Healthcare Cost Analysis

Background and Objective:

A nationwide survey of hospital costs conducted by the US Agency for Healthcare consists of hospital records of inpatient samples. The given data is restricted to the city of Wisconsin and relates to patients in the age group 0-17 years. The agency wants to analyze the data to research on healthcare costs and their utilization.

Import dataset

setwd("C:/Learning/Data Analytics/Datasicence with R/Project/Healthcare - cost analysis")
HospitalCosts=read.csv("hospital_costs.csv", header=TRUE)
head(HospitalCosts)

names(HospitalCosts)

[1] "ï..AGE" "FEMALE" "LOS"    "RACE"   "TOTCHG" "APRDRG"

names(HospitalCosts)[1] = "AGE"

names(HospitalCosts)

[1] "AGE"    "FEMALE" "LOS"    "RACE"   "TOTCHG" "APRDRG"

1. Record patient statistics:

The agency wants to find the age category of people who frequently visit the hospital and has the maximum expenditure.

• Age: Age of the patient discharged
• Totchg: Hospital discharge costs

summary(HospitalCosts)

      AGE           FEMALE          LOS          RACE         TOTCHG          APRDRG   
 Min.   : 0.0   Min.   :0.00   Min.   : 0   Min.   :1.0   Min.   :  532   Min.   : 21  
 1st Qu.: 0.0   1st Qu.:0.00   1st Qu.: 2   1st Qu.:1.0   1st Qu.: 1216   1st Qu.:640  
 Median : 0.0   Median :1.00   Median : 2   Median :1.0   Median : 1536   Median :640  
 Mean   : 5.1   Mean   :0.51   Mean   : 3   Mean   :1.1   Mean   : 2774   Mean   :616  
 3rd Qu.:13.0   3rd Qu.:1.00   3rd Qu.: 3   3rd Qu.:1.0   3rd Qu.: 2530   3rd Qu.:751  
 Max.   :17.0   Max.   :1.00   Max.   :41   Max.   :6.0   Max.   :48388   Max.   :952  
                                            NA's   :1                                  

Get number of hospital visits based on age

summary(as.factor(HospitalCosts$AGE))

  0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17 
307  10   1   3   2   2   2   3   2   2   4   8  15  18  25  29  29  38 

• Total number of hospital for 0-1 age group is 307

hist(HospitalCosts$AGE, main="Histogram of Age Group and their hospital visits",
     xlab="Age group", border="black", col=c("light green", "dark green"), xlim=c(0,20), ylim=c(0,350))

• As can be seen here, the maximum number of hospital visits are for age group is 0-1 years

Summarize expenditure based on age group

ExpenseBasedOnAge = aggregate(TOTCHG ~ AGE, FUN=sum, data=HospitalCosts)

Get the maximum expense and its age group

which.max(tapply(ExpenseBasedOnAge$TOTCHG, ExpenseBasedOnAge$TOTCHG, FUN=sum))

678118 
    18 

barplot(tapply(ExpenseBasedOnAge$TOTCHG, ExpenseBasedOnAge$AGE, FUN=sum))

• Maximum expenditure for 0-1 yr is 678118

2. Diagnosis-related group that has maximum hospitalization and expenditure

In order of severity of the diagnosis and treatments and to find out the expensive treatments, the agency wants to find the diagnosis-related group that has maximum hospitalization and expenditure.

• Aprdrg: All Patient Refined Diagnosis Related Groups
• Totchg: Hospital discharge costs

summary(as.factor(HospitalCosts$APRDRG))

 21  23  49  50  51  53  54  57  58  92  97 114 115 137 138 139 141 143 204 206 225 249 254 308 313 317 
  1   1   1   1   1  10   1   2   1   1   1   1   2   1   4   5   1   1   1   1   2   6   1   1   1   1 
344 347 420 421 422 560 561 566 580 581 602 614 626 633 634 636 639 640 710 720 723 740 750 751 753 754 
  2   3   2   1   3   2   1   1   1   3   1   3   6   4   2   3   4 267   1   1   2   1   1  14  36  37 
755 756 758 760 776 811 812 863 911 930 952 
 13   2  20   2   1   2   3   1   1   2   1 

Get the diagnosis-related group and its hospitalization expenditure

DiagnosisCost = aggregate(TOTCHG ~ APRDRG, FUN = sum, data = HospitalCosts)

Get the max diagnostic cost

DiagnosisCost[which.max(DiagnosisCost$TOTCHG), ]

• As can be seen here 640 diagnosis related group had a max cost of 437978

3. Race vs Hospitalization costs

To make sure that there is no malpractice, the agency needs to analyze if the race of the patient is related to the hospitalization costs.

