Cirrhosis
GS
4/9/2021
library(tidymodels)
library(tidyverse)
library(ggpubr)
library(ggcorrplot)
library(GGally)
library(mice)
library(survival)
library(survminer)
theme_set(theme_bw())
tidymodels_prefer()Cirrhosis
Context Cirrhosis is a late stage of scarring (fibrosis) of the liver caused by many forms of liver diseases and conditions, such as hepatitis and chronic alcoholism. The following data contains the information collected from the Mayo Clinic trial in primary biliary cirrhosis (PBC) of the liver conducted between 1974 and 1984. A description of the clinical background for the trial and the covariates recorded here is in Chapter 0, especially Section 0.2 of Fleming and Harrington, Counting Processes and Survival Analysis, Wiley, 1991. A more extended discussion can be found in Dickson, et al., Hepatology 10:1-7 (1989) and in Markus, et al., N Eng J of Med 320:1709-13 (1989).
A total of 424 PBC patients, referred to Mayo Clinic during that ten-year interval, met eligibility criteria for the randomized placebo-controlled trial of the drug D-penicillamine. The first 312 cases in the dataset participated in the randomized trial and contain largely complete data. The additional 112 cases did not participate in the clinical trial but consented to have basic measurements recorded and to be followed for survival. Six of those cases were lost to follow-up shortly after diagnosis, so the data here are on an additional 106 cases as well as the 312 randomized participants.
Attribute Information 1) ID: unique identifier 2) N_Days: number of days between registration and the earlier of death, transplantation, or study analysis time in July 1986 3) Status: status of the patient C (censored), CL (censored due to liver tx), or D (death) 4) Drug: type of drug D-penicillamine or placebo 5) Age: age in [days] 6) Sex: M (male) or F (female) 7) Ascites: presence of ascites N (No) or Y (Yes) 8) Hepatomegaly: presence of hepatomegaly N (No) or Y (Yes) 9) Spiders: presence of spiders N (No) or Y (Yes) 10) Edema: presence of edema N (no edema and no diuretic therapy for edema), S (edema present without diuretics, or edema resolved by diuretics), or Y (edema despite diuretic therapy) 11) Bilirubin: serum bilirubin in [mg/dl] 12) Cholesterol: serum cholesterol in [mg/dl] 13) Albumin: albumin in [gm/dl] 14) Copper: urine copper in [ug/day] 15) Alk_Phos: alkaline phosphatase in [U/liter] 16) SGOT: SGOT in [U/ml] 17) Triglycerides: triglicerides in [mg/dl] 18) Platelets: platelets per cubic [ml/1000] 19) Prothrombin: prothrombin time in seconds [s] 20) Stage: histologic stage of disease (1, 2, 3, or 4)
cirrhosis <- read_csv('cirrhosis.csv')
glimpse(cirrhosis)Rows: 418
Columns: 20
$ ID <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1~
