data managment

2.1 Managing binary variables
2.2 Inspecting the clean data

3 Codebook

4 Table 1

5 Task 1: Ignoring covariates, estimate the effect of treatment vs. control on the two outcomes

5.1 Quantitative outcome: cardbill
5.2 Binary outcome: sixMonthSurvive

6 Task 2: Fitting the propensity score model

6.1 Comparing distribution of propensity scores across treatment groups
6.2 Numerically
6.3 Visually

6.3.1 Boxplot
6.3.2 Density plot

7 Task 3: Rubin’s Rules For Assessing Overlap Before Propensity Adjustment

7.1 Rubin’s Rule 1
7.2 Rubin’s Rule 2

8 Task 4: Greedy 1:1 matching on the linear PS

8.1 Love Plot of standardized differences before and after 1:1 matching
8.2 Using ggplot
8.3 Using cobalt to make the Love Plot
8.4 Extracting Variance Ratios
8.5 Creating a dataframe containing the matched sample
8.6 Reassessing Rubin’s Rules after 1:1 matching without replacement

8.6.1 Rubin’s Rule 1
8.6.2 Rubin’s Rule 2

9 Task 5: Estimating the causal effect of the treatment on both outcomes after 1:1 matching without replacement

9.1 The Quantitative Outcome
9.2 The Binary Outcome

10 Task 6 1:1 Matching With replacement

10.1 Love Plot of standardized differences before and after 1:1 matching
10.2 Using ggplot
10.3 Using cobalt to make the Love Plot
10.4 Extracting Variance Ratios

10.4.1 Using ‘cobalt’ to make a Love Plot of Variance Ratios

10.5 Creating a dataframe containing the matched sample

10.5.1 How many times were the non-treated patients matched?

10.6 Reassessing Rubin’s Rules after 1:1 matching with replacement

10.6.1 Rubin’s Rule 1
10.6.2 Rubin’s Rule 2

10.7 Estimating the causal effect of the treatment on both outcomes after 1:1 matching with replacement

10.7.1 The Quantitative Outcome
10.7.2 The Binary Outcome

11 Task 7: Subclassification by Propensity Score Quintile

11.1 Check Balance and Propensity Score Overlap in Each Quintile

11.1.1 Numerically
11.1.2 Graphically

11.2 Creating a Standardized Difference Calculation Function
11.3 Plotting the post-subclassification standardized differences
11.4 Rubin’s Rules post subclassification

11.4.1 Rule 1
11.4.2 Rule 2

12 Task 8: Estimated effect after subclassification

12.1 Quantitative outcome
12.2 Binary Outcome

13 Task 9: Weighting

13.1 Calculating the ATT and ATE weights

13.1.1 ATT weights
13.1.2 ATE weights

13.2 Working with the ATT weights

13.2.1 Rubin’s Rules
13.2.2 Estimated effect on outcomes after ATT weighting

13.3 Working with the ATE weights

13.3.1 Rubin’s Rules
13.3.2 Estimated effect on outcomes after ATE weighting

14 Task 10: Using TWANG for propensity score estimation and ATT weighting

14.1 Estimated effect on outcomes after TWANG ATT weighting

14.1.1 Quantitative outcome
14.1.2 Binary outcome

15 Task 11: After direct adjustment with linear PS

15.1 Quantitative outcome
15.2 Binary outcome

16 Task 12: “Double Robust” Approach: Weighting + Direct Adjustment

16.1 Quantitative outcome

16.1.1 ATT weights
16.1.2 ATE weights
16.1.3 TWANG ATT weights

16.2 Binary outcome

16.2.1 ATT weights
16.2.2 ATE weights
16.2.3 TWANG ATT weights

16.3 Session Information

# Load packages
library(broom)
library(patchwork)
library(cobalt)
library(Matching)
library(tableone)
library(twang)
library(janitor)
library(here)
library(magrittr)
library(lme4)
library(tidyverse)

Note: we will also use the broom.mixed package, but we are not loading it as to prevent it conflicting with the functions of broom.

If you notice any errors or encounter any problems with this example, please contact Wyatt Bensken.

1 Load data

Information on the lindner dataset can be found at this site.^1,2

¹ Rdocumentation. (n.d.). lindner: Lindner Center Data On 996 PCI Patients Analyzed By Kereiakes Et Al. (2000). Retrieved from https://www.rdocumentation.org/packages/MatchLinReg/versions/0.7.0/topics/lindner

² Kereiakes DJ, Obenchain RL, Barber BL, et al. Abciximab provides cost effective survival advantage in high volume interventional practice. Am Heart J 2000; 140: 603-610.

lindner_raw <- read.csv("data/lindner.csv")

lindner_raw %>%
  head(10)

   lifepres cardbill abcix stent height female diabetic acutemi ejecfrac
1       0.0    14301     1     0    163      1        1       0       56
2      11.6     3563     1     0    168      0        0       0       56
3      11.6     4694     1     0    188      0        0       0       50
4      11.6     7366     1     0    175      0        1       0       50
5      11.6     8247     1     0    168      1        0       0       55
6      11.6     8319     1     0    178      0        0       0       50
7      11.6     8410     1     0    185      0        0       0       58
8      11.6     8517     1     0    173      1        0       0       30
9      11.6     8763     1     0    152      1        0       0       60
10     11.6     8823     1     0    180      0        0       0       60
   ves1proc sixMonthSurvive
1         1           FALSE
2         1            TRUE
3         1            TRUE
4         1            TRUE
5         1            TRUE
6         1            TRUE
7         1            TRUE
8         1            TRUE
9         1            TRUE
10        1            TRUE

colSums(is.na(lindner_raw))

       lifepres        cardbill           abcix           stent          height 
              0               0               0               0               0 
         female        diabetic         acutemi        ejecfrac        ves1proc 
              0               0               0               0               0 
sixMonthSurvive 
              0

After reading in the data, we can print the first 10 rows to get a sense of what our data looks like. We see it contains information on 996 participants, and there is no missing data.

2 Data managment

2.1 Managing binary variables

In the course of this example, we’ll want both a numeric and factored version of each binary variable.

In all numeric versions of binary variables: 1 indicates ‘yes’ to having trait/characteristic, 0 indicates ‘no’ to having trait/characteristic.
Variable names with trailing "_f" denotes the factored version of each binary variable.

# Six month survival (turning logical variable to a factor)
lindner_raw$sixMonthSurvive_f <- factor(lindner_raw$sixMonthSurvive, levels = c(TRUE,FALSE),
                                        labels = c("yes", "no"))

# Creating numeric (1/0) version of six month survival variable
lindner_raw$sixMonthSurvive <- factor(lindner_raw$sixMonthSurvive_f, levels = c("yes","no"),
                                      labels = c(1, 0))

lindner_raw$sixMonthSurvive <- ifelse(lindner_raw$sixMonthSurvive == "1", 1, 0)

#Add variable named treated (same values as abcix variable)
lindner_raw$treated <- lindner_raw$abcix

# Factoring the exposure of interest variable. Change the name to 'treated' too.
lindner_raw$treated_f <- factor(lindner_raw$abcix, levels = c(1,0),
                                labels = c("treated", "control"))

# Factor version of stent variable
lindner_raw$stent_f <- factor(lindner_raw$stent, levels = c(1,0),
                              labels = c("yes", "no"))

# Factoring the female variable
lindner_raw$female_f <- factor(lindner_raw$female, levels = c(1,0),
                               labels = c("female", "male"))

# Factoring the diabetic variable
lindner_raw$diabetic_f <- factor(lindner_raw$diabetic, levels = c(1,0),
                                 labels = c("yes", "no"))

# Factoring the acutemi variable
lindner_raw$acutemi_f <- factor(lindner_raw$acutemi, levels = c(1,0),
                                labels = c("yes", "no"))

# Add patientid

lindner_raw <- tibble::rowid_to_column(lindner_raw, "patientid")

# Make lindner dataset with "clean" name. 
lindner_clean <- lindner_raw

2.2 Inspecting the clean data

mosaic::inspect(lindner_clean)

Registered S3 method overwritten by 'mosaic':
  method                           from   
  fortify.SpatialPolygonsDataFrame ggplot2


categorical variables:  
               name  class levels   n missing
1 sixMonthSurvive_f factor      2 996       0
2         treated_f factor      2 996       0
3           stent_f factor      2 996       0
4          female_f factor      2 996       0
5        diabetic_f factor      2 996       0
6         acutemi_f factor      2 996       0
                                   distribution
1 yes (97.4%), no (2.6%)                       
2 treated (70.1%), control (29.9%)             
3 yes (66.9%), no (33.1%)                      
4 male (65.3%), female (34.7%)                 
5 no (77.6%), yes (22.4%)                      
6 no (85.6%), yes (14.4%)                      

quantitative variables:  
                 name   class  min       Q1  median       Q3      max
...1        patientid integer    1   249.75   498.5   747.25    996.0
...2         lifepres numeric    0    11.60    11.6    11.60     11.6
...3         cardbill integer 2216 10218.75 12458.0 16660.00 178534.0
...4            abcix integer    0     0.00     1.0     1.00      1.0
...5            stent integer    0     0.00     1.0     1.00      1.0
...6           height integer  108   165.00   173.0   178.00    196.0
...7           female integer    0     0.00     0.0     1.00      1.0
...8         diabetic integer    0     0.00     0.0     0.00      1.0
...9          acutemi integer    0     0.00     0.0     0.00      1.0
...10        ejecfrac integer    0    45.00    55.0    56.00     90.0
...11        ves1proc integer    0     1.00     1.0     2.00      5.0
...12 sixMonthSurvive numeric    0     1.00     1.0     1.00      1.0
...13         treated integer    0     0.00     1.0     1.00      1.0
              mean           sd   n missing
...1  4.985000e+02 2.876647e+02 996       0
...2  1.129719e+01 1.850501e+00 996       0
...3  1.567416e+04 1.118226e+04 996       0
...4  7.008032e-01 4.581362e-01 996       0
...5  6.686747e-01 4.709262e-01 996       0
...6  1.714438e+02 1.065813e+01 996       0
...7  3.473896e-01 4.763800e-01 996       0
...8  2.238956e-01 4.170623e-01 996       0
...9  1.435743e-01 3.508337e-01 996       0
...10 5.096687e+01 1.041326e+01 996       0
...11 1.385542e+00 6.573525e-01 996       0
...12 9.738956e-01 1.595259e-01 996       0
...13 7.008032e-01 4.581362e-01 996       0

3 Codebook

Information was copy/pasted from here ^1,2 (with some changes to reflect this analysis)

cardbill (Quantitative Outcome): “Cardiac related costs incurred within 6 months of patient’s initial PCI; numeric value in 1998 dollars; costs were truncated by death for the 26 patients with lifepres == 0.”
sixMonthSurvive/sixMonthSurvive_f (Binary Outcome): “Survival at six months a recoded version of lifepres.”
treated/treated_f (Exposure): “Numeric treatment selection indicator; 0 implies usual PCI care alone; 1 implies usual PCI care deliberately augmented by either planned or rescue treatment with abciximab.”
stent/stent_f: “Coronary stent deployment; numeric, with 1 meaning YES and 0 meaning NO.”
height: “Height in centimeters; numeric integer from 108 to 196.”
female/female_f: “Female gender; numeric, with 1 meaning YES and 0 meaning NO.”
diabetic/diabetic_f: “Diabetes mellitus diagnosis; numeric, with 1 meaning YES and 0 meaning NO.”
acutemi/acutemi_f: “Acute myocardial infarction within the previous 7 days; numeric, with 1 meaning YES and 0 meaning NO.”
ejecfrac: “Left ejection fraction; numeric value from 0 percent to 90 percent.”
ves1proc: “Number of vessels involved in the patient’s initial PCI procedure; numeric integer from 0 to 5.”
patientid: a made-up order of numbers to assign patient IDs for later use
Note: Percutaneous Coronary Intervention (PCI)

² Kereiakes DJ, Obenchain RL, Barber BL, et al. Abciximab provides cost effective survival advantage in high volume interventional practice. Am Heart J 2000; 140: 603-610.

4 Table 1

var_list = c("cardbill", "sixMonthSurvive_f", "stent_f", "height", "female_f", "diabetic_f", 
             "acutemi_f", "ejecfrac", "ves1proc")

factor_list = c("sixMonthSurvive_f", "stent_f", "female_f", "diabetic_f", "acutemi_f")

CreateTableOne(vars = var_list, strata = "treated_f",
               data = lindner_clean, factorVars = factor_list)

                            Stratified by treated_f
                             treated            control             p      test
  n                               698                298                       
  cardbill (mean (SD))       16126.68 (9383.83) 14614.22 (14514.00)  0.051     
  sixMonthSurvive_f = no (%)       11 ( 1.6)          15 ( 5.0)      0.004     
  stent_f = no (%)                206 (29.5)         124 (41.6)     <0.001     
  height (mean (SD))           171.44 (10.69)     171.45 (10.59)     0.996     
  female_f = male (%)             467 (66.9)         183 (61.4)      0.111     
  diabetic_f = no (%)             555 (79.5)         218 (73.2)      0.034     
  acutemi_f = no (%)              573 (82.1)         280 (94.0)     <0.001     
  ejecfrac (mean (SD))          50.40 (10.42)      52.29 (10.30)     0.009     
  ves1proc (mean (SD))           1.46 (0.71)        1.20 (0.48)     <0.001

As we can see, The mean cardbill was higher in the treated population and a larger percentage of controls did not survive through 6 months.

5 Task 1: Ignoring covariates, estimate the effect of treatment vs. control on the two outcomes

5.1 Quantitative outcome: `cardbill`

lindner_clean %$%
  mosaic::favstats(cardbill ~ treated_f)

  treated_f  min       Q1 median       Q3    max     mean        sd   n missing
1   treated 3563 10902.25  12944 17080.75  96741 16126.68  9383.825 698       0
2   control 2216  8300.00  10423 15895.75 178534 14614.22 14513.996 298       0

Across the entire sample, the mean ($16,127 vs. $14,614) and median ($12,944 vs. $10,423) cardiac care costs were higher in treated individuals than non-treated controls.

ggplot(lindner_clean, aes(x = cardbill, fill = "cardbill")) +
  geom_histogram() +
  theme_bw() +
  labs(y = "Count",
       x = "Cardiac care costs ($)",
       title = "Cardbill appears to be right skewed") +
  guides(fill = FALSE)

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

As we can see in this figure, cardbill appears to be right/positively skewed.

unadjust_quant_outcome <- lm(cardbill ~ treated, data = lindner_clean)

unadjust_quant_outcome_tidy <- tidy(unadjust_quant_outcome, conf.int = TRUE, conf.level = 0.95) %>%
    filter(term == "treated")

unadjust_quant_outcome_tidy

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated    1512.      773.      1.96  0.0506    -3.83     3029.

Treated individuals were estimated to spend 1512.46 (95%CI: -3.83, 3028.76) more dollars than non-treated controls

5.2 Binary outcome: `sixMonthSurvive`

Epi::twoby2(table(lindner_clean$treated_f, lindner_clean$sixMonthSurvive_f))

2 by 2 table analysis: 
------------------------------------------------------ 
Outcome   : yes 
Comparing : treated vs. control 

        yes no    P(yes) 95% conf. interval
treated 687 11    0.9842    0.9718   0.9913
control 283 15    0.9497    0.9182   0.9694

                                   95% conf. interval
             Relative Risk: 1.0364    1.0080   1.0656
         Sample Odds Ratio: 3.3103    1.5020   7.2957
Conditional MLE Odds Ratio: 3.3057    1.3992   8.0624
    Probability difference: 0.0346    0.0115   0.0664

             Exact P-value: 0.0037 
        Asymptotic P-value: 0.0030 
------------------------------------------------------

The odds treated individuals were alive after 6 months was roughly 3.31 times the odds that non-treated individuals were alive after 6 months.

unadjust_binary_outcome <- glm(sixMonthSurvive ~ treated, data = lindner_clean, family = binomial())

unadjust_binary_outcome_tidy <- tidy(unadjust_binary_outcome, conf.int = TRUE, conf.level = 0.95, exponentiate = TRUE) %>%
    filter(term == "treated")

unadjust_binary_outcome_tidy

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     3.31     0.403      2.97 0.00299     1.51      7.48

The odds of being alive after six months in treated individuals was 3.31 (95%CI: 1.51, 7.48) times higher than the odds that a non-treated control would be alive after six months.