#Ho (Null hypothesis):Independent variable (RACE) is not influencing dependent variable (COSTS) #H0:there is no no correlation among residuals, # p-value = 0.7394 <== this is > 0.5 #i.e. they are independent #in case of regression, we need high p value so that we cannot reject the null

summary(as.factor(HospitalCosts$RACE))

   1    2    3    4    5    6 NA's 
 484    6    1    3    3    2    1 

• There is one null value. This needs to be removed

HospitalCosts = na.omit(HospitalCosts)
summary(as.factor(HospitalCosts$RACE))

  1   2   3   4   5   6 
484   6   1   3   3   2 

• As can be seen 484 patients out of 499 fall under group 1, showing that the number of observations for 1 category is way higher than others - hence data is skewed. This will only affect the results from linear regression or ANOVA analysis

raceInfluence=lm(TOTCHG~ RACE, data=HospitalCosts)
summary(raceInfluence)

Call:
lm(formula = TOTCHG ~ RACE, data = HospitalCosts)

Residuals:
   Min     1Q Median     3Q    Max 
 -2256  -1560  -1227   -258  45600 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)     2926        405    7.22  1.9e-12 ***
RACE            -137        339   -0.41     0.69    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3890 on 497 degrees of freedom
Multiple R-squared:  0.00033,   Adjusted R-squared:  -0.00168 
F-statistic: 0.164 on 1 and 497 DF,  p-value: 0.686

• pValue is 0.69 it is much higher than 0.5
• We can say that race doesn’t affect the hospitalization costs

Anaysis using ANOVA

We can also use anova statistical test for estimating how dependent variable, in this case RACE, affects the independent variable, the hospitalization cost

raceInfluenceAOV <- aov(TOTCHG ~ RACE, data=HospitalCosts)
raceInfluenceAOV

summary(raceInfluenceAOV)

             Df   Sum Sq  Mean Sq F value Pr(>F)
RACE          1 2.49e+06  2488459    0.16   0.69
Residuals   497 7.54e+09 15170268               

• The residual variance (deviation from original) (of all other variables) is very high. This implies that there is very little influence from RACE on hospitalization costs
• As can be seen, the degree of freedom (Df) for RACE is 1 and that of residuals is 497 observations
• The F-Value, the test statistic is 0.16 which is much less than 0.5 showing that RACE doesn’t affect teh hospitalization cost.
• The Pr(>F), the p_value of 0.69 is high confirming that RACE does not affect hospitalization cost.

4. To properly utilize the costs, the agency has to analyze the severity of the hospital costs by age and gender for the proper allocation of resources.

summary(HospitalCosts$FEMALE)

  0   1 
244 255 

• As can be seen here, there is equal distribution of male and female in the group

summary(ageGenderInflModel)

Call:
lm(formula = TOTCHG ~ AGE + FEMALE, data = HospitalCosts)

Residuals:
   Min     1Q Median     3Q    Max 
 -3403  -1444   -873   -156  44950 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   2719.4      261.4   10.40  < 2e-16 ***
AGE             86.0       25.5    3.37  0.00081 ***
FEMALE1       -744.2      354.7   -2.10  0.03638 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3850 on 496 degrees of freedom
Multiple R-squared:  0.0259,    Adjusted R-squared:  0.0219 
F-statistic: 6.58 on 2 and 496 DF,  p-value: 0.00151

• Since the pValues of AGE is much lesser than 0.05, the ideal statistical significance level, and it also has three stars (***) next to it, it means AGE has the most statitical significance
• Similarly, gender is also less than 0.05.
• Hence, we can conclude that the model is statistically significant

5. Since the length of stay is the crucial factor for inpatients, the agency wants to find if the length of stay can be predicted from age, gender, and race.