$ N_Days <dbl> 400, 4500, 1012, 1925, 1504, 2503, 1832, 2466, 2400, 51,~
$ Status <chr> "D", "C", "D", "D", "CL", "D", "C", "D", "D", "D", "D", ~
$ Drug <chr> "D-penicillamine", "D-penicillamine", "D-penicillamine",~
$ Age <dbl> 21464, 20617, 25594, 19994, 13918, 24201, 20284, 19379, ~
$ Sex <chr> "F", "F", "M", "F", "F", "F", "F", "F", "F", "F", "F", "~
$ Ascites <chr> "Y", "N", "N", "N", "N", "N", "N", "N", "N", "Y", "N", "~
$ Hepatomegaly <chr> "Y", "Y", "N", "Y", "Y", "Y", "Y", "N", "N", "N", "Y", "~
$ Spiders <chr> "Y", "Y", "N", "Y", "Y", "N", "N", "N", "Y", "Y", "Y", "~
$ Edema <chr> "Y", "N", "S", "S", "N", "N", "N", "N", "N", "Y", "N", "~
$ Bilirubin <dbl> 14.5, 1.1, 1.4, 1.8, 3.4, 0.8, 1.0, 0.3, 3.2, 12.6, 1.4,~
$ Cholesterol <dbl> 261, 302, 176, 244, 279, 248, 322, 280, 562, 200, 259, 2~
$ Albumin <dbl> 2.60, 4.14, 3.48, 2.54, 3.53, 3.98, 4.09, 4.00, 3.08, 2.~
$ Copper <dbl> 156, 54, 210, 64, 143, 50, 52, 52, 79, 140, 46, 94, 40, ~
$ Alk_Phos <dbl> 1718.0, 7394.8, 516.0, 6121.8, 671.0, 944.0, 824.0, 4651~
$ SGOT <dbl> 137.95, 113.52, 96.10, 60.63, 113.15, 93.00, 60.45, 28.3~
$ Tryglicerides <dbl> 172, 88, 55, 92, 72, 63, 213, 189, 88, 143, 79, 95, 130,~
$ Platelets <dbl> 190, 221, 151, 183, 136, NA, 204, 373, 251, 302, 258, 71~
$ Prothrombin <dbl> 12.2, 10.6, 12.0, 10.3, 10.9, 11.0, 9.7, 11.0, 11.0, 11.~
$ Stage <dbl> 4, 3, 4, 4, 3, 3, 3, 3, 2, 4, 4, 4, 3, 4, 3, 3, 4, 4, 3,~sample_n(cirrhosis, 3)# A tibble: 3 x 20
ID N_Days Status Drug Age Sex Ascites Hepatomegaly Spiders Edema
<dbl> <dbl> <chr> <chr> <dbl> <chr> <chr> <chr> <chr> <chr>
1 380 1725 CL <NA> 12053 F <NA> <NA> <NA> N
2 273 1558 C Placebo 17320 F N N Y N
3 252 1770 C D-penicill~ 25006 F N Y Y N
# ... with 10 more variables: Bilirubin <dbl>, Cholesterol <dbl>,
# Albumin <dbl>, Copper <dbl>, Alk_Phos <dbl>, SGOT <dbl>,
# Tryglicerides <dbl>, Platelets <dbl>, Prothrombin <dbl>, Stage <dbl>summary(cirrhosis) ID N_Days Status Drug
Min. : 1.0 Min. : 41 Length:418 Length:418
1st Qu.:105.2 1st Qu.:1093 Class :character Class :character
Median :209.5 Median :1730 Mode :character Mode :character
Mean :209.5 Mean :1918
3rd Qu.:313.8 3rd Qu.:2614
Max. :418.0 Max. :4795
Age Sex Ascites Hepatomegaly
Min. : 9598 Length:418 Length:418 Length:418
1st Qu.:15644 Class :character Class :character Class :character
Median :18628 Mode :character Mode :character Mode :character
Mean :18533
3rd Qu.:21273
Max. :28650
Spiders Edema Bilirubin Cholesterol
Length:418 Length:418 Min. : 0.300 Min. : 120.0
Class :character Class :character 1st Qu.: 0.800 1st Qu.: 249.5
Mode :character Mode :character Median : 1.400 Median : 309.5
Mean : 3.221 Mean : 369.5
3rd Qu.: 3.400 3rd Qu.: 400.0
Max. :28.000 Max. :1775.0
NA's :134
Albumin Copper Alk_Phos SGOT