6 Task 2: Fitting the propensity score model

We will now fit the propensity score, which predicts treatment status based on available covariates. Remember, we’re not worried about overfitting (including too many covariates) when calculating the propensity scores.

psmodel <- glm(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc, family = binomial(), data =lindner_clean)

summary(psmodel)


Call:
glm(formula = treated ~ stent + height + female + diabetic + 
    acutemi + ejecfrac + ves1proc, family = binomial(), data = lindner_clean)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-2.5211  -1.2109   0.6399   0.8827   1.5259  

Coefficients:
             Estimate Std. Error z value Pr(>|z|)    
(Intercept)  2.965651   1.731085   1.713  0.08668 .  
stent        0.573018   0.150454   3.809  0.00014 ***
height      -0.015366   0.009534  -1.612  0.10700    
female      -0.359060   0.206904  -1.735  0.08267 .  
diabetic    -0.406810   0.170623  -2.384  0.01711 *  
acutemi      1.199548   0.270468   4.435 9.20e-06 ***
ejecfrac    -0.014789   0.007403  -1.998  0.04574 *  
ves1proc     0.760502   0.138437   5.493 3.94e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 1215.5  on 995  degrees of freedom
Residual deviance: 1124.3  on 988  degrees of freedom
AIC: 1140.3

Number of Fisher Scoring iterations: 4

Store the raw and linear propensity scores below.

lindner_clean$ps <- psmodel$fitted
lindner_clean$linps <- psmodel$linear.predictors

6.1 Comparing distribution of propensity scores across treatment groups

6.2 Numerically

lindner_clean %$% 
  mosaic::favstats(ps ~ treated_f)

  treated_f       min        Q1    median        Q3       max      mean
1   treated 0.3121753 0.6402644 0.7158289 0.8259514 0.9800181 0.7265015
2   control 0.2323431 0.5558665 0.6462761 0.7093624 0.9583296 0.6406106
         sd   n missing
1 0.1299570 698       0
2 0.1230138 298       0

We can see there are no propensity scores equal to, or very close to, 0 or 1.

6.3 Visually

6.3.1 Boxplot

Now we’ll visualize the distribution of the propensity scores stratified by treatment status.

ggplot(lindner_clean, aes(x = treated_f, y = ps, color = treated_f)) +
geom_boxplot() +
geom_jitter(width = 0.1) +
guides(color = FALSE) +
theme_bw() +
labs(x = "",
     title = "Raw propensity scores, stratified by exposure group")

6.3.2 Density plot

ggplot(lindner_clean, aes(x = linps, fill = treated_f)) +
geom_density(alpha = 0.3) +
  theme_bw()

Both of these plots demonstrate good overlap, suggesting a propensity score analysis may be appropriate.

7 Task 3: Rubin’s Rules For Assessing Overlap Before Propensity Adjustment

7.1 Rubin’s Rule 1

rubin1.unadj <- with(lindner_clean,
abs(100*(mean(linps[treated==1])-mean(linps[treated==0]))/sd(linps)))
rubin1.unadj

[1] 61.86668

As you can see, we fail Rubin’s Rule 1 - in which we want below 50%.

7.2 Rubin’s Rule 2

rubin2.unadj <-with(lindner_clean, var(linps[treated==1])/var(linps[treated==0]))
rubin2.unadj

[1] 1.672048

We also “fail” Rubin’s Rule 2 wherewe are looking for value between 0.8 - 1.2 (ideally, 1).

8 Task 4: Greedy 1:1 matching on the linear PS

The first type of match we will conduct is greedy 1:1 matching, without replacement. As we had only 298 controls, we will not match all of the 698 treated patients.

X <- lindner_clean$linps ## matching on the linear propensity score
Tr <- as.logical(lindner_clean$treated)
match1 <- Match(Tr=Tr, X=X, M = 1, replace=FALSE, ties=FALSE)

Warning in Match(Tr = Tr, X = X, M = 1, replace = FALSE, ties = FALSE):
replace==FALSE, but there are more (weighted) treated obs than control obs. Some
treated obs will not be matched. You may want to estimate ATC instead.

summary(match1)


Estimate...  0 
SE.........  0 
T-stat.....  NaN 
p.val......  NA 

Original number of observations..............  996 
Original number of treated obs...............  698 
Matched number of observations...............  298 
Matched number of observations  (unweighted).  298

Below we’ll assess the match balance from the 1:1 matching.

set.seed(2021)
mb1 <- MatchBalance(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean,
match.out = match1, nboots=500)


***** (V1) stent *****
                       Before Matching       After Matching
mean treatment........    0.70487           0.60738 
mean control..........    0.58389           0.58389 
std mean diff.........     26.505            4.8022 

mean raw eQQ diff.....    0.12081           0.02349 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........   0.060489          0.011745 
med  eCDF diff........   0.060489          0.011745 
max  eCDF diff........    0.12098           0.02349 

var ratio (Tr/Co).....    0.85457           0.98151 
T-test p-value........ 0.00032255           0.49878 


***** (V2) height *****
                       Before Matching       After Matching
mean treatment........     171.44            171.77 
mean control..........     171.45            171.45 
std mean diff.........  -0.033804            3.1486 

mean raw eQQ diff.....    0.56376           0.88591 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....         20                36 

mean eCDF diff........  0.0078996          0.013639 
med  eCDF diff........  0.0060095          0.010067 
max  eCDF diff........   0.024971          0.053691 

var ratio (Tr/Co).....     1.0201           0.93356 
T-test p-value........    0.99608           0.70632 
KS Bootstrap p-value..      0.938             0.528 
KS Naive p-value......    0.99947           0.78362 
KS Statistic..........   0.024971          0.053691 


***** (V3) female *****
                       Before Matching       After Matching
mean treatment........    0.33095           0.37584 
mean control..........    0.38591           0.38591 
std mean diff.........    -11.672            -2.075 

mean raw eQQ diff.....   0.053691          0.010067 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........    0.02748         0.0050336 
med  eCDF diff........    0.02748         0.0050336 
max  eCDF diff........    0.05496          0.010067 

var ratio (Tr/Co).....    0.93253           0.98988 
T-test p-value........    0.10045           0.79492 


***** (V4) diabetic *****
                       Before Matching       After Matching
mean treatment........    0.20487           0.25503 
mean control..........    0.26846           0.26846 
std mean diff.........    -15.743           -3.0743 

mean raw eQQ diff.....   0.063758          0.013423 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........   0.031793         0.0067114 
med  eCDF diff........   0.031793         0.0067114 
max  eCDF diff........   0.063585          0.013423 

var ratio (Tr/Co).....    0.82788           0.96743 
T-test p-value........    0.03402           0.68937 


***** (V5) acutemi *****
                       Before Matching       After Matching
mean treatment........    0.17908         0.0033557 
mean control..........   0.060403          0.060403 
std mean diff.........     30.931           -98.478 

mean raw eQQ diff.....    0.11745          0.057047 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........    0.05934          0.028523 
med  eCDF diff........    0.05934          0.028523 
max  eCDF diff........    0.11868          0.057047 

var ratio (Tr/Co).....     2.5853          0.058929 
T-test p-value........ 4.6617e-09         7.888e-05 


***** (V6) ejecfrac *****
                       Before Matching       After Matching
mean treatment........     50.403            53.349 
mean control..........     52.289            52.289 
std mean diff.........    -18.102            13.166 

mean raw eQQ diff.....     2.0503            1.8255 
med  raw eQQ diff.....          1                 0 
max  raw eQQ diff.....         20                20 

mean eCDF diff........   0.035602          0.026577 
med  eCDF diff........   0.011423          0.033557 
max  eCDF diff........    0.11383          0.053691 

var ratio (Tr/Co).....     1.0238           0.61178 
T-test p-value........  0.0085806           0.15862 
KS Bootstrap p-value..      0.006             0.456 
KS Naive p-value......  0.0089219           0.78362 
KS Statistic..........    0.11383          0.053691 


***** (V7) ves1proc *****
                       Before Matching       After Matching
mean treatment........     1.4628            1.0403 
mean control..........     1.2047            1.2047 
std mean diff.........     36.545           -67.707 

mean raw eQQ diff.....     0.2651           0.16443 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 2 

mean eCDF diff........   0.043323          0.032886 
med  eCDF diff........  0.0090671         0.0067114 
max  eCDF diff........    0.18842           0.13087 

var ratio (Tr/Co).....     2.1614           0.25567 
T-test p-value........   4.21e-11        5.2489e-08 
KS Bootstrap p-value.. < 2.22e-16        < 2.22e-16 
KS Naive p-value...... 7.2635e-07          0.012144 
KS Statistic..........    0.18842           0.13087 


***** (V8) ps *****
                       Before Matching       After Matching
mean treatment........     0.7265           0.60662 
mean control..........    0.64061           0.64061 
std mean diff.........     66.092           -45.866 

mean raw eQQ diff.....   0.085216          0.046911 
med  raw eQQ diff.....   0.081353          0.035726 
max  raw eQQ diff.....    0.12087           0.23215 

mean eCDF diff........    0.17141           0.10312 
med  eCDF diff........    0.17768          0.083893 
max  eCDF diff........    0.27599           0.23154 

var ratio (Tr/Co).....     1.1161           0.36304 
T-test p-value........ < 2.22e-16        4.5737e-12 
KS Bootstrap p-value.. < 2.22e-16        < 2.22e-16 
KS Naive p-value......  3.042e-14        2.3042e-07 
KS Statistic..........    0.27599           0.23154 


***** (V9) linps *****
                       Before Matching       After Matching
mean treatment........     1.1148           0.44175 
mean control..........    0.63332           0.63332 
std mean diff.........     60.484           -61.383 

mean raw eQQ diff.....     0.4787            0.2442 
med  raw eQQ diff.....    0.35992           0.15424 
max  raw eQQ diff.....     1.0113            2.1601 

mean eCDF diff........    0.17141           0.10312 
med  eCDF diff........    0.17768          0.083893 
max  eCDF diff........    0.27599           0.23154 

var ratio (Tr/Co).....      1.672           0.25702 
T-test p-value........ < 2.22e-16        6.4926e-13 
KS Bootstrap p-value.. < 2.22e-16        < 2.22e-16 
KS Naive p-value......  3.042e-14        2.3042e-07 
KS Statistic..........    0.27599           0.23154 


Before Matching Minimum p.value: < 2.22e-16 
Variable Name(s): ves1proc ps linps  Number(s): 7 8 9 

After Matching Minimum p.value: < 2.22e-16 
Variable Name(s): ves1proc ps linps  Number(s): 7 8 9

covnames <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")

This is Dr. Love’s code to extract the standardized differences.

pre.szd <- NULL; post.szd <- NULL
for(i in 1:length(covnames)) {
pre.szd[i] <- mb1$BeforeMatching[[i]]$sdiff.pooled
post.szd[i] <- mb1$AfterMatching[[i]]$sdiff.pooled
}

We can now print our table of standardized differences.

match_szd <- data.frame(covnames, pre.szd, post.szd, row.names=covnames)
print(match_szd, digits=3)

         covnames pre.szd post.szd
stent       stent  25.445     4.80
height     height  -0.034     3.15
female     female -11.466    -2.08
diabetic diabetic -14.983    -3.07
acutemi   acutemi  37.145   -98.48
ejecfrac ejecfrac -18.208    13.17
ves1proc ves1proc  42.734   -67.71
ps             ps  67.880   -45.87
linps       linps  67.664   -61.38

8.1 Love Plot of standardized differences before and after 1:1 matching

8.2 Using ggplot

In this figure, blue points are post-matching while white are pre-match

lp_wo_rep <- ggplot(match_szd, aes(x = pre.szd, y = reorder(covnames, pre.szd))) +
  geom_point(col = "black", size = 3, pch = 1) +
  geom_point(aes(x = post.szd, y = reorder(covnames, pre.szd)), size = 3, col = "blue") +
  theme_bw() +
  geom_vline(aes(xintercept = 0)) +
  geom_vline(aes(xintercept = 10), linetype = "dashed", col = "red") +
  geom_vline(aes(xintercept = -10), linetype = "dashed", col = "red") +
  labs(x = "Standardized Difference (%)", 
     y = "",
     title = "Love Plot",
     subtitle = "1:1 matching without replacement")

lp_wo_rep

Just visually, we can see this match isn’t all that great.

8.3 Using `cobalt` to make the Love Plot

There’s a more automated way to build the Love Plot - as we see here.

cobalt_tab <- bal.tab(match1, treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean, un = TRUE)

cobalt_tab

Balance Measures
            Type Diff.Un Diff.Adj
stent     Binary  0.1210   0.0235
height   Contin. -0.0003   0.0301
female    Binary -0.0550  -0.0101
diabetic  Binary -0.0636  -0.0134
acutemi   Binary  0.1187  -0.0570
ejecfrac Contin. -0.1810   0.1018
ves1proc Contin.  0.3654  -0.2329
ps       Contin.  0.6609  -0.2616
linps    Contin.  0.6048  -0.2407

Sample sizes
          Control Treated
All           298     698
Matched       298     298
Unmatched       0     400

p <- love.plot(cobalt_tab, threshold = .1, size = 1.5,
               var.order = "unadjusted",
               title = "Standardized Differences after 1:1 Matching without replacement",
               stars = "std")

p + theme_bw()

8.4 Extracting Variance Ratios

We can also look at variance ratios.

pre.vratio <- NULL; post.vratio <- NULL
for(i in 1:length(covnames)) {
pre.vratio[i] <- mb1$BeforeMatching[[i]]$var.ratio
post.vratio[i] <- mb1$AfterMatching[[i]]$var.ratio
}
## Table of Variance Ratios
match_vrat <- data.frame(names = covnames, pre.vratio, post.vratio, row.names=covnames)
print(match_vrat, digits=2)

            names pre.vratio post.vratio
stent       stent       0.85       0.982
height     height       1.02       0.934
female     female       0.93       0.990
diabetic diabetic       0.83       0.967
acutemi   acutemi       2.59       0.059
ejecfrac ejecfrac       1.02       0.612
ves1proc ves1proc       2.16       0.256
ps             ps       1.12       0.363
linps       linps       1.67       0.257

8.5 Creating a dataframe containing the matched sample

We will created a dataframe which includes our matched sample, and do a quick count for a sanity check.

matches <- factor(rep(match1$index.treated, 2))
lindner_clean.matchedsample <- cbind(matches, lindner_clean[c(match1$index.control, match1$index.treated),])

lindner_clean.matchedsample %>% count(treated_f)

  treated_f   n
1   treated 298
2   control 298

8.6 Reassessing Rubin’s Rules after 1:1 matching without replacement

8.6.1 Rubin’s Rule 1

rubin1.match <- with(lindner_clean.matchedsample,
abs(100*(mean(linps[treated==1])-mean(linps[treated==0]))/sd(linps)))
rubin1.match

[1] 38.54801

The new value for Rubin’s Rule 1 is 38.55. While not ideal this technically passes Rubin’s Rule 1 and is an improvement from the pre-match value of 61.87.

8.6.2 Rubin’s Rule 2

rubin2.match <- with(lindner_clean.matchedsample, var(linps[treated==1])/var(linps[treated==0]))
rubin2.match

[1] 0.2570156

The new value for Rubin’s Rule 2 is 0.26. This does not pass Rubin’s Rule 2 and is not an improvement from the pre-match value of 1.67.

9 Task 5: Estimating the causal effect of the treatment on both outcomes after 1:1 matching without replacement

9.1 The Quantitative Outcome

We’ll use a mixed model to estimate the effect of the treatment on cardbill. The matches will be treated as a random effect in the model (syntax “(1| matches.f)”, and the treatment group will be treated as a fixed effect. We will use restricted maximum likelihood (REML) to estimate coefficient values.

#to appease lme4, factor the matches 
lindner_clean.matchedsample$matches.f <- as.factor(lindner_clean.matchedsample$matches)

# fit the mixed model
matched_mixedmodel.out1 <- lmer(cardbill ~ treated + (1 | matches.f), REML = TRUE, data=lindner_clean.matchedsample)

summary(matched_mixedmodel.out1)

Linear mixed model fit by REML ['lmerMod']
Formula: cardbill ~ treated + (1 | matches.f)
   Data: lindner_clean.matchedsample

REML criterion at convergence: 12815.3

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.0515 -0.4301 -0.2536  0.0770 13.7921 

Random effects:
 Groups    Name        Variance  Std.Dev.
 matches.f (Intercept)   6010429  2452   
 Residual              128676424 11344   
Number of obs: 596, groups:  matches.f, 298

Fixed effects:
            Estimate Std. Error t value
(Intercept)  14614.2      672.3  21.738
treated       -385.5      929.3  -0.415

Correlation of Fixed Effects:
        (Intr)
treated -0.691

confint(matched_mixedmodel.out1)

Computing profile confidence intervals ...

Warning in optwrap(optimizer, par = start, fn = function(x) dd(mkpar(npar1, :
convergence code -4 from nloptwrap: NLOPT_ROUNDOFF_LIMITED: Roundoff errors led
to a breakdown of the optimization algorithm. In this case, the returned minimum
may still be useful. (e.g. this error occurs in NEWUOA if one tries to achieve a
tolerance too close to machine precision.)

                2.5 %    97.5 %
.sig01          0.000  4652.350
.sigma      10472.769 12218.166
(Intercept) 13296.650 15931.793
treated     -2209.701  1438.727

tidy_mixed_matched <- broom.mixed::tidy(matched_mixedmodel.out1, conf.int = TRUE, conf.level = 0.95) %>% 
  filter(term == "treated")

tidy_mixed_matched

# A tibble: 1 x 8
  effect group term    estimate std.error statistic conf.low conf.high
  <chr>  <chr> <chr>      <dbl>     <dbl>     <dbl>    <dbl>     <dbl>
1 fixed  <NA>  treated    -385.      929.    -0.415   -2207.     1436.

Treated individuals were estimated to spend $-385.49 (95%CI: -2206.88, 1435.91) less than non-treated individuals. As this result is not significant at an $\alpha$ of 0.05, a sensitivity analysis on the quantitative outcome will not make sense.