Min. :1.960 Min. : 4.00 Min. : 289.0 Min. : 26.35
1st Qu.:3.243 1st Qu.: 41.25 1st Qu.: 871.5 1st Qu.: 80.60
Median :3.530 Median : 73.00 Median : 1259.0 Median :114.70
Mean :3.497 Mean : 97.65 Mean : 1982.7 Mean :122.56
3rd Qu.:3.770 3rd Qu.:123.00 3rd Qu.: 1980.0 3rd Qu.:151.90
Max. :4.640 Max. :588.00 Max. :13862.4 Max. :457.25
NA's :108 NA's :106 NA's :106
Tryglicerides Platelets Prothrombin Stage
Min. : 33.00 Min. : 62.0 Min. : 9.00 Min. :1.000
1st Qu.: 84.25 1st Qu.:188.5 1st Qu.:10.00 1st Qu.:2.000
Median :108.00 Median :251.0 Median :10.60 Median :3.000
Mean :124.70 Mean :257.0 Mean :10.73 Mean :3.024
3rd Qu.:151.00 3rd Qu.:318.0 3rd Qu.:11.10 3rd Qu.:4.000
Max. :598.00 Max. :721.0 Max. :18.00 Max. :4.000
NA's :136 NA's :11 NA's :2 NA's :6 cirrhosis <- cirrhosis %>%
mutate(Age = round(Age/365, 1))
cirrhosis <- cirrhosis %>%
mutate(Stage = as_factor(Stage))We see some NAs
md.pattern(cirrhosis)
ID N_Days Status Age Sex Edema Bilirubin Albumin Prothrombin Stage
276 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1
28 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1
91 1 1 1 1 1 1 1 1 1 1
4 1 1 1 1 1 1 1 1 1 1
7 1 1 1 1 1 1 1 1 1 1
6 1 1 1 1 1 1 1 1 1 0
2 1 1 1 1 1 1 1 1 0 1
0 0 0 0 0 0 0 0 2 6
Platelets Drug Ascites Hepatomegaly Spiders Alk_Phos SGOT Copper
276 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1
28 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 0
91 1 0 0 0 0 0 0 0
4 0 1 1 1 1 1 1 1
7 0 0 0 0 0 0 0 0
6 1 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0 0
11 106 106 106 106 106 106 108
Cholesterol Tryglicerides
276 1 1 0
2 1 0 1
28 0 0 2
2 1 1 1
91 0 0 9
4 1 1 1
7 0 0 10
6 0 0 10
2 0 0 10
134 136 1033# Delete the NAs in variable Drug
cirrhosis <- cirrhosis %>%
filter(!is.na(Drug))
dim(cirrhosis)[1] 312 20# Imputing numerical variables with rf
cirrhosis_mice <- mice(cirrhosis, m = 5, method = "rf")
iter imp variable
1 1 Cholesterol Copper Tryglicerides Platelets
1 2 Cholesterol Copper Tryglicerides Platelets
1 3 Cholesterol Copper Tryglicerides Platelets
1 4 Cholesterol Copper Tryglicerides Platelets
1 5 Cholesterol Copper Tryglicerides Platelets
2 1 Cholesterol Copper Tryglicerides Platelets
2 2 Cholesterol Copper Tryglicerides Platelets
2 3 Cholesterol Copper Tryglicerides Platelets
2 4 Cholesterol Copper Tryglicerides Platelets
2 5 Cholesterol Copper Tryglicerides Platelets
3 1 Cholesterol Copper Tryglicerides Platelets
3 2 Cholesterol Copper Tryglicerides Platelets
3 3 Cholesterol Copper Tryglicerides Platelets
3 4 Cholesterol Copper Tryglicerides Platelets
3 5 Cholesterol Copper Tryglicerides Platelets
4 1 Cholesterol Copper Tryglicerides Platelets
4 2 Cholesterol Copper Tryglicerides Platelets
4 3 Cholesterol Copper Tryglicerides Platelets
4 4 Cholesterol Copper Tryglicerides Platelets
4 5 Cholesterol Copper Tryglicerides Platelets
5 1 Cholesterol Copper Tryglicerides Platelets
5 2 Cholesterol Copper Tryglicerides Platelets
5 3 Cholesterol Copper Tryglicerides Platelets
5 4 Cholesterol Copper Tryglicerides Platelets
5 5 Cholesterol Copper Tryglicerides Plateletscirrhosis_miceClass: mids
Number of multiple imputations: 5
Imputation methods:
ID N_Days Status Drug Age
"" "" "" "" ""
Sex Ascites Hepatomegaly Spiders Edema
"" "" "" "" ""
Bilirubin Cholesterol Albumin Copper Alk_Phos
"" "rf" "" "rf" ""
SGOT Tryglicerides Platelets Prothrombin Stage
"" "rf" "rf" "" ""
PredictorMatrix:
ID N_Days Status Drug Age Sex Ascites Hepatomegaly Spiders Edema
ID 0 1 0 0 1 0 0 0 0 0
N_Days 1 0 0 0 1 0 0 0 0 0
Status 1 1 0 0 1 0 0 0 0 0
Drug 1 1 0 0 1 0 0 0 0 0
Age 1 1 0 0 0 0 0 0 0 0
Sex 1 1 0 0 1 0 0 0 0 0
Bilirubin Cholesterol Albumin Copper Alk_Phos SGOT Tryglicerides
ID 1 1 1 1 1 1 1
N_Days 1 1 1 1 1 1 1
Status 1 1 1 1 1 1 1
Drug 1 1 1 1 1 1 1
Age 1 1 1 1 1 1 1
Sex 1 1 1 1 1 1 1
Platelets Prothrombin Stage
ID 1 1 1
N_Days 1 1 1
Status 1 1 1
Drug 1 1 1
Age 1 1 1
Sex 1 1 1
Number of logged events: 7
it im dep meth out
1 0 0 constant Status
2 0 0 constant Drug
3 0 0 constant Sex
4 0 0 constant Ascites
5 0 0 constant Hepatomegaly
6 0 0 constant Spiderscirrhosis_imp<- complete(cirrhosis_mice, 3)
summary(cirrhosis_imp) ID N_Days Status Drug
Min. : 1.00 Min. : 41 Length:312 Length:312
1st Qu.: 78.75 1st Qu.:1191 Class :character Class :character
Median :156.50 Median :1840 Mode :character Mode :character
Mean :156.50 Mean :2006
3rd Qu.:234.25 3rd Qu.:2697
Max. :312.00 Max. :4556
Age Sex Ascites Hepatomegaly
Min. :26.30 Length:312 Length:312 Length:312
1st Qu.:42.30 Class :character Class :character Class :character
Median :49.85 Mode :character Mode :character Mode :character
Mean :50.05
3rd Qu.:56.73
Max. :78.50
Spiders Edema Bilirubin Cholesterol
Length:312 Length:312 Min. : 0.300 Min. : 120.0
Class :character Class :character 1st Qu.: 0.800 1st Qu.: 248.0
Mode :character Mode :character Median : 1.350 Median : 309.5
Mean : 3.256 Mean : 367.2
3rd Qu.: 3.425 3rd Qu.: 399.2
Max. :28.000 Max. :1775.0
Albumin Copper Alk_Phos SGOT
Min. :1.96 Min. : 4.00 Min. : 289.0 Min. : 26.35
1st Qu.:3.31 1st Qu.: 41.75 1st Qu.: 871.5 1st Qu.: 80.60
Median :3.55 Median : 73.00 Median : 1259.0 Median :114.70
Mean :3.52 Mean : 97.59 Mean : 1982.7 Mean :122.56
3rd Qu.:3.80 3rd Qu.:123.00 3rd Qu.: 1980.0 3rd Qu.:151.90
Max. :4.64 Max. :588.00 Max. :13862.4 Max. :457.25
Tryglicerides Platelets Prothrombin Stage
Min. : 33.0 Min. : 62.0 Min. : 9.00 1: 16
1st Qu.: 85.0 1st Qu.:200.0 1st Qu.:10.00 2: 67
Median :108.0 Median :258.5 Median :10.60 3:120