#check the mean cardbill in the matched sample
lindner_clean.matchedsample %>% group_by(treated_f) %>% summarise(mean = mean(cardbill))

# A tibble: 2 x 2
  treated_f   mean
* <fct>      <dbl>
1 treated   14229.
2 control   14614.

#check the mean cardbill in the entire sample
lindner_clean %>% group_by(treated_f) %>% summarise(mean = mean(cardbill))

# A tibble: 2 x 2
  treated_f   mean
* <fct>      <dbl>
1 treated   16127.
2 control   14614.

In treated individuals, the mean cardbill was lower within the matched sample than the entire sample (note the mean within the control group was the same as every control participant is in the matched sample. The mean changed in the treated group as only 298/698 treated patients are in the matched sample). This is a sanity check to assess if the mixed model results make sense; and it looks like they do.

9.2 The Binary Outcome

We will use conditional logistic regression to estimate the log odds (and ORs) of being alive after 6 months based on treatment status.

binary_outcome_adjusted <- survival::clogit(sixMonthSurvive ~ treated + strata(matches), data=lindner_clean.matchedsample)

summary(binary_outcome_adjusted)

Call:
coxph(formula = Surv(rep(1, 596L), sixMonthSurvive) ~ treated + 
    strata(matches), data = lindner_clean.matchedsample, method = "exact")

  n= 596, number of events= 578 

          coef exp(coef) se(coef)     z Pr(>|z|)  
treated 1.6094    5.0000   0.6325 2.545   0.0109 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

        exp(coef) exp(-coef) lower .95 upper .95
treated         5        0.2     1.448     17.27

Concordance= 0.833  (se = 0.124 )
Likelihood ratio test= 8.73  on 1 df,   p=0.003
Wald test            = 6.48  on 1 df,   p=0.01
Score (logrank) test = 8  on 1 df,   p=0.005

#Tidy model
tidy_binary_outcome_adjusted <- tidy(binary_outcome_adjusted, exponentiate = TRUE, conf.int = 0.95)

The odds of being alive after six months were 5 times higher in treated individuals than non-treated individuals (95%CI 1.45, 17.27)

10 Task 6 1:1 Matching With replacement

As we saw in the 1:1 matching without replacement, 400 treated participants were excluded from the sample. This is a waste of data and we’ll address this by again matching 1 treated participant to 1 control participant. However, this time we’ll match with replacement, meaning each time a control participant is matched to a treated participant, the control participant will be placed back into the pool of possible patients a treated individual can be matched to. Thus, some control participants will be matched multiple times (not all control participants have to be matched to a treated participant). In the Lindner dataset 1:1 matching with replacement is a more reasonable choice.

X <- lindner_clean$linps ## matching on the linear propensity score
Tr <- as.logical(lindner_clean$treated)
match1 <- Match(Tr=Tr, X=X, M = 1, replace=TRUE, ties=FALSE) # notice replace =  TRUE
summary(match1)


Estimate...  0 
SE.........  0 
T-stat.....  NaN 
p.val......  NA 

Original number of observations..............  996 
Original number of treated obs...............  698 
Matched number of observations...............  698 
Matched number of observations  (unweighted).  698

As you can see, this time we matched 698 treated individuals with 698 control participants. To reiterate, as we matched with replacement, and there were less control participants than treated participants, some control participants were matched multiple times.

Below we’ll assess the match balance from the 1:1 matching with replacement.

set.seed(202102)
mb1 <- MatchBalance(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean,
match.out = match1, nboots=500)


***** (V1) stent *****
                       Before Matching       After Matching
mean treatment........    0.70487           0.70487 
mean control..........    0.58389           0.72779 
std mean diff.........     26.505           -5.0222 

mean raw eQQ diff.....    0.12081          0.022923 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........   0.060489          0.011461 
med  eCDF diff........   0.060489          0.011461 
max  eCDF diff........    0.12098          0.022923 

var ratio (Tr/Co).....    0.85457            1.0501 
T-test p-value........ 0.00032255           0.23555 


***** (V2) height *****
                       Before Matching       After Matching
mean treatment........     171.44            171.44 
mean control..........     171.45            171.62 
std mean diff.........  -0.033804           -1.6209 

mean raw eQQ diff.....    0.56376           0.83811 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....         20                22 

mean eCDF diff........  0.0078996          0.010261 
med  eCDF diff........  0.0060095          0.008596 
max  eCDF diff........   0.024971          0.038682 

var ratio (Tr/Co).....     1.0201           0.80936 
T-test p-value........    0.99608            0.7661 
KS Bootstrap p-value..      0.968             0.396 
KS Naive p-value......    0.99947           0.67329 
KS Statistic..........   0.024971          0.038682 


***** (V3) female *****
                       Before Matching       After Matching
mean treatment........    0.33095           0.33095 
mean control..........    0.38591           0.29943 
std mean diff.........    -11.672            6.6934 

mean raw eQQ diff.....   0.053691          0.031519 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........    0.02748          0.015759 
med  eCDF diff........    0.02748          0.015759 
max  eCDF diff........    0.05496          0.031519 

var ratio (Tr/Co).....    0.93253            1.0555 
T-test p-value........    0.10045            0.1537 


***** (V4) diabetic *****
                       Before Matching       After Matching
mean treatment........    0.20487           0.20487 
mean control..........    0.26846           0.22923 
std mean diff.........    -15.743           -6.0301 

mean raw eQQ diff.....   0.063758          0.024355 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........   0.031793          0.012178 
med  eCDF diff........   0.031793          0.012178 
max  eCDF diff........   0.063585          0.024355 

var ratio (Tr/Co).....    0.82788           0.92199 
T-test p-value........    0.03402           0.21126 


***** (V5) acutemi *****
                       Before Matching       After Matching
mean treatment........    0.17908           0.17908 
mean control..........   0.060403           0.16762 
std mean diff.........     30.931            2.9871 

mean raw eQQ diff.....    0.11745          0.011461 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........    0.05934         0.0057307 
med  eCDF diff........    0.05934         0.0057307 
max  eCDF diff........    0.11868          0.011461 

var ratio (Tr/Co).....     2.5853            1.0537 
T-test p-value........ 4.6617e-09           0.44149 


***** (V6) ejecfrac *****
                       Before Matching       After Matching
mean treatment........     50.403            50.403 
mean control..........     52.289            50.812 
std mean diff.........    -18.102           -3.9327 

mean raw eQQ diff.....     2.0503           0.80516 
med  raw eQQ diff.....          1                 0 
max  raw eQQ diff.....         20                20 

mean eCDF diff........   0.035602          0.012247 
med  eCDF diff........   0.011423          0.008596 
max  eCDF diff........    0.11383           0.06447 

var ratio (Tr/Co).....     1.0238            1.1088 
T-test p-value........  0.0085806           0.43271 
KS Bootstrap p-value..      0.004             0.044 
KS Naive p-value......  0.0089219            0.1099 
KS Statistic..........    0.11383           0.06447 


***** (V7) ves1proc *****
                       Before Matching       After Matching
mean treatment........     1.4628            1.4628 
mean control..........     1.2047            1.4642 
std mean diff.........     36.545          -0.20289 

mean raw eQQ diff.....     0.2651          0.044413 
med  raw eQQ diff.....          0                 0 
max  raw eQQ diff.....          1                 1 

mean eCDF diff........   0.043323         0.0074021 
med  eCDF diff........  0.0090671          0.004298 
max  eCDF diff........    0.18842          0.018625 

var ratio (Tr/Co).....     2.1614            1.0942 
T-test p-value........   4.21e-11           0.95523 
KS Bootstrap p-value.. < 2.22e-16             0.594 
KS Naive p-value...... 7.2635e-07           0.99973 
KS Statistic..........    0.18842          0.018625 


***** (V8) ps *****
                       Before Matching       After Matching
mean treatment........     0.7265            0.7265 
mean control..........    0.64061            0.7262 
std mean diff.........     66.092           0.23256 

mean raw eQQ diff.....   0.085216         0.0014016 
med  raw eQQ diff.....   0.081353        0.00063595 
max  raw eQQ diff.....    0.12087          0.021689 

mean eCDF diff........    0.17141         0.0031873 
med  eCDF diff........    0.17768         0.0014327 
max  eCDF diff........    0.27599          0.024355 

var ratio (Tr/Co).....     1.1161            1.0083 
T-test p-value........ < 2.22e-16         0.0032848 
KS Bootstrap p-value.. < 2.22e-16             0.978 
KS Naive p-value......  3.042e-14           0.98578 
KS Statistic..........    0.27599          0.024355 


***** (V9) linps *****
                       Before Matching       After Matching
mean treatment........     1.1148            1.1148 
mean control..........    0.63332             1.108 
std mean diff.........     60.484             0.859 

mean raw eQQ diff.....     0.4787          0.016276 
med  raw eQQ diff.....    0.35992         0.0028864 
max  raw eQQ diff.....     1.0113           0.75735 

mean eCDF diff........    0.17141         0.0031873 
med  eCDF diff........    0.17768         0.0014327 
max  eCDF diff........    0.27599          0.024355 

var ratio (Tr/Co).....      1.672            1.0466 
T-test p-value........ < 2.22e-16         0.0016161 
KS Bootstrap p-value.. < 2.22e-16             0.978 
KS Naive p-value......  3.042e-14           0.98578 
KS Statistic..........    0.27599          0.024355 


Before Matching Minimum p.value: < 2.22e-16 
Variable Name(s): ves1proc ps linps  Number(s): 7 8 9 

After Matching Minimum p.value: 0.0016161 
Variable Name(s): linps  Number(s): 9

covnames <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")

Dr. Love’s code to extract the standardized differences.

pre.szd <- NULL; post.szd <- NULL
for(i in 1:length(covnames)) {
pre.szd[i] <- mb1$BeforeMatching[[i]]$sdiff.pooled
post.szd[i] <- mb1$AfterMatching[[i]]$sdiff.pooled
}

Table of standardized differences

match_szd <- data.frame(covnames, pre.szd, post.szd, row.names=covnames)
print(match_szd, digits=3)

         covnames pre.szd post.szd
stent       stent  25.445   -5.022
height     height  -0.034   -1.621
female     female -11.466    6.693
diabetic diabetic -14.983   -6.030
acutemi   acutemi  37.145    2.987
ejecfrac ejecfrac -18.208   -3.933
ves1proc ves1proc  42.734   -0.203
ps             ps  67.880    0.233
linps       linps  67.664    0.859

10.1 Love Plot of standardized differences before and after 1:1 matching

10.2 Using ggplot

In this figure, blue points are post-matching while white are pre-match.

lp_w_rep <- ggplot(match_szd, aes(x = pre.szd, y = reorder(covnames, pre.szd))) +
  geom_point(col = "black", size = 3, pch = 1) +
  geom_point(aes(x = post.szd, y = reorder(covnames, pre.szd)), size = 3, col = "blue") +
  theme_bw() +
  geom_vline(aes(xintercept = 0)) +
  geom_vline(aes(xintercept = 10), linetype = "dashed", col = "red") +
  geom_vline(aes(xintercept = -10), linetype = "dashed", col = "red") +
  labs(x = "Standardized Difference (%)", 
     y = "",
     title = "Love Plot",
     subtitle = "1:1 matching with replacement")

lp_w_rep

Visually, the Love Plot using 1:1 matching with replacement looks pretty good.

# comparison of love plots with and without replacement
lp_wo_rep +  lp_w_rep

When we look at the plots without replacement and with replacement side-by-side, it definitely looks better than the 1:1 matching without replacement.

10.3 Using `cobalt` to make the Love Plot

Again, we can also use an automated way to make the Love Plot.

cobalt_tab <- bal.tab(match1, treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean, un = TRUE,
                      stats = c("m","v"))

cobalt_tab

Balance Measures
            Type Diff.Un V.Ratio.Un Diff.Adj V.Ratio.Adj
stent     Binary  0.1210          .  -0.0229           .
height   Contin. -0.0003     1.0201  -0.0162      0.8033
female    Binary -0.0550          .   0.0315           .
diabetic  Binary -0.0636          .  -0.0244           .
acutemi   Binary  0.1187          .   0.0115           .
ejecfrac Contin. -0.1810     1.0238  -0.0393      1.1004
ves1proc Contin.  0.3654     2.1614  -0.0020      1.0860
ps       Contin.  0.6609     1.1161   0.0023      1.0007
linps    Contin.  0.6048     1.6720   0.0086      1.0387

Sample sizes
                     Control Treated
All                   298.       698
Matched (ESS)         112.16     698
Matched (Unweighted)  229.       698
Unmatched              69.         0

p <- love.plot(cobalt_tab, threshold = .1, size = 1.5,
               var.order = "unadjusted",
               title = "Standardized Differences after 1:1 Matching With Replacement",
               stars = "std")

p + theme_bw()

10.4 Extracting Variance Ratios

pre.vratio <- NULL; post.vratio <- NULL
for(i in 1:length(covnames)) {
pre.vratio[i] <- mb1$BeforeMatching[[i]]$var.ratio
post.vratio[i] <- mb1$AfterMatching[[i]]$var.ratio
}
## Table of Variance Ratios
match_vrat <- data.frame(names = covnames, pre.vratio, post.vratio, row.names=covnames)
print(match_vrat, digits=2)

            names pre.vratio post.vratio
stent       stent       0.85        1.05
height     height       1.02        0.81
female     female       0.93        1.06
diabetic diabetic       0.83        0.92
acutemi   acutemi       2.59        1.05
ejecfrac ejecfrac       1.02        1.11
ves1proc ves1proc       2.16        1.09
ps             ps       1.12        1.01
linps       linps       1.67        1.05

10.4.1 Using ‘cobalt’ to make a Love Plot of Variance Ratios

p <- love.plot(cobalt_tab, stats = "v", threshold = .1, size = 3,
               var.order = "unadjusted",
               title = "Variance Ratios after 1:1 Matching With Replacement",
               stars = "")

p + theme_bw()

10.5 Creating a dataframe containing the matched sample

matches <- factor(rep(match1$index.treated, 2))
lindner_clean.matchedsample <- cbind(matches, lindner_clean[c(match1$index.control, match1$index.treated),])

lindner_clean.matchedsample %>% count(treated_f)

  treated_f   n
1   treated 698
2   control 698

10.5.1 How many times were the non-treated patients matched?

lindner_clean.matchedsample %>% filter(treated_f == "control") %>% 
    count(patientid) %>%
    janitor::tabyl(n)

  n n_n     percent
  1  84 0.366812227
  2  53 0.231441048
  3  36 0.157205240
  4  20 0.087336245
  5   8 0.034934498
  6   6 0.026200873
  7   5 0.021834061
  8   3 0.013100437
  9   1 0.004366812
 10   2 0.008733624
 11   2 0.008733624
 12   2 0.008733624
 13   1 0.004366812
 15   1 0.004366812
 16   3 0.013100437
 17   2 0.008733624

10.6 Reassessing Rubin’s Rules after 1:1 matching with replacement

10.6.1 Rubin’s Rule 1

rubin1.match.rep <- with(lindner_clean.matchedsample,
abs(100*(mean(linps[treated==1])-mean(linps[treated==0]))/sd(linps)))
rubin1.match.rep

[1] 0.8690187

The new value for Rubin’s Rule 1 is 0.87. This value passes Rubin’s Rule 1 and is an improvement from the Rubin’s Rule 1 value obtained during 1:1 matching without replacement, 38.55. The pre-match value was 61.87.

10.6.2 Rubin’s Rule 2

rubin2.match.rep <- with(lindner_clean.matchedsample, var(linps[treated==1])/var(linps[treated==0]))
rubin2.match.rep

[1] 1.046553

The new value for Rubin’s Rule 2 is 1.05. This passes Rule 2 and is an improvement from the Rubin’s Rule 2 value obtained during 1:1 matching without replacement, 0.26. The pre-match value was 1.67.

10.7 Estimating the causal effect of the treatment on both outcomes after 1:1 matching with replacement

10.7.1 The Quantitative Outcome

Again, we’ll use a mixed model to estimate the effect of the treatment on cardbill. The matches will be treated as a random effect in the model (syntax “(1| matches.f)”. and the treatment group will be treated as a fixed effect. We will use restricted maximum likelihood (REML) to estimate coefficient values.

#to appease lme4, factor the matches 
lindner_clean.matchedsample$matches.f <- as.factor(lindner_clean.matchedsample$matches)

# fit the mixed model
matched_mixedmodel.rep.out1 <- lmer(cardbill ~ treated + (1 | matches.f), REML = TRUE, data=lindner_clean.matchedsample)

summary(matched_mixedmodel.rep.out1)

Linear mixed model fit by REML ['lmerMod']
Formula: cardbill ~ treated + (1 | matches.f)
   Data: lindner_clean.matchedsample

REML criterion at convergence: 30148

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.1569 -0.4789 -0.2828  0.1116 13.2194 

Random effects:
 Groups    Name        Variance  Std.Dev.
 matches.f (Intercept)   7604218  2758   
 Residual              135785615 11653   
Number of obs: 1396, groups:  matches.f, 698

Fixed effects:
            Estimate Std. Error t value
(Intercept)  16337.4      453.2  36.046
treated       -210.7      623.8  -0.338

Correlation of Fixed Effects:
        (Intr)
treated -0.688

confint(matched_mixedmodel.rep.out1)

Computing profile confidence intervals ...

                2.5 %    97.5 %
.sig01          0.000  4287.944
.sigma      11059.236 12282.671
(Intercept) 15449.068 17225.702
treated     -1434.047  1012.643

tidy_mixed_matched_rep <- broom.mixed::tidy(matched_mixedmodel.rep.out1, conf.int = TRUE, conf.level = 0.95) %>% 
  filter(term == "treated")

tidy_mixed_matched_rep

# A tibble: 1 x 8
  effect group term    estimate std.error statistic conf.low conf.high
  <chr>  <chr> <chr>      <dbl>     <dbl>     <dbl>    <dbl>     <dbl>
1 fixed  <NA>  treated    -211.      624.    -0.338   -1433.     1012.

Treated individuals were estimated to spend $-210.7 less (95%CI -1433.24, 1011.84) than non-treated individuals. This finding is not significant at an $\alpha$ of 0.05, thus, the sensitivity analysis on the Quantitative outcome will still not make sense.

#sanity check for model
lindner_clean.matchedsample %>% group_by(treated_f) %>% summarise(mean_card = mean(cardbill))

# A tibble: 2 x 2
  treated_f mean_card
* <fct>         <dbl>
1 treated      16127.
2 control      16337.

The mixed model above predicted treated individuals would spend roughly $-210.7 less than control participants. After doing a quick check of the mean cardbill within the matched sample, the mixed model results make sense.

10.7.2 The Binary Outcome

We will use conditional logistic regression to estimate the log odds (and ORs) of being alive after 6 months based on treatment status.

binary_outcome_adjusted_rep <- survival::clogit(sixMonthSurvive ~ treated + strata(matches), data=lindner_clean.matchedsample)

summary(binary_outcome_adjusted_rep)

Call:
coxph(formula = Surv(rep(1, 1396L), sixMonthSurvive) ~ treated + 
    strata(matches), data = lindner_clean.matchedsample, method = "exact")

  n= 1396, number of events= 1321 

          coef exp(coef) se(coef)     z Pr(>|z|)    
treated 1.8405    6.3000   0.3404 5.407 6.41e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

        exp(coef) exp(-coef) lower .95 upper .95
treated       6.3     0.1587     3.233     12.28

Concordance= 0.863  (se = 0.057 )
Likelihood ratio test= 42.88  on 1 df,   p=6e-11
Wald test            = 29.24  on 1 df,   p=6e-08
Score (logrank) test = 38.48  on 1 df,   p=6e-10

#Tidy model
tidy_binary_outcome_adjusted_rep <- tidy(binary_outcome_adjusted_rep, exponentiate = TRUE, conf.int = 0.95)

tidy_binary_outcome_adjusted_rep

# A tibble: 1 x 7
  term    estimate std.error statistic      p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>        <dbl>    <dbl>     <dbl>
1 treated     6.30     0.340      5.41 0.0000000641     3.23      12.3

The odds of being alive after six months were 6.3 times higher in treated individuals than non-treated controls (95%CI 3.23, 12.28)

11 Task 7: Subclassification by Propensity Score Quintile

#cut into quintiles
lindner_clean$stratum <- Hmisc::cut2(lindner_clean$ps, g=5)
lindner_clean$quintile <- factor(lindner_clean$stratum, labels=1:5)

#Sanity check: check to make sure quntiles are evenish, numbers make sense, etc.
lindner_clean %>% count(stratum, quintile)

        stratum quintile   n
1 [0.232,0.581)        1 200
2 [0.581,0.669)        2 199
3 [0.669,0.726)        3 200
4 [0.726,0.826)        4 199
5 [0.826,0.980]        5 198

11.1 Check Balance and Propensity Score Overlap in Each Quintile

11.1.1 Numerically

Only 20 controls were were in the largest quintile, which seems a bit low.

lindner_clean %>% count(quintile, treated_f)

   quintile treated_f   n
1         1   treated 105
2         1   control  95
3         2   treated 124
4         2   control  75
5         3   treated 135
6         3   control  65
7         4   treated 156
8         4   control  43
9         5   treated 178
10        5   control  20

11.1.2 Graphically

ggplot(lindner_clean, aes(x = treated_f, y = round(ps,2), group = quintile, color = treated_f)) +
geom_jitter(width = 0.2) +
guides(color = FALSE) +
facet_wrap(~ quintile, scales = "free_y") +
labs(x = "", y = "Propensity for Treatment",
title = "Quintile Subclassification in the Lindner data")

11.2 Creating a Standardized Difference Calculation Function

Here we implement Dr. Love’s function to calculate the standardizes differences is utilized below.

szd <- function(covlist, g) {
covlist2 <- as.matrix(covlist)
g <- as.factor(g)
res <- NA
for(i in 1:ncol(covlist2)) {
cov <- as.numeric(covlist2[,i])
num <- 100*diff(tapply(cov, g, mean, na.rm=TRUE))
den <- sqrt(mean(tapply(cov, g, var, na.rm=TRUE)))
res[i] <- round(num/den,2)
}
names(res) <- names(covlist)
res
}

Now we’ll split data into quintiles - and give them each their own dataframe.

quin1 <- filter(lindner_clean, quintile==1)
quin2 <- filter(lindner_clean, quintile==2)
quin3 <- filter(lindner_clean, quintile==3)
quin4 <- filter(lindner_clean, quintile==4)
quin5 <- filter(lindner_clean, quintile==5)

Now we’ll run the function above to calculate the standardized differences for each covariate in each quintile.

covs <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")
d.q1 <- szd(quin1[covs], quin1$treated)
d.q2 <- szd(quin2[covs], quin2$treated)
d.q3 <- szd(quin3[covs], quin3$treated)
d.q4 <- szd(quin4[covs], quin4$treated)
d.q5 <- szd(quin5[covs], quin5$treated)
d.all <- szd(lindner_clean[covs], lindner_clean$treated)
lindner_clean.szd <- tibble(covs, Overall = d.all, Q1 = d.q1, Q2 = d.q2, Q3 = d.q3, Q4 = d.q4, Q5 = d.q5)
lindner_clean.szd <- gather(lindner_clean.szd, "quint", "sz.diff", 2:7)

11.3 Plotting the post-subclassification standardized differences

ggplot(lindner_clean.szd, aes(x = sz.diff, y = reorder(covs, -sz.diff), group = quint)) +
  geom_point() +
geom_vline(xintercept = 0) +
geom_vline(xintercept = c(-10,10), linetype = "dashed", col = "blue") +
facet_wrap(~ quint) +
labs(x = "Standardized Difference, %", y = "",
title = "Comparing Standardized Differences by PS Quintile")

Warning: Removed 1 rows containing missing values (geom_point).

The results of the standardized differences by quintile are failry variable.

11.4 Rubin’s Rules post subclassification

11.4.1 Rule 1

rubin1.q1 <- with(quin1, abs(100*(mean(linps[treated==1]) - mean(linps[treated==0]))/sd(linps)))

rubin1.q2 <- with(quin2, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.q3 <- with(quin3, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.q4 <- with(quin4, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.q5 <- with(quin5, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.sub <- c(rubin1.q1, rubin1.q2, rubin1.q3, rubin1.q4, rubin1.q5)
names(rubin1.sub)=c("Q1", "Q2", "Q3", "Q4", "Q5")

rubin1.sub

       Q1        Q2        Q3        Q4        Q5 
42.633282 10.122973  9.054266 23.662028 20.717673

All are under 50. Not great, but OK. For comparison, the original Rubin’s Rule 1 value was 61.87.

11.4.2 Rule 2

rubin2.q1 <- with(quin1, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q2 <- with(quin2, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q3 <- with(quin3, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q4 <- with(quin4, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q5 <- with(quin5, var(linps[treated==1])/var(linps[treated==0]))

rubin2.sub <- c(rubin2.q1, rubin2.q2, rubin2.q3, rubin2.q4, rubin2.q5)
names(rubin2.sub)=c("Q1", "Q2", "Q3", "Q4", "Q5")
rubin2.sub

       Q1        Q2        Q3        Q4        Q5 
0.6582169 1.2083230 1.1754770 1.2154060 1.2353984

All but Q1 are at least close to passing Rule 2. For comparison, the original Rubin’s Rule 2 value was 1.67.

12 Task 8: Estimated effect after subclassification

12.1 Quantitative outcome

quin1.out1 <- lm(cardbill ~ treated, data=quin1)
quin2.out1 <- lm(cardbill ~ treated, data=quin2)
quin3.out1 <- lm(cardbill ~ treated, data=quin3)
quin4.out1 <- lm(cardbill ~ treated, data=quin4)
quin5.out1 <- lm(cardbill ~ treated, data=quin5)

coef(summary(quin1.out1)); coef(summary(quin2.out1)); coef(summary(quin3.out1)); coef(summary(quin4.out1)); coef(summary(quin5.out1))

               Estimate Std. Error     t value     Pr(>|t|)
(Intercept) 14262.49474   1083.197 13.16704155 7.497113e-29
treated       -67.69474   1494.953 -0.04528217 9.639280e-01

             Estimate Std. Error  t value     Pr(>|t|)
(Intercept) 15038.427   1794.884 8.378497 1.000329e-14
treated      1412.154   2273.799 0.621055 5.352814e-01

             Estimate Std. Error  t value     Pr(>|t|)
(Intercept) 13259.415   1099.734 12.05693 1.846022e-25
treated      2837.814   1338.554  2.12006 3.524616e-02

            Estimate Std. Error  t value     Pr(>|t|)
(Intercept) 14474.19   1620.396 8.932501 2.966193e-16
treated      2979.16   1830.144 1.627828 1.051596e-01

             Estimate Std. Error   t value     Pr(>|t|)
(Intercept) 19398.350   1967.305  9.860368 7.011002e-19
treated     -3498.063   2074.886 -1.685906 9.340509e-02

The mean of the five quintile-specific estimated regression coefficients is below.

est.st <- (coef(quin1.out1)[2] + coef(quin2.out1)[2] + coef(quin3.out1)[2] +
coef(quin4.out1)[2] + coef(quin5.out1)[2])/5

est.st

treated 
732.674

The mean SE is below.

se.q1 <- summary(quin1.out1)$coefficients[2,2]
se.q2 <- summary(quin2.out1)$coefficients[2,2]
se.q3 <- summary(quin3.out1)$coefficients[2,2]
se.q4 <- summary(quin4.out1)$coefficients[2,2]
se.q5 <- summary(quin5.out1)$coefficients[2,2]

se.st <- sqrt((se.q1^2 + se.q2^2 + se.q3^2 + se.q4^2 + se.q5^2)*(1/25))
se.st

[1] 821.008

The mean estimate, with a 95% CI, is below.

strat.result1 <- data_frame(estimate = est.st,
conf.low = est.st - 1.96*se.st,
conf.high = est.st + 1.96*se.st)

Warning: `data_frame()` was deprecated in tibble 1.1.0.
Please use `tibble()` instead.

strat.result1

# A tibble: 1 x 3
  estimate conf.low conf.high
     <dbl>    <dbl>     <dbl>
1     733.    -877.     2342.

So treated individuals were estimated to spend $732.67 more (95%CI -876.5, 2341.85) than non treated individuals.

12.2 Binary Outcome

quin1.out2 <- glm(sixMonthSurvive ~ treated, data=quin1, family=binomial())
quin2.out2 <- glm(sixMonthSurvive ~ treated, data=quin2, family=binomial())
quin3.out2 <- glm(sixMonthSurvive ~ treated, data=quin3, family=binomial())
quin4.out2 <- glm(sixMonthSurvive ~ treated, data=quin4, family=binomial())
quin5.out2 <- glm(sixMonthSurvive ~ treated, data=quin5, family=binomial())

coef(summary(quin1.out2)); coef(summary(quin2.out2)); coef(summary(quin3.out2)); coef(summary(quin4.out2)); coef(summary(quin5.out2))

            Estimate Std. Error  z value     Pr(>|z|)
(Intercept) 3.124565  0.5108708 6.116155 9.586018e-10
treated     1.519826  1.1272001 1.348319 1.775557e-01

            Estimate Std. Error  z value     Pr(>|z|)
(Intercept) 2.876386  0.5138915 5.597262 2.177636e-08
treated     1.935799  1.1278865 1.716306 8.610597e-02

            Estimate Std. Error  z value     Pr(>|z|)
(Intercept) 3.028522  0.5911534 5.123073 3.005960e-07
treated     1.869318  1.1648042 1.604834 1.085303e-01

            Estimate Std. Error   z value     Pr(>|z|)
(Intercept) 3.737670   1.011815 3.6940239 0.0002207331
treated     0.194156   1.167726 0.1662684 0.8679457146

            Estimate Std. Error  z value    Pr(>|z|)
(Intercept) 1.734601  0.6262243 2.769936 0.005606735
treated     1.809253  0.7732630 2.339764 0.019295953

Estimated log-odds (averaged over the quintiles).

est.st.log <- (coef(quin1.out2)[2] + coef(quin2.out2)[2] + coef(quin3.out2)[2] +
coef(quin4.out2)[2] + coef(quin5.out2)[2])/5

est.st.log

treated 
1.46567

Estimated odds ratio (averaged over the quintiles).

exp(est.st.log)

 treated 
4.330444

The average SE (averaged over the quintiles).

se.q1.log <- summary(quin1.out2)$coefficients[2,2]
se.q2.log <- summary(quin2.out2)$coefficients[2,2]
se.q3.log <- summary(quin3.out2)$coefficients[2,2]
se.q4.log <- summary(quin4.out2)$coefficients[2,2]
se.q5.log <- summary(quin5.out2)$coefficients[2,2]

se.st.log <- sqrt((se.q1.log^2 + se.q2.log^2 + se.q3.log^2 + se.q4.log^2 + se.q5.log^2)*(1/25))
se.st.log #log odds

[1] 0.4841899

strat.result2 <- data_frame(estimate = exp(est.st.log),
conf.low = exp(est.st.log - 1.96*se.st.log),
conf.high = exp(est.st.log + 1.96*se.st.log))

strat.result2

# A tibble: 1 x 3
  estimate conf.low conf.high
     <dbl>    <dbl>     <dbl>
1     4.33     1.68      11.2

The odds of being alive after 6 months was 4.33 (95%CI 1.68, 11.19) times higher in treated individuals than non-treated individuals.

13 Task 9: Weighting

13.1 Calculating the ATT and ATE weights

13.1.1 ATT weights

First, we can use tge average treatment effect on the treated (ATT) approach where we weight treated subjects as 1 and controls as ps/(1-ps)

lindner_clean$wts1 <- ifelse(lindner_clean$treated==1, 1, lindner_clean$ps/(1-lindner_clean$ps))

13.1.2 ATE weights

We can also use the average treatment effect (ATE) weights where we weight treated subjects by 1/ps and controls by 1/(1-PS)

lindner_clean$wts2 <- ifelse(lindner_clean$treated==1, 1/lindner_clean$ps, 1/(1-lindner_clean$ps))

13.2 Working with the ATT weights

ggplot(lindner_clean, aes(x = ps, y = wts1, color = treated_f)) +
geom_point() +
guides(color = FALSE) +
facet_wrap(~ treated_f) +
labs(x = "Estimated Propensity for Treatment",
y = "ATT weight",
title = "ATT weighting structure")

#turn dataset into a dataframe for twang (its a tibble now)
lindner_clean_df <- data.frame(lindner_clean)

#name covariates
covlist <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")

bal.wts1 <- dx.wts(x=lindner_clean_df$wts1, data=lindner_clean_df, vars=covlist,
treat.var="treated", estimand="ATT")

bal.wts1

  type n.treat n.ctrl ess.treat ess.ctrl     max.es    mean.es     max.ks
1  unw     698    298       698 298.0000 0.66091743 0.29567509 0.27599469
2          698    298       698 149.4503 0.08471131 0.03315857 0.06089807
     mean.ks iter
1 0.13749095   NA
2 0.03182485   NA

bal.table(bal.wts1)

$unw
           tx.mn  tx.sd   ct.mn  ct.sd std.eff.sz   stat     p    ks ks.pval
stent      0.705  0.456   0.584  0.494      0.265  3.624 0.000 0.121   0.004
height   171.443 10.695 171.446 10.589      0.000 -0.005 0.996 0.025   0.999
female     0.331  0.471   0.386  0.488     -0.117 -1.647 0.100 0.055   0.531
diabetic   0.205  0.404   0.268  0.444     -0.157 -2.127 0.034 0.064   0.349
acutemi    0.179  0.384   0.060  0.239      0.309  5.923 0.000 0.119   0.005
ejecfrac  50.403 10.419  52.289 10.297     -0.181 -2.640 0.008 0.114   0.008
ves1proc   1.463  0.706   1.205  0.480      0.365  6.693 0.000 0.188   0.000
ps         0.727  0.130   0.641  0.123      0.661  9.928 0.000 0.276   0.000
linps      1.115  0.796   0.633  0.616      0.605 10.321 0.000 0.276   0.000

[[2]]
           tx.mn  tx.sd   ct.mn  ct.sd std.eff.sz   stat     p    ks ks.pval
stent      0.705  0.456   0.702  0.458      0.005  0.065 0.948 0.002   1.000
height   171.443 10.695 171.568 11.934     -0.012 -0.102 0.919 0.042   0.974
female     0.331  0.471   0.311  0.464      0.042  0.497 0.620 0.020   1.000
diabetic   0.205  0.404   0.235  0.425     -0.074 -0.716 0.474 0.030   1.000
acutemi    0.179  0.384   0.180  0.385     -0.001 -0.011 0.991 0.001   1.000
ejecfrac  50.403 10.419  50.384 10.358      0.002  0.019 0.985 0.032   0.999
ves1proc   1.463  0.706   1.523  0.749     -0.085 -0.647 0.518 0.038   0.990
ps         0.727  0.130   0.730  0.134     -0.030 -0.273 0.785 0.061   0.725
linps      1.115  0.796   1.153  0.839     -0.048 -0.360 0.719 0.061   0.725

bal.before.wts1 <- bal.table(bal.wts1)[1]
bal.after.wts1 <- bal.table(bal.wts1)[2]
balance.att.weights <- data_frame(names = rownames(bal.before.wts1$unw),
pre.weighting = 100*bal.before.wts1$unw$std.eff.sz,
ATT.weighted = 100*bal.after.wts1[[1]]$std.eff.sz)
balance.att.weights <- gather(balance.att.weights, timing, szd, 2:3)

Now we can plot the standardized differences after ATT weighting.

ggplot(balance.att.weights, aes(x = szd, y = reorder(names, szd), color = timing)) +
  geom_point() +
  geom_vline(xintercept = 0) +
  geom_vline(xintercept = c(-10,10), linetype = "dashed", col = "blue") +
  labs(x = "Standardized Difference", 
       y = "",
       title = "Standardized Difference before and after ATT Weighting")

The standardized differences look much better here in this approach.