Mean :124.8 Mean :262.5 Mean :10.73 4:109
3rd Qu.:151.0 3rd Qu.:324.0 3rd Qu.:11.10
Max. :598.0 Max. :563.0 Max. :17.10 cirrhosis_imp %>%
select(-ID) %>%
select(Age, Bilirubin, Cholesterol, Albumin, Copper, Alk_Phos, SGOT, Tryglicerides, Platelets, Prothrombin, Stage, Drug, Sex) %>%
ggpairs(aes(fill = Drug))
cirrhosis_imp %>%
select(is.numeric) %>%
cor() %>%
ggcorrplot(type = "upper",
hc.order = T,
lab = T,
sig.level = .5)
df <- cirrhosis_imp %>%
group_by(Sex, Stage) %>%
summarise(counts = n())
ggplot(df, aes(x = Stage, y = counts)) +
geom_bar(aes(fill = Sex), stat = "identity", position = "dodge") +
geom_text(aes(label = counts, group = Sex), position = position_dodge(0.9), vjust = -.3, size = 3.5) +
scale_fill_manual(values = c("#EEAB5F", "#EE5F93"))
ggplot(cirrhosis_imp, aes(N_Days, Cholesterol, color = Sex)) +
geom_line()
cirrhosis_imp %>%
select(-ID) %>%
select(Age, Bilirubin, Cholesterol, Albumin, Copper, Alk_Phos, SGOT, Tryglicerides, Platelets, Prothrombin, Stage, Drug, Sex) %>%
ggpairs(aes(fill = Drug))
cirrhosis_imp %>%
select(is.numeric) %>%
cor() %>%
ggcorrplot(type = "upper",
hc.order = T,
lab = T,
sig.level = .5)
df <- cirrhosis_imp %>%
group_by(Sex, Stage) %>%
summarise(counts = n())
ggplot(df, aes(x = Stage, y = counts)) +
geom_bar(aes(fill = Sex), stat = "identity", position = "dodge") +
geom_text(aes(label = counts, group = Sex), position = position_dodge(0.9), vjust = -.3, size = 3.5) +
scale_fill_manual(values = c("#EEAB5F", "#EE5F93"))
ggplot(cirrhosis_imp, aes(N_Days, Cholesterol, color = Sex)) +
geom_line()
cirrhosis_imp %>%
count(Status) Status n
1 C 168
2 CL 19
3 D 125cirrhosis_surv <- cirrhosis_imp %>%
mutate(Status = if_else(Status == "D", 1, 0))
surv_obj <- Surv(cirrhosis_surv$N_Days, cirrhosis_surv$Status)
fit_mono <- survfit(surv_obj ~ 1, data = cirrhosis_surv)
fit_monoCall: survfit(formula = surv_obj ~ 1, data = cirrhosis_surv)
n events median 0.95LCL 0.95UCL
312 125 3395 3086 3853 ggsurvplot(fit_mono, color = "#2E9FDF")
fit_comp_drug <- survfit(surv_obj ~ Drug, data = cirrhosis_surv)
fit_comp_drugCall: survfit(formula = surv_obj ~ Drug, data = cirrhosis_surv)
n events median 0.95LCL 0.95UCL
Drug=D-penicillamine 158 65 3282 2583 NA
Drug=Placebo 154 60 3428 3090 NAggsurvplot(fit_comp_drug,
conf.int = T,
pval = T,
risk.table = T,
surv.median.line = "hv",
palette = c("#EE5F93", "#2E9FDF"))
survdiff(surv_obj ~ Drug, data = cirrhosis_surv)Call:
survdiff(formula = surv_obj ~ Drug, data = cirrhosis_surv)
N Observed Expected (O-E)^2/E (O-E)^2/V
Drug=D-penicillamine 158 65 63.2 0.0502 0.102
Drug=Placebo 154 60 61.8 0.0513 0.102
Chisq= 0.1 on 1 degrees of freedom, p= 0.7 coxph(surv_obj ~ ., data = cirrhosis_surv) Call:
coxph(formula = surv_obj ~ ., data = cirrhosis_surv)
coef exp(coef) se(coef) z p