13.2.1 Rubin’s Rules

13.2.1.1 Rule 1

Numbers from balance table above: (-0.048 * 100) = 4.8%. So passes Rule 1.

13.2.1.2 Rule 2

Numbers from balance table above:(0.796²)/(0.839²) = 0.9001237. Passes Rule 2

13.2.2 Estimated effect on outcomes after ATT weighting

13.2.2.1 Quantitative outcome

To estimate the effect of the treatment on cardbill, we’ll use svyglm from the survey package to apply the ATT weights in a linear model.

lindnerwt1.design <- svydesign(ids=~1, weights=~wts1, data=lindner_clean) # using ATT weights

adjout1.wt1 <- svyglm(cardbill ~ treated, design=lindnerwt1.design)

wt_att_results1 <- tidy(adjout1.wt1, conf.int = TRUE) %>% filter(term == "treated")

wt_att_results1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated    -239.     1417.    -0.169   0.866   -3017.     2538.

Estimate (95%CI) -239.28 (-3016.54, 2537.99)

13.2.2.2 Binary outcome

We’ll do similar coding for the binary outcome.

adjout2.wt1 <- svyglm(sixMonthSurvive ~ treated, design=lindnerwt1.design, family=quasibinomial())

wt_att_results2 <- tidy(adjout2.wt1, conf.int = TRUE, exponentiate = TRUE) %>%
filter(term == "treated")
wt_att_results2

# A tibble: 1 x 7
  term    estimate std.error statistic  p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
1 treated     6.50     0.537      3.49 0.000509     2.27      18.6

Estimate (95%CI) 6.5 (2.27, 18.63)

13.3 Working with the ATE weights

Now, we’ll go through the same steps with the ATE weights.

ggplot(lindner_clean, aes(x = ps, y = wts2, color = treated_f)) +
geom_point() +
guides(color = FALSE) +
facet_wrap(~ treated_f) +
labs(x = "Estimated Propensity for Treatment",
y = "ATE weights",
title = "ATE weighting structure")

bal.wts2 <- dx.wts(x=lindner_clean_df$wts2, data=lindner_clean_df, vars=covlist,
treat.var="treated", estimand="ATE")

bal.wts2

  type n.treat n.ctrl ess.treat ess.ctrl     max.es    mean.es     max.ks
1  unw     698    298   698.000 298.0000 0.64205075 0.29974928 0.27599469
2          698    298   671.093 199.6805 0.06759172 0.02390944 0.04595042
     mean.ks iter
1 0.13749095   NA
2 0.02622715   NA

bal.table(bal.wts2)

$unw
           tx.mn  tx.sd   ct.mn  ct.sd std.eff.sz   stat     p    ks ks.pval
stent      0.705  0.456   0.584  0.494      0.257  3.624 0.000 0.121   0.004
height   171.443 10.695 171.446 10.589      0.000 -0.005 0.996 0.025   0.999
female     0.331  0.471   0.386  0.488     -0.115 -1.647 0.100 0.055   0.531
diabetic   0.205  0.404   0.268  0.444     -0.152 -2.127 0.034 0.064   0.349
acutemi    0.179  0.384   0.060  0.239      0.338  5.923 0.000 0.119   0.005
ejecfrac  50.403 10.419  52.289 10.297     -0.181 -2.640 0.008 0.114   0.008
ves1proc   1.463  0.706   1.205  0.480      0.393  6.693 0.000 0.188   0.000
ps         0.727  0.130   0.641  0.123      0.642  9.928 0.000 0.276   0.000
linps      1.115  0.796   0.633  0.616      0.619 10.321 0.000 0.276   0.000

[[2]]
           tx.mn  tx.sd   ct.mn  ct.sd std.eff.sz   stat     p    ks ks.pval
stent      0.670  0.470   0.667  0.472      0.006  0.081 0.936 0.003   1.000
height   171.404 10.602 171.532 11.552     -0.012 -0.124 0.902 0.038   0.974
female     0.344  0.475   0.333  0.472      0.022  0.283 0.777 0.010   1.000
diabetic   0.223  0.416   0.245  0.431     -0.052 -0.601 0.548 0.022   1.000
acutemi    0.143  0.351   0.144  0.352     -0.003 -0.026 0.979 0.001   1.000
ejecfrac  50.943 10.109  50.948 10.377      0.000 -0.006 0.995 0.042   0.934
ves1proc   1.384  0.663   1.428  0.696     -0.068 -0.586 0.558 0.028   0.999
ps         0.701  0.133   0.704  0.137     -0.018 -0.185 0.853 0.046   0.884
linps      0.973  0.774   0.999  0.815     -0.034 -0.292 0.771 0.046   0.884

bal.before.wts2 <- bal.table(bal.wts2)[1]
bal.after.wts2 <- bal.table(bal.wts2)[2]
balance.ate.weights <- data_frame(names = rownames(bal.before.wts2$unw),
pre.weighting = 100*bal.before.wts2$unw$std.eff.sz,

ATE.weighted = 100*bal.after.wts2[[1]]$std.eff.sz)
balance.ate.weights <- gather(balance.ate.weights, timing, szd, 2:3)

ggplot(balance.ate.weights, aes(x = szd, y = reorder(names, szd), color = timing)) +
geom_point() +
geom_vline(xintercept = 0) +
geom_vline(xintercept = c(-10,10), linetype = "dashed", col = "blue") +
labs(x = "Standardized Difference", y = "",
title = "Standardized Difference before and after ATE Weighting")

Again, the standardized differences look good here.

13.3.1 Rubin’s Rules

13.3.1.1 Rule 1

-0.033*100 = 3.3%. Passes Rule 1 (numbers from ATE weight balance table above).

13.3.1.2 Rule 2

(0.774²)/(0.815²) = 0.9019173. Passes Rule 2 (numbers from ATE weight balance table above).

13.3.2 Estimated effect on outcomes after ATE weighting

13.3.2.1 Quantitative outcome

lindnerwt2.design <- svydesign(ids=~1, weights=~wts2, data=lindner_clean) # using ATE weights

adjout1.wt2 <- svyglm(cardbill ~ treated, design=lindnerwt2.design)

wt_ate_results1 <- tidy(adjout1.wt2, conf.int = TRUE) %>% filter(term == "treated")
wt_ate_results1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     147.     1192.     0.124   0.902   -2190.     2484.

Estimate 147.26 (95% CI: -2189.63, 2484.15)

13.3.2.2 Binary outcome

adjout2.wt2 <- svyglm(sixMonthSurvive ~ treated, design=lindnerwt2.design, family=quasibinomial())

wt_ate_results2 <- tidy(adjout2.wt2, conf.int = TRUE, exponentiate = TRUE) %>%
filter(term == "treated")
wt_ate_results2

# A tibble: 1 x 7
  term    estimate std.error statistic  p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
1 treated     5.74     0.503      3.47 0.000538     2.14      15.4

Estimate 5.74 (95% CI: 2.14, 15.38)

14 Task 10: Using TWANG for propensity score estimation and ATT weighting

ps.toy <- ps(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc,
data = lindner_clean_df,
n.trees = 3000,
interaction.depth = 2,
stop.method = c("es.mean"),
estimand = "ATT",
verbose = FALSE)

plot(ps.toy)

summary(ps.toy)

            n.treat n.ctrl ess.treat ess.ctrl     max.es    mean.es    max.ks
unw             698    298       698   298.00 0.36544982 0.19933096 0.1884195
es.mean.ATT     698    298       698   172.19 0.08373615 0.04075872 0.0388038
            max.ks.p    mean.ks iter
unw               NA 0.09791845   NA
es.mean.ATT       NA 0.02469335 1628

plot(ps.toy, plots = 2)

plot(ps.toy, plots = 3)

bal.tab(ps.toy, full.stop.method = "es.mean.att")

Call
 ps(formula = treated ~ stent + height + female + diabetic + acutemi + 
    ejecfrac + ves1proc, data = lindner_clean_df, n.trees = 3000, 
    interaction.depth = 2, verbose = FALSE, estimand = "ATT", 
    stop.method = c("es.mean"))

Balance Measures
               Type Diff.Adj
prop.score Distance   0.2497
stent        Binary   0.0263
height      Contin.  -0.0068
female       Binary   0.0082
diabetic     Binary  -0.0235
acutemi      Binary   0.0321
ejecfrac    Contin.  -0.0614
ves1proc    Contin.   0.0001

Effective sample sizes
           Control Treated
Unadjusted  298.       698
Adjusted    172.19     698

p <- love.plot(bal.tab(ps.toy),
threshold = .1, size = 1.5,
title = "Standardized Differences and TWANG ATT Weighting")

Warning: Standardized mean differences and raw mean differences are present in the same plot. 
Use the 'stars' argument to distinguish between them and appropriately label the x-axis.

p + theme_bw()

Compared to the manual ATT/ATE weights, the standardized differences look a bit worse here.

14.1 Estimated effect on outcomes after TWANG ATT weighting

14.1.1 Quantitative outcome

toywt3.design <- svydesign(ids=~1,
weights=~get.weights(ps.toy,
stop.method = "es.mean"),
data=lindner_clean) # using twang ATT weights

adjout1.wt3 <- svyglm(cardbill ~ treated, design=toywt3.design)
wt_twangatt_results1 <- tidy(adjout1.wt3, conf.int = TRUE) %>% filter(term == "treated")
wt_twangatt_results1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     501.     1102.     0.454   0.650   -1660.     2661.

Estimate 500.51 (95% CI: -1660.15, 2661.17)

14.1.2 Binary outcome

adjout2.wt3 <- svyglm(sixMonthSurvive ~ treated, design=toywt3.design,
family=quasibinomial())

wt_twangatt_results2 <- tidy(adjout2.wt3, conf.int = TRUE, exponentiate = TRUE) %>%
filter(term == "treated")
wt_twangatt_results2

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     4.02     0.487      2.86 0.00438     1.55      10.4

Estimate 4.02 (95% CI: 1.55, 10.44)

15 Task 11: After direct adjustment with linear PS

Here we’ll directly adjust for the linear propensity score by including it as a covariate in the model.

15.1 Quantitative outcome

direct_out1 <- lm(cardbill ~ treated + linps, data=lindner_clean)

adj_out1 <- tidy(direct_out1, conf.int = TRUE) %>% filter(term == "treated")
adj_out1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated    1168.      805.      1.45   0.147    -412.     2748.

Estimate 1167.9 (95% CI:-412.22, 2748.02)

15.2 Binary outcome

direct_out2 <- glm(sixMonthSurvive ~ treated + linps, data=lindner_clean, family=binomial())

adj_out2 <- tidy(direct_out2, exponentiate = TRUE, conf.int = TRUE) %>%
filter(term == "treated")
adj_out2

# A tibble: 1 x 7
  term    estimate std.error statistic  p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
1 treated     4.64     0.438      3.50 0.000463     1.99      11.3

Estimate 4.64 (95% CI: 1.99, 11.27)

16 Task 12: “Double Robust” Approach: Weighting + Direct Adjustment

Here we’ll adjust for the linear propensity score and the ATT/ATE/TWANG weights when predicting the quantitative outcome.

16.1 Quantitative outcome

16.1.1 ATT weights

design_att <- svydesign(ids=~1, weights=~wts1, data=lindner_clean) # using ATT weights

dr.out1.wt1 <- svyglm(cardbill ~ treated + linps, design=design_att)
dr_att_out1 <- tidy(dr.out1.wt1, conf.int = TRUE) %>% filter(term == "treated")
dr_att_out1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated    -127.     1217.    -0.104   0.917   -2511.     2258.

Estimate -126.72 (95% CI: -2511.33, 2257.89)

16.1.2 ATE weights

design_ate<- svydesign(ids=~1, weights=~wts2, data=lindner_clean) # using ATE weights

dr.out1.wt2 <- svyglm(cardbill ~ treated + linps, design=design_ate)
dr_ate_out1 <- tidy(dr.out1.wt2, conf.int = TRUE) %>% filter(term == "treated")
dr_ate_out1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     217.     1069.     0.203   0.839   -1879.     2312.

Estimate 216.77 (95% CI: -1878.59, 2312.13)

16.1.3 TWANG ATT weights

wts3 <- get.weights(ps.toy, stop.method = "es.mean")
twang.design <- svydesign(ids=~1, weights=~wts3, data=lindner_clean) # twang ATT weights

dr.out1.wt3 <- svyglm(cardbill ~ treated + linps, design=twang.design)
dr_twangatt_out1 <- tidy(dr.out1.wt3, conf.int = TRUE) %>% filter(term == "treated")
dr_twangatt_out1

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     375.     1103.     0.340   0.734   -1787.     2537.

Estimate 375.05 (95% CI: -1787.05, 2537.16)

16.2 Binary outcome

Now we’ll adjust for the linear propensity score and the ATT/ATE/TWANG weights when predicting the binary outcome.

16.2.1 ATT weights

dr.out2.wt1 <- svyglm(sixMonthSurvive ~ treated + linps, design=design_att,
family=quasibinomial())

dr_att_out2 <- tidy(dr.out2.wt1, exponentiate = TRUE, conf.int = TRUE) %>%
filter(term == "treated")
dr_att_out2

# A tibble: 1 x 7
  term    estimate std.error statistic  p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
1 treated     6.90     0.563      3.43 0.000634     2.29      20.8

Estimate 6.9 (95% CI: 2.29, 20.81)

16.2.2 ATE weights

dr.out2.wt2 <- svyglm(sixMonthSurvive ~ treated + linps, design=design_ate,
family=quasibinomial())

dr_ate_out2 <- tidy(dr.out2.wt2, exponentiate = TRUE, conf.int = TRUE) %>%
  filter(term == "treated")

dr_ate_out2

# A tibble: 1 x 7
  term    estimate std.error statistic  p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>    <dbl>    <dbl>     <dbl>
1 treated     5.95     0.517      3.45 0.000590     2.16      16.4

Estimate 5.95 (95% CI: 2.16, 16.39)

16.2.3 TWANG ATT weights

dr.out2.wt3 <- svyglm(sixMonthSurvive ~ treated + linps, design=twang.design,
family=quasibinomial())

dr_twangatt_out2 <- tidy(dr.out2.wt3, exponentiate = TRUE, conf.int = TRUE) %>%
filter(term == "treated")
dr_twangatt_out2

# A tibble: 1 x 7
  term    estimate std.error statistic p.value conf.low conf.high
  <chr>      <dbl>     <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
1 treated     4.87     0.554      2.86 0.00436     1.64      14.4

Estimate 4.87 (95% CI: 1.64, 14.44)

16.3 Session Information

xfun::session_info()

R version 4.0.3 (2020-10-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19041)

Locale:
  LC_COLLATE=English_United States.1252 
  LC_CTYPE=English_United States.1252   
  LC_MONETARY=English_United States.1252
  LC_NUMERIC=C                          
  LC_TIME=English_United States.1252    