ID 2.856e-03 1.003e+00 3.656e-03 0.781 0.4346
N_Days -3.321e-01 7.174e-01 7.220e-02 -4.599 4.24e-06
Status 1.073e+01 4.562e+04 1.703e+01 0.630 0.5286
DrugPlacebo 5.334e-01 1.705e+00 6.491e-01 0.822 0.4113
Age -4.843e-02 9.527e-01 3.611e-02 -1.341 0.1799
SexM 3.133e-01 1.368e+00 8.565e-01 0.366 0.7145
AscitesY 1.611e-03 1.002e+00 7.432e-01 0.002 0.9983
HepatomegalyY 5.921e-01 1.808e+00 8.087e-01 0.732 0.4640
SpidersY 2.999e-01 1.350e+00 6.013e-01 0.499 0.6180
EdemaS -2.054e+00 1.282e-01 8.945e-01 -2.296 0.0217
EdemaY 5.863e-01 1.797e+00 8.248e-01 0.711 0.4772
Bilirubin -2.604e-02 9.743e-01 5.660e-02 -0.460 0.6455
Cholesterol -6.373e-04 9.994e-01 1.277e-03 -0.499 0.6176
Albumin 6.676e-01 1.949e+00 7.314e-01 0.913 0.3614
Copper 3.523e-04 1.000e+00 2.441e-03 0.144 0.8852
Alk_Phos -2.209e-04 9.998e-01 2.076e-04 -1.064 0.2874
SGOT 9.046e-04 1.001e+00 5.622e-03 0.161 0.8722
Tryglicerides 5.399e-04 1.001e+00 2.784e-03 0.194 0.8462
Platelets -2.752e-04 9.997e-01 3.860e-03 -0.071 0.9432
Prothrombin 2.501e-01 1.284e+00 3.804e-01 0.657 0.5110
Stage2 -5.204e+00 5.492e-03 1.208e+00 -4.310 1.63e-05
Stage3 -6.071e+00 2.309e-03 7.218e-01 -8.411 < 2e-16
Stage4 -5.897e+00 2.747e-03 6.285e-01 -9.382 < 2e-16
Likelihood ratio test=1266 on 23 df, p=< 2.2e-16
n= 312, number of events= 125 cox_model <- coxph(surv_obj ~ Drug + Stage + Edema, data = cirrhosis_surv)
summary(cox_model)Call:
coxph(formula = surv_obj ~ Drug + Stage + Edema, data = cirrhosis_surv)
n= 312, number of events= 125
coef exp(coef) se(coef) z Pr(>|z|)
DrugPlacebo -0.1393 0.8700 0.1833 -0.760 0.44732
Stage2 1.6081 4.9935 1.0317 1.559 0.11906
Stage3 2.0246 7.5734 1.0143 1.996 0.04592 *
Stage4 2.8305 16.9531 1.0126 2.795 0.00519 **
EdemaS 0.6093 1.8392 0.2710 2.248 0.02455 *
EdemaY 2.0281 7.5996 0.2707 7.492 6.78e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
DrugPlacebo 0.870 1.14942 0.6075 1.246
Stage2 4.993 0.20026 0.6610 37.721
Stage3 7.573 0.13204 1.0374 55.288
Stage4 16.953 0.05899 2.3299 123.359
EdemaS 1.839 0.54371 1.0813 3.128
EdemaY 7.600 0.13159 4.4707 12.918
Concordance= 0.755 (se = 0.022 )
Likelihood ratio test= 94.65 on 6 df, p=<2e-16
Wald test = 108.3 on 6 df, p=<2e-16
Score (logrank) test = 161.8 on 6 df, p=<2e-16fit_comp_sex <- survfit(surv_obj ~ Sex, data = cirrhosis_surv)
fit_comp_sexCall: survfit(formula = surv_obj ~ Sex, data = cirrhosis_surv)
n events median 0.95LCL 0.95UCL
Sex=F 276 103 3428 3170 NA
Sex=M 36 22 2386 1297 NAggsurvplot(fit_comp_sex,
conf.int = T,
pval = T,
risk.table = T,
surv.median.line = "hv",
palette = c("#EE5F93", "#2E9FDF"))
survdiff(surv_obj ~ Sex, data = cirrhosis_surv)Call:
survdiff(formula = surv_obj ~ Sex, data = cirrhosis_surv)
N Observed Expected (O-E)^2/E (O-E)^2/V
Sex=F 276 103 110.4 0.494 4.27