Package version:
  askpass_1.1              assertthat_0.2.1         backports_1.2.1         
  base64enc_0.1-3          BH_1.75.0.0              blob_1.2.1              
  boot_1.3-27              brio_1.1.1               broom_0.7.5             
  broom.mixed_0.2.6        bslib_0.2.4              callr_3.5.1             
  cellranger_1.1.0         checkmate_2.0.0          class_7.3-17            
  cli_2.3.1                clipr_0.7.1              cluster_2.1.0           
  cmprsk_2.2-10            cobalt_4.3.0             coda_0.19-4             
  colorspace_2.0-0         compiler_4.0.3           cpp11_0.2.6             
  crayon_1.4.1             crosstalk_1.1.1          cubelyr_1.0.1           
  curl_4.3                 data.table_1.14.0        DBI_1.1.1               
  dbplyr_2.1.0             desc_1.2.0               diffobj_0.3.3           
  digest_0.6.27            dplyr_1.0.4              e1071_1.7-4             
  ellipsis_0.3.1           Epi_2.43                 etm_1.1.1               
  evaluate_0.14            fansi_0.4.2              farver_2.0.3            
  forcats_0.5.1            foreign_0.8-81           Formula_1.2-4           
  fs_1.5.0                 gbm_2.1.8                gdata_2.18.0            
  generics_0.1.0           ggdendro_0.1.22          ggforce_0.3.2           
  ggformula_0.10.1         ggplot2_3.3.3            ggrepel_0.9.1           
  ggridges_0.5.3           ggstance_0.3.5           glue_1.4.2              
  gmodels_2.18.1           graphics_4.0.3           grDevices_4.0.3         
  grid_4.0.3               gridExtra_2.3            gtable_0.3.0            
  gtools_3.8.2             haven_2.3.1              here_1.0.1              
  highr_0.8                Hmisc_4.4-2              hms_1.0.0               
  htmlTable_2.1.0          htmltools_0.5.1.1        htmlwidgets_1.5.3       
  httr_1.4.2               isoband_0.2.3            janitor_2.1.0           
  jpeg_0.1-8.1             jquerylib_0.1.3          jsonlite_1.7.2          
  knitr_1.31               labeling_0.4.2           labelled_2.7.0          
  lattice_0.20-41          latticeExtra_0.6-29      lazyeval_0.2.2          
  leaflet_2.0.4.1          leaflet.providers_1.9.0  lifecycle_1.0.0         
  lme4_1.1-26              lubridate_1.7.9.2        magrittr_2.0.1          
  markdown_1.1             MASS_7.3-53.1            Matching_4.9-7          
  Matrix_1.2-18            methods_4.0.3            mgcv_1.8-33             
  mime_0.10                minqa_1.2.4              mitools_2.4             
  modelr_0.1.8             mosaic_1.8.3             mosaicCore_0.9.0        
  mosaicData_0.20.2        munsell_0.5.0            nlme_3.1-149            
  nloptr_1.2.2.2           nnet_7.3-15              numDeriv_2016.8-1.1     
  openssl_1.4.3            parallel_4.0.3           patchwork_1.1.1         
  pillar_1.5.0             pkgbuild_1.2.0           pkgconfig_2.0.3         
  pkgload_1.2.0            plyr_1.8.6               png_0.1-7               
  polyclip_1.10-0          praise_1.0.0             prettyunits_1.1.1       
  processx_3.4.5           progress_1.2.2           ps_1.5.0                
  purrr_0.3.4              R6_2.5.0                 rappdirs_0.3.3          
  raster_3.4.5             RColorBrewer_1.1-2       Rcpp_1.0.6              
  RcppArmadillo_0.10.2.1.0 RcppEigen_0.3.3.9.1      readr_1.4.0             
  readxl_1.3.1             rematch_1.0.1            rematch2_2.1.2          
  reprex_1.0.0             reshape2_1.4.4           rlang_0.4.10            
  rmarkdown_2.7            rpart_4.1-15             rprojroot_2.0.2         
  rstudioapi_0.13          rvest_0.3.6              sass_0.3.1              
  scales_1.1.1             selectr_0.4.2            snakecase_0.11.0        
  sp_1.4.5                 splines_4.0.3            statmod_1.4.35          
  stats_4.0.3              stringi_1.5.3            stringr_1.4.0           
  survey_4.0               survival_3.2-7           sys_3.4                 
  tableone_0.12.0          testthat_3.0.2           tibble_3.1.0            
  tidyr_1.1.2              tidyselect_1.1.0         tidyverse_1.3.0         
  tinytex_0.29             TMB_1.7.19               tools_4.0.3             
  twang_1.6                tweenr_1.0.1             utf8_1.1.4              
  utils_4.0.3              vctrs_0.3.6              viridis_0.5.1           
  viridisLite_0.3.0        waldo_0.2.4              withr_2.4.1             
  xfun_0.21                xml2_1.3.2               xtable_1.8-4            
  yaml_2.2.1               zoo_1.8-8

---
title: "The Lindner Example"
author: "Wyatt P. Bensken and Harry Persaud"
date: 'Version: `r Sys.Date()`'
output:
    html_document:
        toc: yes
        toc_float: TRUE
        number_sections: TRUE
        code_folding: show
        code_download: TRUE
    pdf_document:
        toc: yes
        number_sections: TRUE
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(comment = NA)
```

```{r, warning=FALSE, message=FALSE}
# Load packages
library(broom)
library(patchwork)
library(cobalt)
library(Matching)
library(tableone)
library(twang)
library(janitor)
library(here)
library(magrittr)
library(lme4)
library(tidyverse)
```

Note: we will also use the `broom.mixed` package, but we are not loading it as to prevent it conflicting with the functions of `broom`.

**If you notice any errors or encounter any problems with this example, please contact Wyatt Bensken**.

# Load data

Information on the lindner dataset can be found at [this](https://www.rdocumentation.org/packages/MatchLinReg/versions/0.7.0/topics/lindner) site.^1,2^

^1^ Rdocumentation. (n.d.). lindner: Lindner Center Data On 996 PCI Patients Analyzed By Kereiakes Et Al. (2000). Retrieved from https://www.rdocumentation.org/packages/MatchLinReg/versions/0.7.0/topics/lindner


^2^ Kereiakes DJ, Obenchain RL, Barber BL, et al. Abciximab provides cost effective survival advantage in high volume interventional practice. Am Heart J 2000; 140: 603-610.

```{r}
lindner_raw <- read.csv("data/lindner.csv")

lindner_raw %>%
  head(10)

colSums(is.na(lindner_raw))

```

After reading in the data, we can print the first 10 rows to get a sense of what our data looks like. We see it contains information on 996 participants, and there is no missing data.

# Data managment

## Managing binary variables

In the course of this example, we'll want both a numeric and factored version of each binary variable. 

- In all numeric versions of binary variables: 1 indicates 'yes' to having trait/characteristic, 0 indicates 'no' to having trait/characteristic.

- Variable names with trailing "_f" denotes the factored version of each binary variable.

```{r}
# Six month survival (turning logical variable to a factor)
lindner_raw$sixMonthSurvive_f <- factor(lindner_raw$sixMonthSurvive, levels = c(TRUE,FALSE),
                                        labels = c("yes", "no"))

# Creating numeric (1/0) version of six month survival variable
lindner_raw$sixMonthSurvive <- factor(lindner_raw$sixMonthSurvive_f, levels = c("yes","no"),
                                      labels = c(1, 0))

lindner_raw$sixMonthSurvive <- ifelse(lindner_raw$sixMonthSurvive == "1", 1, 0)

#Add variable named treated (same values as abcix variable)
lindner_raw$treated <- lindner_raw$abcix

# Factoring the exposure of interest variable. Change the name to 'treated' too.
lindner_raw$treated_f <- factor(lindner_raw$abcix, levels = c(1,0),
                                labels = c("treated", "control"))

# Factor version of stent variable
lindner_raw$stent_f <- factor(lindner_raw$stent, levels = c(1,0),
                              labels = c("yes", "no"))

# Factoring the female variable
lindner_raw$female_f <- factor(lindner_raw$female, levels = c(1,0),
                               labels = c("female", "male"))

# Factoring the diabetic variable
lindner_raw$diabetic_f <- factor(lindner_raw$diabetic, levels = c(1,0),
                                 labels = c("yes", "no"))

# Factoring the acutemi variable
lindner_raw$acutemi_f <- factor(lindner_raw$acutemi, levels = c(1,0),
                                labels = c("yes", "no"))

# Add patientid

lindner_raw <- tibble::rowid_to_column(lindner_raw, "patientid")

# Make lindner dataset with "clean" name. 
lindner_clean <- lindner_raw
```

## Inspecting the clean data

```{r}
mosaic::inspect(lindner_clean)
```


# Codebook

Information was copy/pasted from [here](https://www.rdocumentation.org/packages/MatchLinReg/versions/0.7.0/topics/lindner) ^1,2^ (with some changes to reflect this analysis)

- `cardbill` (**Quantitative Outcome**): "Cardiac related costs incurred within 6 months of patient's initial PCI; numeric value in 1998 dollars; costs were truncated by death for the 26 patients with lifepres == 0."

- `sixMonthSurvive`/`sixMonthSurvive_f` (**Binary Outcome**): "Survival at six months a recoded version of lifepres."

- `treated`/`treated_f` (**Exposure**): "Numeric treatment selection indicator; 0 implies usual PCI care alone; 1 implies usual PCI care deliberately augmented by either planned or rescue treatment with abciximab."

- `stent`/`stent_f`: "Coronary stent deployment; numeric, with 1 meaning YES and 0 meaning NO."

- `height`: "Height in centimeters; numeric integer from 108 to 196."

- `female`/`female_f`: "Female gender; numeric, with 1 meaning YES and 0 meaning NO."

- `diabetic`/`diabetic_f`: "Diabetes mellitus diagnosis; numeric, with 1 meaning YES and 0 meaning NO."

- `acutemi`/`acutemi_f`: "Acute myocardial infarction within the previous 7 days; numeric, with 1 meaning YES and 0 meaning NO."

- `ejecfrac`: "Left ejection fraction; numeric value from 0 percent to 90 percent."

- `ves1proc`: "Number of vessels involved in the patient's initial PCI procedure; numeric integer from 0 to 5."

- `patientid`: a made-up order of numbers to assign patient IDs for later use

* Note: Percutaneous Coronary Intervention (PCI)

^1^ Rdocumentation. (n.d.). lindner: Lindner Center Data On 996 PCI Patients Analyzed By Kereiakes Et Al. (2000). Retrieved from https://www.rdocumentation.org/packages/MatchLinReg/versions/0.7.0/topics/lindner

^2^ Kereiakes DJ, Obenchain RL, Barber BL, et al. Abciximab provides cost effective survival advantage in high volume interventional practice. Am Heart J 2000; 140: 603-610.

# Table 1

```{r}
var_list = c("cardbill", "sixMonthSurvive_f", "stent_f", "height", "female_f", "diabetic_f", 
             "acutemi_f", "ejecfrac", "ves1proc")

factor_list = c("sixMonthSurvive_f", "stent_f", "female_f", "diabetic_f", "acutemi_f")

CreateTableOne(vars = var_list, strata = "treated_f",
               data = lindner_clean, factorVars = factor_list)
```

As we can see, The mean `cardbill` was higher in the treated population and a larger percentage of controls did not survive through 6 months.

# Task 1: Ignoring covariates, estimate the effect of treatment vs. control on the two outcomes

## Quantitative outcome: `cardbill`

```{r}
lindner_clean %$%
  mosaic::favstats(cardbill ~ treated_f)
```

- Across the entire sample, the mean (\$16,127 vs. \$14,614) and median (\$12,944 vs. \$10,423) cardiac care costs were higher in treated individuals than non-treated controls.

```{r}
ggplot(lindner_clean, aes(x = cardbill, fill = "cardbill")) +
  geom_histogram() +
  theme_bw() +
  labs(y = "Count",
       x = "Cardiac care costs ($)",
       title = "Cardbill appears to be right skewed") +
  guides(fill = FALSE)
```

As we can see in this figure, `cardbill` appears to be right/positively skewed.

```{r}
unadjust_quant_outcome <- lm(cardbill ~ treated, data = lindner_clean)

unadjust_quant_outcome_tidy <- tidy(unadjust_quant_outcome, conf.int = TRUE, conf.level = 0.95) %>%
    filter(term == "treated")

unadjust_quant_outcome_tidy
```

Treated individuals were estimated to spend `r round(unadjust_quant_outcome_tidy$estimate,2)` (95%CI: `r round(unadjust_quant_outcome_tidy$conf.low,2)`, `r round(unadjust_quant_outcome_tidy$conf.high,2)`) more dollars than non-treated controls 

## Binary outcome: `sixMonthSurvive`

```{r}
Epi::twoby2(table(lindner_clean$treated_f, lindner_clean$sixMonthSurvive_f))
```

The odds treated individuals were alive after 6 months was roughly 3.31 times the odds that non-treated individuals were alive after 6 months.

```{r}
unadjust_binary_outcome <- glm(sixMonthSurvive ~ treated, data = lindner_clean, family = binomial())

unadjust_binary_outcome_tidy <- tidy(unadjust_binary_outcome, conf.int = TRUE, conf.level = 0.95, exponentiate = TRUE) %>%
    filter(term == "treated")

unadjust_binary_outcome_tidy
```

The  odds of being alive after six months in treated individuals was  `r round(unadjust_binary_outcome_tidy$estimate,2)` (95%CI: `r round(unadjust_binary_outcome_tidy$conf.low,2)`, `r round(unadjust_binary_outcome_tidy$conf.high,2)`) times higher than the odds that a  non-treated control would be alive after six months.

# Task 2: Fitting the propensity score model

We will now fit the propensity score, which predicts treatment status based on available covariates. Remember, we're not worried about overfitting (including too many covariates) when calculating the propensity scores.

```{r}
psmodel <- glm(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc, family = binomial(), data =lindner_clean)

summary(psmodel)
```

Store the raw and linear propensity scores below.

```{r}
lindner_clean$ps <- psmodel$fitted
lindner_clean$linps <- psmodel$linear.predictors
```

## Comparing distribution of propensity scores across treatment groups

## Numerically

```{r}
lindner_clean %$% 
  mosaic::favstats(ps ~ treated_f)
```

We can see there are no propensity scores equal to, or very close to, 0 or 1. 

## Visually

### Boxplot 

Now we'll visualize the distribution of the propensity scores stratified by treatment status.  

```{r}
ggplot(lindner_clean, aes(x = treated_f, y = ps, color = treated_f)) +
geom_boxplot() +
geom_jitter(width = 0.1) +
guides(color = FALSE) +
theme_bw() +
labs(x = "",
     title = "Raw propensity scores, stratified by exposure group")
```

### Density plot

```{r}
ggplot(lindner_clean, aes(x = linps, fill = treated_f)) +
geom_density(alpha = 0.3) +
  theme_bw()
```

Both of these plots demonstrate good overlap, suggesting a propensity score analysis may be appropriate.

# Task 3: Rubin's Rules For Assessing Overlap Before Propensity Adjustment

##  Rubin's Rule 1

```{r}
rubin1.unadj <- with(lindner_clean,
abs(100*(mean(linps[treated==1])-mean(linps[treated==0]))/sd(linps)))
rubin1.unadj
```

As you can see, we fail Rubin's Rule 1 - in which we want below 50%.

## Rubin's Rule 2

```{r}
rubin2.unadj <-with(lindner_clean, var(linps[treated==1])/var(linps[treated==0]))
rubin2.unadj
```

We also "fail" Rubin's Rule 2 wherewe are looking for value between 0.8 - 1.2 (ideally, 1).

# Task 4: Greedy 1:1 matching on the linear PS

The first type of match we will conduct is greedy 1:1 matching, without replacement. As we had only 298 controls, we will not match all of the 698 treated patients.

```{r}
X <- lindner_clean$linps ## matching on the linear propensity score
Tr <- as.logical(lindner_clean$treated)
match1 <- Match(Tr=Tr, X=X, M = 1, replace=FALSE, ties=FALSE)
summary(match1)
```


Below we'll assess the match balance from the 1:1 matching.

```{r}
set.seed(2021)
mb1 <- MatchBalance(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean,
match.out = match1, nboots=500)
```

```{r}
covnames <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")
```

This is Dr. Love's code to extract the standardized differences.

```{r}
pre.szd <- NULL; post.szd <- NULL
for(i in 1:length(covnames)) {
pre.szd[i] <- mb1$BeforeMatching[[i]]$sdiff.pooled
post.szd[i] <- mb1$AfterMatching[[i]]$sdiff.pooled
}
```

We can now print our table of standardized differences.

```{r}
match_szd <- data.frame(covnames, pre.szd, post.szd, row.names=covnames)
print(match_szd, digits=3)
```

## Love Plot of standardized differences before and after 1:1 matching

## Using ggplot

In this figure, blue points are post-matching while white are pre-match

```{r}
lp_wo_rep <- ggplot(match_szd, aes(x = pre.szd, y = reorder(covnames, pre.szd))) +
  geom_point(col = "black", size = 3, pch = 1) +
  geom_point(aes(x = post.szd, y = reorder(covnames, pre.szd)), size = 3, col = "blue") +
  theme_bw() +
  geom_vline(aes(xintercept = 0)) +
  geom_vline(aes(xintercept = 10), linetype = "dashed", col = "red") +
  geom_vline(aes(xintercept = -10), linetype = "dashed", col = "red") +
  labs(x = "Standardized Difference (%)", 
     y = "",
     title = "Love Plot",
     subtitle = "1:1 matching without replacement")

lp_wo_rep
```

Just visually, we can see this match isn't all that great.

## Using `cobalt` to make the Love Plot

There's a more automated way to build the Love Plot - as we see here.

```{r}
cobalt_tab <- bal.tab(match1, treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean, un = TRUE)

cobalt_tab
```

```{r}
p <- love.plot(cobalt_tab, threshold = .1, size = 1.5,
               var.order = "unadjusted",
               title = "Standardized Differences after 1:1 Matching without replacement",
               stars = "std")

p + theme_bw()
```

## Extracting Variance Ratios

We can also look at variance ratios.

```{r}
pre.vratio <- NULL; post.vratio <- NULL
for(i in 1:length(covnames)) {
pre.vratio[i] <- mb1$BeforeMatching[[i]]$var.ratio
post.vratio[i] <- mb1$AfterMatching[[i]]$var.ratio
}
## Table of Variance Ratios
match_vrat <- data.frame(names = covnames, pre.vratio, post.vratio, row.names=covnames)
print(match_vrat, digits=2)
```

## Creating a dataframe containing the matched sample

We will created a dataframe which includes our matched sample, and do a quick count for a sanity check.