Sex=M 36 22 14.6 3.728 4.27
Chisq= 4.3 on 1 degrees of freedom, p= 0.04 coxph(surv_obj ~ ., data = cirrhosis_surv) Call:
coxph(formula = surv_obj ~ ., data = cirrhosis_surv)
coef exp(coef) se(coef) z p
ID 2.856e-03 1.003e+00 3.656e-03 0.781 0.4346
N_Days -3.321e-01 7.174e-01 7.220e-02 -4.599 4.24e-06
Status 1.073e+01 4.562e+04 1.703e+01 0.630 0.5286
DrugPlacebo 5.334e-01 1.705e+00 6.491e-01 0.822 0.4113
Age -4.843e-02 9.527e-01 3.611e-02 -1.341 0.1799
SexM 3.133e-01 1.368e+00 8.565e-01 0.366 0.7145
AscitesY 1.611e-03 1.002e+00 7.432e-01 0.002 0.9983
HepatomegalyY 5.921e-01 1.808e+00 8.087e-01 0.732 0.4640
SpidersY 2.999e-01 1.350e+00 6.013e-01 0.499 0.6180
EdemaS -2.054e+00 1.282e-01 8.945e-01 -2.296 0.0217
EdemaY 5.863e-01 1.797e+00 8.248e-01 0.711 0.4772
Bilirubin -2.604e-02 9.743e-01 5.660e-02 -0.460 0.6455
Cholesterol -6.373e-04 9.994e-01 1.277e-03 -0.499 0.6176
Albumin 6.676e-01 1.949e+00 7.314e-01 0.913 0.3614
Copper 3.523e-04 1.000e+00 2.441e-03 0.144 0.8852
Alk_Phos -2.209e-04 9.998e-01 2.076e-04 -1.064 0.2874
SGOT 9.046e-04 1.001e+00 5.622e-03 0.161 0.8722
Tryglicerides 5.399e-04 1.001e+00 2.784e-03 0.194 0.8462
Platelets -2.752e-04 9.997e-01 3.860e-03 -0.071 0.9432
Prothrombin 2.501e-01 1.284e+00 3.804e-01 0.657 0.5110
Stage2 -5.204e+00 5.492e-03 1.208e+00 -4.310 1.63e-05
Stage3 -6.071e+00 2.309e-03 7.218e-01 -8.411 < 2e-16
Stage4 -5.897e+00 2.747e-03 6.285e-01 -9.382 < 2e-16
Likelihood ratio test=1266 on 23 df, p=< 2.2e-16
n= 312, number of events= 125 cox_model <- coxph(surv_obj ~ Drug + Stage + Edema, data = cirrhosis_surv)
summary(cox_model)Call:
coxph(formula = surv_obj ~ Drug + Stage + Edema, data = cirrhosis_surv)
n= 312, number of events= 125
coef exp(coef) se(coef) z Pr(>|z|)
DrugPlacebo -0.1393 0.8700 0.1833 -0.760 0.44732
Stage2 1.6081 4.9935 1.0317 1.559 0.11906
Stage3 2.0246 7.5734 1.0143 1.996 0.04592 *
Stage4 2.8305 16.9531 1.0126 2.795 0.00519 **
EdemaS 0.6093 1.8392 0.2710 2.248 0.02455 *
EdemaY 2.0281 7.5996 0.2707 7.492 6.78e-14 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
exp(coef) exp(-coef) lower .95 upper .95
DrugPlacebo 0.870 1.14942 0.6075 1.246
Stage2 4.993 0.20026 0.6610 37.721
Stage3 7.573 0.13204 1.0374 55.288
Stage4 16.953 0.05899 2.3299 123.359
EdemaS 1.839 0.54371 1.0813 3.128
EdemaY 7.600 0.13159 4.4707 12.918
Concordance= 0.755 (se = 0.022 )
Likelihood ratio test= 94.65 on 6 df, p=<2e-16
Wald test = 108.3 on 6 df, p=<2e-16
Score (logrank) test = 161.8 on 6 df, p=<2e-16ggboxplot(cirrhosis_surv, x= "Sex", y = "Cholesterol", color = "Sex") +
stat_compare_means() 
ggplot(cirrhosis_surv, aes(Sex, Cholesterol, color = Sex)) +
geom_boxplot() +
theme(legend.position = "none") +
stat_compare_means(aes(label = ..p.signif..), label.y = 1500, label.x = 1.5)