```{r}
matches <- factor(rep(match1$index.treated, 2))
lindner_clean.matchedsample <- cbind(matches, lindner_clean[c(match1$index.control, match1$index.treated),])

lindner_clean.matchedsample %>% count(treated_f)
```

## Reassessing Rubin's Rules after 1:1 matching without replacement

### Rubin's Rule 1

```{r}
rubin1.match <- with(lindner_clean.matchedsample,
abs(100*(mean(linps[treated==1])-mean(linps[treated==0]))/sd(linps)))
rubin1.match
```

The new value for Rubin's Rule 1 is `r round(rubin1.match,2)`. While not ideal this technically passes Rubin's Rule 1 and is an improvement from the pre-match value of `r round(rubin1.unadj,2)`.

### Rubin's Rule 2

```{r}
rubin2.match <- with(lindner_clean.matchedsample, var(linps[treated==1])/var(linps[treated==0]))
rubin2.match
```

The new value for Rubin's Rule 2 is `r round(rubin2.match,2)`. This does not pass Rubin's Rule 2 and is not an improvement from the pre-match value of `r round(rubin2.unadj,2)`.

# Task 5: Estimating the causal effect of the treatment on both outcomes after 1:1 matching without replacement

## The Quantitative Outcome

We'll use a mixed model to estimate the effect of the treatment on `cardbill`. The matches will be treated as a random effect in the model (syntax "(1| matches.f)", and the treatment group will be treated as a fixed effect. We will use restricted maximum likelihood (REML)  to estimate coefficient values.

```{r}
#to appease lme4, factor the matches 
lindner_clean.matchedsample$matches.f <- as.factor(lindner_clean.matchedsample$matches)

# fit the mixed model
matched_mixedmodel.out1 <- lmer(cardbill ~ treated + (1 | matches.f), REML = TRUE, data=lindner_clean.matchedsample)

summary(matched_mixedmodel.out1)
confint(matched_mixedmodel.out1)
```


```{r, warning=FALSE, message=FALSE}
tidy_mixed_matched <- broom.mixed::tidy(matched_mixedmodel.out1, conf.int = TRUE, conf.level = 0.95) %>% 
  filter(term == "treated")

tidy_mixed_matched
```

Treated individuals were estimated to spend \$`r round(tidy_mixed_matched$estimate,2)` (95%CI: `r round(tidy_mixed_matched$conf.low,2)`, `r round(tidy_mixed_matched$conf.high,2)`) less than non-treated individuals. As this result is not significant at an $\alpha$ of 0.05, a sensitivity analysis on the quantitative outcome will not make sense.

```{r}
#check the mean cardbill in the matched sample
lindner_clean.matchedsample %>% group_by(treated_f) %>% summarise(mean = mean(cardbill))

#check the mean cardbill in the entire sample
lindner_clean %>% group_by(treated_f) %>% summarise(mean = mean(cardbill))
```

In treated individuals, the mean `cardbill` was lower within the matched sample than the entire sample (note the mean within the control group was the same as every control participant is in the matched sample. The mean changed in the treated group as only 298/698 treated patients are in the matched sample). This is a sanity check to assess if the mixed model results make sense; and it looks like they do.

## The Binary Outcome

We will use conditional logistic regression to estimate the log odds (and ORs) of being alive after 6 months based on treatment status.

```{r}
binary_outcome_adjusted <- survival::clogit(sixMonthSurvive ~ treated + strata(matches), data=lindner_clean.matchedsample)

summary(binary_outcome_adjusted)
```

```{r}
#Tidy model
tidy_binary_outcome_adjusted <- tidy(binary_outcome_adjusted, exponentiate = TRUE, conf.int = 0.95)
```

The odds of being alive after six months were `r tidy_binary_outcome_adjusted$estimate` times higher in treated individuals than non-treated individuals (95%CI `r round(tidy_binary_outcome_adjusted$conf.low,2)`, `r round(tidy_binary_outcome_adjusted$conf.high,2)`)

# Task 6 1:1 Matching With replacement

- As we saw in the 1:1 matching without replacement, 400 treated participants were excluded from the sample. This is a waste of data and we'll address this by again matching 1 treated participant to 1 control participant. However, this time we'll match with replacement, meaning each time a control participant is matched to a treated participant, the control participant will be placed back into the pool of possible patients a treated individual can be matched to. Thus, some control participants will be matched multiple times (not all control participants have to be matched to a treated participant). In the Lindner dataset 1:1 matching with replacement is a more reasonable choice.

```{r}
X <- lindner_clean$linps ## matching on the linear propensity score
Tr <- as.logical(lindner_clean$treated)
match1 <- Match(Tr=Tr, X=X, M = 1, replace=TRUE, ties=FALSE) # notice replace =  TRUE
summary(match1)
```

As you can see, this time we matched 698 treated individuals with 698 control participants. To reiterate, as we matched with replacement, and there were less control participants than treated participants, some control participants were matched multiple times.

Below we'll assess the match balance from the 1:1 matching with replacement.

```{r}
set.seed(202102)
mb1 <- MatchBalance(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean,
match.out = match1, nboots=500)
```

```{r}
covnames <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")
```

Dr. Love's code to extract the standardized differences.

```{r}
pre.szd <- NULL; post.szd <- NULL
for(i in 1:length(covnames)) {
pre.szd[i] <- mb1$BeforeMatching[[i]]$sdiff.pooled
post.szd[i] <- mb1$AfterMatching[[i]]$sdiff.pooled
}
```

Table of standardized differences

```{r}
match_szd <- data.frame(covnames, pre.szd, post.szd, row.names=covnames)
print(match_szd, digits=3)
```

## Love Plot of standardized differences before and after 1:1 matching

## Using ggplot

In this figure, blue points are post-matching while white are pre-match.

```{r}
lp_w_rep <- ggplot(match_szd, aes(x = pre.szd, y = reorder(covnames, pre.szd))) +
  geom_point(col = "black", size = 3, pch = 1) +
  geom_point(aes(x = post.szd, y = reorder(covnames, pre.szd)), size = 3, col = "blue") +
  theme_bw() +
  geom_vline(aes(xintercept = 0)) +
  geom_vline(aes(xintercept = 10), linetype = "dashed", col = "red") +
  geom_vline(aes(xintercept = -10), linetype = "dashed", col = "red") +
  labs(x = "Standardized Difference (%)", 
     y = "",
     title = "Love Plot",
     subtitle = "1:1 matching with replacement")

lp_w_rep
```

- Visually, the Love Plot using 1:1 matching with replacement looks pretty good.

```{r}
# comparison of love plots with and without replacement
lp_wo_rep +  lp_w_rep
```

When we look at the plots without replacement and with replacement side-by-side, it definitely looks better than the 1:1 matching without replacement.

## Using `cobalt` to make the Love Plot

Again, we can also use an automated way to make the Love Plot.

```{r}
cobalt_tab <- bal.tab(match1, treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc + ps + linps, data=lindner_clean, un = TRUE,
                      stats = c("m","v"))

cobalt_tab
```

```{r}
p <- love.plot(cobalt_tab, threshold = .1, size = 1.5,
               var.order = "unadjusted",
               title = "Standardized Differences after 1:1 Matching With Replacement",
               stars = "std")

p + theme_bw()
```

## Extracting Variance Ratios

```{r}
pre.vratio <- NULL; post.vratio <- NULL
for(i in 1:length(covnames)) {
pre.vratio[i] <- mb1$BeforeMatching[[i]]$var.ratio
post.vratio[i] <- mb1$AfterMatching[[i]]$var.ratio
}
## Table of Variance Ratios
match_vrat <- data.frame(names = covnames, pre.vratio, post.vratio, row.names=covnames)
print(match_vrat, digits=2)
```

### Using 'cobalt' to make a Love Plot of Variance Ratios

```{r}
p <- love.plot(cobalt_tab, stats = "v", threshold = .1, size = 3,
               var.order = "unadjusted",
               title = "Variance Ratios after 1:1 Matching With Replacement",
               stars = "")

p + theme_bw()
```


## Creating a dataframe containing the matched sample

```{r}
matches <- factor(rep(match1$index.treated, 2))
lindner_clean.matchedsample <- cbind(matches, lindner_clean[c(match1$index.control, match1$index.treated),])

lindner_clean.matchedsample %>% count(treated_f)
```
### How many times were the non-treated patients matched?

```{r}
lindner_clean.matchedsample %>% filter(treated_f == "control") %>% 
    count(patientid) %>%
    janitor::tabyl(n)
```


## Reassessing Rubin's Rules after 1:1 matching with replacement

### Rubin's Rule 1

```{r}
rubin1.match.rep <- with(lindner_clean.matchedsample,
abs(100*(mean(linps[treated==1])-mean(linps[treated==0]))/sd(linps)))
rubin1.match.rep
```

The new value for Rubin's Rule 1 is `r round(rubin1.match.rep, 2)`. This value passes Rubin's Rule 1 and is an improvement from the Rubin's Rule 1 value obtained during 1:1 matching without replacement, `r round(rubin1.match,2)`. The pre-match value was `r round(rubin1.unadj,2)`.

### Rubin's Rule 2

```{r}
rubin2.match.rep <- with(lindner_clean.matchedsample, var(linps[treated==1])/var(linps[treated==0]))
rubin2.match.rep
```

The new value for Rubin's Rule 2 is `r round(rubin2.match.rep, 2)`. This passes Rule 2 and is an improvement from the Rubin's Rule 2 value obtained during 1:1 matching without replacement, `r round(rubin2.match,2)`. The pre-match value was `r round(rubin2.unadj,2)`.

## Estimating the causal effect of the treatment on both outcomes after 1:1 matching with replacement

### The Quantitative Outcome

Again, we'll use a mixed model to estimate the effect of the treatment on `cardbill`. The matches will be treated as a random effect in the model (syntax "(1| matches.f)". and the treatment group will be treated as a fixed effect. We will use restricted maximum likelihood (REML)  to estimate coefficient values.

```{r}
#to appease lme4, factor the matches 
lindner_clean.matchedsample$matches.f <- as.factor(lindner_clean.matchedsample$matches)

# fit the mixed model
matched_mixedmodel.rep.out1 <- lmer(cardbill ~ treated + (1 | matches.f), REML = TRUE, data=lindner_clean.matchedsample)

summary(matched_mixedmodel.rep.out1)
confint(matched_mixedmodel.rep.out1)
```

```{r, warning=FALSE, message=FALSE}
tidy_mixed_matched_rep <- broom.mixed::tidy(matched_mixedmodel.rep.out1, conf.int = TRUE, conf.level = 0.95) %>% 
  filter(term == "treated")

tidy_mixed_matched_rep
```

Treated individuals were estimated to spend \$`r round(tidy_mixed_matched_rep$estimate,2)` less (95%CI `r round(tidy_mixed_matched_rep$conf.low,2)`, `r round(tidy_mixed_matched_rep$conf.high,2)`) than non-treated individuals. This finding is not significant at an $\alpha$ of 0.05, thus, the sensitivity analysis on the Quantitative outcome will still not make sense.

```{r}
#sanity check for model
lindner_clean.matchedsample %>% group_by(treated_f) %>% summarise(mean_card = mean(cardbill))
```

- The mixed model above predicted treated individuals would spend roughly \$`r round(tidy_mixed_matched_rep$estimate,2)` less than control participants. After doing a quick check of the mean `cardbill` within the matched sample, the mixed model results make sense. 

### The Binary Outcome

We will use conditional logistic regression to estimate the log odds (and ORs) of being alive after 6 months based on treatment status.

```{r}
binary_outcome_adjusted_rep <- survival::clogit(sixMonthSurvive ~ treated + strata(matches), data=lindner_clean.matchedsample)

summary(binary_outcome_adjusted_rep)
```

```{r}
#Tidy model
tidy_binary_outcome_adjusted_rep <- tidy(binary_outcome_adjusted_rep, exponentiate = TRUE, conf.int = 0.95)

tidy_binary_outcome_adjusted_rep
```

The odds of being alive after six months were `r round(tidy_binary_outcome_adjusted_rep$estimate,2)` times higher in treated individuals than non-treated controls (95%CI `r round(tidy_binary_outcome_adjusted_rep$conf.low,2)`, `r round(tidy_binary_outcome_adjusted_rep$conf.high,2)`)

# Task 7: Subclassification by Propensity Score Quintile

```{r}
#cut into quintiles
lindner_clean$stratum <- Hmisc::cut2(lindner_clean$ps, g=5)
lindner_clean$quintile <- factor(lindner_clean$stratum, labels=1:5)

#Sanity check: check to make sure quntiles are evenish, numbers make sense, etc.
lindner_clean %>% count(stratum, quintile) 
```

## Check Balance and Propensity Score Overlap in Each Quintile

### Numerically

Only 20 controls were were in the largest quintile, which seems a bit low. 

```{r}
lindner_clean %>% count(quintile, treated_f)
```

### Graphically

```{r}
ggplot(lindner_clean, aes(x = treated_f, y = round(ps,2), group = quintile, color = treated_f)) +
geom_jitter(width = 0.2) +
guides(color = FALSE) +
facet_wrap(~ quintile, scales = "free_y") +
labs(x = "", y = "Propensity for Treatment",
title = "Quintile Subclassification in the Lindner data")
```

## Creating a Standardized Difference Calculation Function

Here we implement Dr. Love's function to calculate the standardizes differences is utilized below.

```{r}
szd <- function(covlist, g) {
covlist2 <- as.matrix(covlist)
g <- as.factor(g)
res <- NA
for(i in 1:ncol(covlist2)) {
cov <- as.numeric(covlist2[,i])
num <- 100*diff(tapply(cov, g, mean, na.rm=TRUE))
den <- sqrt(mean(tapply(cov, g, var, na.rm=TRUE)))
res[i] <- round(num/den,2)
}
names(res) <- names(covlist)
res
}
```

Now we'll split data into quintiles - and give them each their own dataframe.

```{r}
quin1 <- filter(lindner_clean, quintile==1)
quin2 <- filter(lindner_clean, quintile==2)
quin3 <- filter(lindner_clean, quintile==3)
quin4 <- filter(lindner_clean, quintile==4)
quin5 <- filter(lindner_clean, quintile==5)
```

Now we'll run the function above to calculate the standardized differences for each covariate in each quintile.

```{r}
covs <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")
d.q1 <- szd(quin1[covs], quin1$treated)
d.q2 <- szd(quin2[covs], quin2$treated)
d.q3 <- szd(quin3[covs], quin3$treated)
d.q4 <- szd(quin4[covs], quin4$treated)
d.q5 <- szd(quin5[covs], quin5$treated)
d.all <- szd(lindner_clean[covs], lindner_clean$treated)
lindner_clean.szd <- tibble(covs, Overall = d.all, Q1 = d.q1, Q2 = d.q2, Q3 = d.q3, Q4 = d.q4, Q5 = d.q5)
lindner_clean.szd <- gather(lindner_clean.szd, "quint", "sz.diff", 2:7)
```

## Plotting the post-subclassification standardized differences 

```{r}
ggplot(lindner_clean.szd, aes(x = sz.diff, y = reorder(covs, -sz.diff), group = quint)) +
  geom_point() +
geom_vline(xintercept = 0) +
geom_vline(xintercept = c(-10,10), linetype = "dashed", col = "blue") +
facet_wrap(~ quint) +
labs(x = "Standardized Difference, %", y = "",
title = "Comparing Standardized Differences by PS Quintile")
```

The results of the standardized differences by quintile are failry variable.

## Rubin's Rules post subclassification

### Rule 1

```{r}
rubin1.q1 <- with(quin1, abs(100*(mean(linps[treated==1]) - mean(linps[treated==0]))/sd(linps)))

rubin1.q2 <- with(quin2, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.q3 <- with(quin3, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.q4 <- with(quin4, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.q5 <- with(quin5, abs(100*(mean(linps[treated==1]) -mean(linps[treated==0]))/sd(linps)))

rubin1.sub <- c(rubin1.q1, rubin1.q2, rubin1.q3, rubin1.q4, rubin1.q5)
names(rubin1.sub)=c("Q1", "Q2", "Q3", "Q4", "Q5")

rubin1.sub
```

All are under 50. Not great, but OK. For comparison, the original Rubin's Rule 1 value was 61.87.

### Rule 2

```{r}
rubin2.q1 <- with(quin1, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q2 <- with(quin2, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q3 <- with(quin3, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q4 <- with(quin4, var(linps[treated==1])/var(linps[treated==0]))
rubin2.q5 <- with(quin5, var(linps[treated==1])/var(linps[treated==0]))

rubin2.sub <- c(rubin2.q1, rubin2.q2, rubin2.q3, rubin2.q4, rubin2.q5)
names(rubin2.sub)=c("Q1", "Q2", "Q3", "Q4", "Q5")
rubin2.sub
```

All but Q1 are at least close to passing Rule 2.  For comparison, the original Rubin's Rule 2 value was 1.67.

# Task 8: Estimated effect after subclassification

## Quantitative outcome

```{r}
quin1.out1 <- lm(cardbill ~ treated, data=quin1)
quin2.out1 <- lm(cardbill ~ treated, data=quin2)
quin3.out1 <- lm(cardbill ~ treated, data=quin3)
quin4.out1 <- lm(cardbill ~ treated, data=quin4)
quin5.out1 <- lm(cardbill ~ treated, data=quin5)

coef(summary(quin1.out1)); coef(summary(quin2.out1)); coef(summary(quin3.out1)); coef(summary(quin4.out1)); coef(summary(quin5.out1)) 
```

The mean of the five quintile-specific estimated regression coefficients is below.

```{r}
est.st <- (coef(quin1.out1)[2] + coef(quin2.out1)[2] + coef(quin3.out1)[2] +
coef(quin4.out1)[2] + coef(quin5.out1)[2])/5

est.st
```

The mean SE is below.

```{r}
se.q1 <- summary(quin1.out1)$coefficients[2,2]
se.q2 <- summary(quin2.out1)$coefficients[2,2]
se.q3 <- summary(quin3.out1)$coefficients[2,2]
se.q4 <- summary(quin4.out1)$coefficients[2,2]
se.q5 <- summary(quin5.out1)$coefficients[2,2]

se.st <- sqrt((se.q1^2 + se.q2^2 + se.q3^2 + se.q4^2 + se.q5^2)*(1/25))
se.st
```

The mean estimate, with a 95% CI, is below.

```{r}
strat.result1 <- data_frame(estimate = est.st,
conf.low = est.st - 1.96*se.st,
conf.high = est.st + 1.96*se.st)
strat.result1
```

So treated individuals were estimated to spend \$`r round(strat.result1$estimate, 2)` more (95%CI `r round(strat.result1$conf.low, 2)`, `r round(strat.result1$conf.high, 2)`) than non treated individuals.

## Binary Outcome

```{r}
quin1.out2 <- glm(sixMonthSurvive ~ treated, data=quin1, family=binomial())
quin2.out2 <- glm(sixMonthSurvive ~ treated, data=quin2, family=binomial())
quin3.out2 <- glm(sixMonthSurvive ~ treated, data=quin3, family=binomial())
quin4.out2 <- glm(sixMonthSurvive ~ treated, data=quin4, family=binomial())
quin5.out2 <- glm(sixMonthSurvive ~ treated, data=quin5, family=binomial())

coef(summary(quin1.out2)); coef(summary(quin2.out2)); coef(summary(quin3.out2)); coef(summary(quin4.out2)); coef(summary(quin5.out2))
```

Estimated log-odds (averaged over the quintiles).

```{r}
est.st.log <- (coef(quin1.out2)[2] + coef(quin2.out2)[2] + coef(quin3.out2)[2] +
coef(quin4.out2)[2] + coef(quin5.out2)[2])/5

est.st.log
```

Estimated odds ratio (averaged over the quintiles).

```{r}
exp(est.st.log)
```

The average SE (averaged over the quintiles).

```{r}
se.q1.log <- summary(quin1.out2)$coefficients[2,2]
se.q2.log <- summary(quin2.out2)$coefficients[2,2]
se.q3.log <- summary(quin3.out2)$coefficients[2,2]
se.q4.log <- summary(quin4.out2)$coefficients[2,2]
se.q5.log <- summary(quin5.out2)$coefficients[2,2]

se.st.log <- sqrt((se.q1.log^2 + se.q2.log^2 + se.q3.log^2 + se.q4.log^2 + se.q5.log^2)*(1/25))
se.st.log #log odds
```

```{r}
strat.result2 <- data_frame(estimate = exp(est.st.log),
conf.low = exp(est.st.log - 1.96*se.st.log),
conf.high = exp(est.st.log + 1.96*se.st.log))

strat.result2
```

The odds of being alive after 6 months was `r round(strat.result2$estimate, 2)` (95%CI `r round(strat.result2$conf.low, 2)`, `r round(strat.result2$conf.high, 2)`) times higher in treated individuals than non-treated individuals. 

# Task 9: Weighting

## Calculating the ATT and ATE weights

### ATT weights

First, we can use tge average treatment effect on the treated (ATT) approach where we weight treated subjects as 1 and controls as ps/(1-ps)

```{r}
lindner_clean$wts1 <- ifelse(lindner_clean$treated==1, 1, lindner_clean$ps/(1-lindner_clean$ps))
```

### ATE weights

We can also use the average treatment effect (ATE) weights where we weight treated subjects by 1/ps and controls by 1/(1-PS)

```{r}
lindner_clean$wts2 <- ifelse(lindner_clean$treated==1, 1/lindner_clean$ps, 1/(1-lindner_clean$ps))
```

## Working with the ATT weights

```{r}
ggplot(lindner_clean, aes(x = ps, y = wts1, color = treated_f)) +
geom_point() +
guides(color = FALSE) +
facet_wrap(~ treated_f) +
labs(x = "Estimated Propensity for Treatment",
y = "ATT weight",
title = "ATT weighting structure")
```

```{r}
#turn dataset into a dataframe for twang (its a tibble now)
lindner_clean_df <- data.frame(lindner_clean)

#name covariates
covlist <- c("stent", "height", "female", "diabetic", "acutemi", "ejecfrac", "ves1proc", "ps", "linps")
```

```{r}
bal.wts1 <- dx.wts(x=lindner_clean_df$wts1, data=lindner_clean_df, vars=covlist,
treat.var="treated", estimand="ATT")

bal.wts1
```

```{r}
bal.table(bal.wts1)
```

```{r}
bal.before.wts1 <- bal.table(bal.wts1)[1]
bal.after.wts1 <- bal.table(bal.wts1)[2]
balance.att.weights <- data_frame(names = rownames(bal.before.wts1$unw),
pre.weighting = 100*bal.before.wts1$unw$std.eff.sz,
ATT.weighted = 100*bal.after.wts1[[1]]$std.eff.sz)
balance.att.weights <- gather(balance.att.weights, timing, szd, 2:3)
```

Now we can plot the standardized differences after ATT weighting.

```{r}
ggplot(balance.att.weights, aes(x = szd, y = reorder(names, szd), color = timing)) +
  geom_point() +
  geom_vline(xintercept = 0) +
  geom_vline(xintercept = c(-10,10), linetype = "dashed", col = "blue") +
  labs(x = "Standardized Difference", 
       y = "",
       title = "Standardized Difference before and after ATT Weighting")
```

The standardized differences look much better here in this approach.

### Rubin's Rules

#### Rule 1

**Numbers from balance table above**: (-0.048 * 100)  = 4.8%. So passes Rule 1.

#### Rule 2

**Numbers from balance table above**:(0.796^2^)/(0.839^2^) = 0.9001237. Passes Rule 2

### Estimated effect on outcomes after ATT weighting

#### Quantitative outcome

To estimate the effect of the treatment on `cardbill`, we'll use svyglm from the `survey` package to apply the ATT weights in a linear model.  

```{r}
lindnerwt1.design <- svydesign(ids=~1, weights=~wts1, data=lindner_clean) # using ATT weights

adjout1.wt1 <- svyglm(cardbill ~ treated, design=lindnerwt1.design)

wt_att_results1 <- tidy(adjout1.wt1, conf.int = TRUE) %>% filter(term == "treated")

wt_att_results1
```

**Estimate (95%CI)** `r round(wt_att_results1$estimate,2)` (`r round(wt_att_results1$conf.low,2)`, `r round(wt_att_results1$conf.high,2)`)

#### Binary outcome

We'll do similar coding for the binary outcome.

```{r}
adjout2.wt1 <- svyglm(sixMonthSurvive ~ treated, design=lindnerwt1.design, family=quasibinomial())

wt_att_results2 <- tidy(adjout2.wt1, conf.int = TRUE, exponentiate = TRUE) %>%
filter(term == "treated")
wt_att_results2
```

**Estimate (95%CI)** `r round(wt_att_results2$estimate,2)` (`r round(wt_att_results2$conf.low,2)`, `r round(wt_att_results2$conf.high,2)`)

## Working with the ATE weights

Now, we'll go through the same steps with the ATE weights.

```{r}
ggplot(lindner_clean, aes(x = ps, y = wts2, color = treated_f)) +
geom_point() +
guides(color = FALSE) +
facet_wrap(~ treated_f) +
labs(x = "Estimated Propensity for Treatment",
y = "ATE weights",
title = "ATE weighting structure")
```

```{r}
bal.wts2 <- dx.wts(x=lindner_clean_df$wts2, data=lindner_clean_df, vars=covlist,
treat.var="treated", estimand="ATE")

bal.wts2
```

```{r}
bal.table(bal.wts2)
```

```{r}
bal.before.wts2 <- bal.table(bal.wts2)[1]
bal.after.wts2 <- bal.table(bal.wts2)[2]
balance.ate.weights <- data_frame(names = rownames(bal.before.wts2$unw),
pre.weighting = 100*bal.before.wts2$unw$std.eff.sz,

ATE.weighted = 100*bal.after.wts2[[1]]$std.eff.sz)
balance.ate.weights <- gather(balance.ate.weights, timing, szd, 2:3)
```

```{r}
ggplot(balance.ate.weights, aes(x = szd, y = reorder(names, szd), color = timing)) +
geom_point() +
geom_vline(xintercept = 0) +
geom_vline(xintercept = c(-10,10), linetype = "dashed", col = "blue") +
labs(x = "Standardized Difference", y = "",
title = "Standardized Difference before and after ATE Weighting")
```

Again, the standardized differences look good here.

### Rubin's Rules

#### Rule 1

-0.033*100 = 3.3%. Passes Rule 1 (numbers from ATE weight balance table above).

#### Rule 2

(0.774^2^)/(0.815^2^) = 0.9019173. Passes Rule 2 (numbers from ATE weight balance table above).

### Estimated effect on outcomes after ATE weighting

#### Quantitative outcome

```{r}
lindnerwt2.design <- svydesign(ids=~1, weights=~wts2, data=lindner_clean) # using ATE weights

adjout1.wt2 <- svyglm(cardbill ~ treated, design=lindnerwt2.design)

wt_ate_results1 <- tidy(adjout1.wt2, conf.int = TRUE) %>% filter(term == "treated")
wt_ate_results1
```

- **Estimate ** `r round(wt_ate_results1$estimate, 2)` (95% CI: `r round(wt_ate_results1$conf.low,2)`, `r round(wt_ate_results1$conf.high,2)`)

#### Binary outcome

```{r}
adjout2.wt2 <- svyglm(sixMonthSurvive ~ treated, design=lindnerwt2.design, family=quasibinomial())

wt_ate_results2 <- tidy(adjout2.wt2, conf.int = TRUE, exponentiate = TRUE) %>%
filter(term == "treated")
wt_ate_results2
```

- **Estimate** `r round(wt_ate_results2$estimate,2)`  (95% CI: `r round(wt_ate_results2$conf.low,2)`, `r round(wt_ate_results2$conf.high,2)`)

# Task 10: Using TWANG for propensity score estimation and ATT weighting

```{r}
ps.toy <- ps(treated ~ stent + height + female + diabetic + acutemi + ejecfrac + ves1proc,
data = lindner_clean_df,
n.trees = 3000,
interaction.depth = 2,
stop.method = c("es.mean"),
estimand = "ATT",
verbose = FALSE)

```

```{r}
plot(ps.toy)
```

```{r}
summary(ps.toy)
```

```{r}
plot(ps.toy, plots = 2)
```

```{r}
plot(ps.toy, plots = 3)
```

```{r}
bal.tab(ps.toy, full.stop.method = "es.mean.att")
```

```{r}
p <- love.plot(bal.tab(ps.toy),
threshold = .1, size = 1.5,
title = "Standardized Differences and TWANG ATT Weighting")
p + theme_bw()
```

Compared to the manual ATT/ATE weights, the standardized differences look a bit worse here.

## Estimated effect on outcomes after TWANG ATT weighting

### Quantitative outcome

```{r}
toywt3.design <- svydesign(ids=~1,
weights=~get.weights(ps.toy,
stop.method = "es.mean"),
data=lindner_clean) # using twang ATT weights

adjout1.wt3 <- svyglm(cardbill ~ treated, design=toywt3.design)
wt_twangatt_results1 <- tidy(adjout1.wt3, conf.int = TRUE) %>% filter(term == "treated")
wt_twangatt_results1
```

- **Estimate** `r round(wt_twangatt_results1$estimate,2)` (95% CI: `r round(wt_twangatt_results1$conf.low,2)`, `r round(wt_twangatt_results1$conf.high,2)`)

### Binary outcome

```{r}
adjout2.wt3 <- svyglm(sixMonthSurvive ~ treated, design=toywt3.design,
family=quasibinomial())

wt_twangatt_results2 <- tidy(adjout2.wt3, conf.int = TRUE, exponentiate = TRUE) %>%
filter(term == "treated")
wt_twangatt_results2
```

- **Estimate** `r round(wt_twangatt_results2$estimate,2)` (95% CI: `r round(wt_twangatt_results2$conf.low,2)`, `r round(wt_twangatt_results2$conf.high,2)`)

# Task 11: After direct adjustment with linear PS

Here we'll directly adjust for the linear propensity score by including it as a covariate in the model.

## Quantitative outcome

```{r}
direct_out1 <- lm(cardbill ~ treated + linps, data=lindner_clean)

adj_out1 <- tidy(direct_out1, conf.int = TRUE) %>% filter(term == "treated")
adj_out1
```

- **Estimate** `r round(adj_out1$estimate,2)` (95% CI:`r round(adj_out1$conf.low,2)`, `r round(adj_out1$conf.high,2)`)

## Binary outcome

```{r}
direct_out2 <- glm(sixMonthSurvive ~ treated + linps, data=lindner_clean, family=binomial())

adj_out2 <- tidy(direct_out2, exponentiate = TRUE, conf.int = TRUE) %>%
filter(term == "treated")
adj_out2
```

- **Estimate** `r round(adj_out2$estimate,2)` (95% CI: `r round(adj_out2$conf.low,2)`, `r round(adj_out2$conf.high,2)`)

# Task 12: "Double Robust" Approach: Weighting + Direct Adjustment

Here we'll adjust for the linear propensity score and the ATT/ATE/TWANG weights when predicting the quantitative outcome.

## Quantitative outcome

### ATT weights

```{r}
design_att <- svydesign(ids=~1, weights=~wts1, data=lindner_clean) # using ATT weights

dr.out1.wt1 <- svyglm(cardbill ~ treated + linps, design=design_att)
dr_att_out1 <- tidy(dr.out1.wt1, conf.int = TRUE) %>% filter(term == "treated")
dr_att_out1
```

- **Estimate** `r round(dr_att_out1$estimate,2)` (95% CI: `r round(dr_att_out1$conf.low,2)`, `r round(dr_att_out1$conf.high,2)`)

### ATE weights

```{r}
design_ate<- svydesign(ids=~1, weights=~wts2, data=lindner_clean) # using ATE weights

dr.out1.wt2 <- svyglm(cardbill ~ treated + linps, design=design_ate)
dr_ate_out1 <- tidy(dr.out1.wt2, conf.int = TRUE) %>% filter(term == "treated")
dr_ate_out1
```

- **Estimate** `r round(dr_ate_out1$estimate,2)` (95% CI: `r round(dr_ate_out1$conf.low,2)`, `r round(dr_ate_out1$conf.high,2)`)

### TWANG ATT weights

```{r}
wts3 <- get.weights(ps.toy, stop.method = "es.mean")
twang.design <- svydesign(ids=~1, weights=~wts3, data=lindner_clean) # twang ATT weights

dr.out1.wt3 <- svyglm(cardbill ~ treated + linps, design=twang.design)
dr_twangatt_out1 <- tidy(dr.out1.wt3, conf.int = TRUE) %>% filter(term == "treated")
dr_twangatt_out1
```

- **Estimate** `r round(dr_twangatt_out1$estimate,2)` (95% CI: `r round(dr_twangatt_out1$conf.low,2)`, `r round(dr_twangatt_out1$conf.high,2)`)

## Binary outcome

Now we'll adjust for the linear propensity score and the ATT/ATE/TWANG weights when predicting the binary outcome.

### ATT weights

```{r}
dr.out2.wt1 <- svyglm(sixMonthSurvive ~ treated + linps, design=design_att,
family=quasibinomial())

dr_att_out2 <- tidy(dr.out2.wt1, exponentiate = TRUE, conf.int = TRUE) %>%
filter(term == "treated")
dr_att_out2
```

- **Estimate** `r round(dr_att_out2$estimate,2)` (95% CI: `r round(dr_att_out2$conf.low,2)`, `r round(dr_att_out2$conf.high,2)`)

### ATE weights

```{r}
dr.out2.wt2 <- svyglm(sixMonthSurvive ~ treated + linps, design=design_ate,
family=quasibinomial())

dr_ate_out2 <- tidy(dr.out2.wt2, exponentiate = TRUE, conf.int = TRUE) %>%
  filter(term == "treated")

dr_ate_out2
```

- **Estimate** `r round(dr_ate_out2$estimate,2)` (95% CI: `r round(dr_ate_out2$conf.low,2)`, `r round(dr_ate_out2$conf.high,2)`)

### TWANG ATT weights

```{r}
dr.out2.wt3 <- svyglm(sixMonthSurvive ~ treated + linps, design=twang.design,
family=quasibinomial())

dr_twangatt_out2 <- tidy(dr.out2.wt3, exponentiate = TRUE, conf.int = TRUE) %>%
filter(term == "treated")
dr_twangatt_out2
```

- **Estimate** `r round(dr_twangatt_out2$estimate,2)` (95% CI: `r round(dr_twangatt_out2$conf.low,2)`, `r round(dr_twangatt_out2$conf.high,2)`)

## Session Information

```{r}
xfun::session_info()
```





The Lindner Example

Wyatt P. Bensken and Harry Persaud

Version: 2021-02-25