summary(ageGenderRaceInflModel)

Call:
lm(formula = LOS ~ AGE + FEMALE + RACE, data = HospitalCostsNA)

Residuals:
   Min     1Q Median     3Q    Max 
 -3.21  -1.21  -0.86   0.14  37.79 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   2.8569     0.2316   12.34   <2e-16 ***
AGE          -0.0394     0.0226   -1.74    0.082 .  
FEMALE        0.3539     0.3129    1.13    0.259    
RACE2        -0.3750     1.3957   -0.27    0.788    
RACE3         0.7892     3.3858    0.23    0.816    
RACE4         0.5949     1.9572    0.30    0.761    
RACE5        -0.8569     1.9627   -0.44    0.663    
RACE6        -0.7188     2.3929   -0.30    0.764    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.4 on 491 degrees of freedom
Multiple R-squared:  0.0087,    Adjusted R-squared:  -0.00543 
F-statistic: 0.616 on 7 and 491 DF,  p-value: 0.743

• The p-value is higher than 0.05 for age, gender and race, indicating there is no linear relationship between these variables and length of stay.
• Hence, age, gender and race cannot be used to predict the length of stay of inpatients.

6. Complete analysis

The agency wants to find the variable that mainly affects hospital costs.

Significance method - build a model using all independent variables vs dependent variable

summary(hospitalCostModel)

Call:
lm(formula = TOTCHG ~ ., data = HospitalCosts)

Residuals:
   Min     1Q Median     3Q    Max 
 -6377   -700   -174    122  43378 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 5218.677    507.647   10.28   <2e-16 ***
AGE          134.695     17.471    7.71    7e-14 ***
FEMALE1     -390.692    247.739   -1.58     0.12    
LOS          743.152     34.923   21.28   <2e-16 ***
RACE        -212.429    227.933   -0.93     0.35    
APRDRG        -7.791      0.682  -11.43   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2610 on 493 degrees of freedom
Multiple R-squared:  0.554, Adjusted R-squared:  0.549 
F-statistic:  122 on 5 and 493 DF,  p-value: <2e-16

• As it is apparent from the coefficient values, Age, Length of stay (LOS) and patient refined diagnosis related groups(APRDRG) have three stars (***) next to it. So they are the ones with statistical significance
• Also, RACE is the least significant. build a model after removing RACE

summary(hcm1)

Call:
lm(formula = TOTCHG ~ AGE + FEMALE + LOS + APRDRG, data = HospitalCostsNA)

Residuals:
   Min     1Q Median     3Q    Max 
 -6344   -687   -168    132  43387 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 4971.980    433.116   11.48  < 2e-16 ***
AGE          134.241     17.462    7.69  8.2e-14 ***
FEMALE      -383.082    247.571   -1.55     0.12    
LOS          743.618     34.914   21.30  < 2e-16 ***
APRDRG        -7.767      0.681  -11.40  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2610 on 494 degrees of freedom
Multiple R-squared:  0.553, Adjusted R-squared:  0.549 
F-statistic:  153 on 4 and 494 DF,  p-value: <2e-16

summary(hcm2)

Call:
lm(formula = TOTCHG ~ AGE + LOS + APRDRG, data = HospitalCostsNA)

Residuals:
   Min     1Q Median     3Q    Max 
 -6603   -719   -169    124  43350 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 4960.170    433.658   11.44  < 2e-16 ***
AGE          128.552     17.095    7.52  2.6e-13 ***
LOS          740.806     34.916   21.22  < 2e-16 ***
APRDRG        -8.006      0.664  -12.05  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2620 on 495 degrees of freedom
Multiple R-squared:  0.551, Adjusted R-squared:  0.548 
F-statistic:  202 on 3 and 495 DF,  p-value: <2e-16

• Since APRDRG has -ve t-value, dropping it.

summary(hcm3)

Call:
lm(formula = TOTCHG ~ AGE + LOS, data = HospitalCostsNA)

Residuals:
   Min     1Q Median     3Q    Max 
 -4783  -1103   -458   -133  41382 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    200.7      203.5    0.99     0.32    
AGE             98.0       19.2    5.10  4.8e-07 ***
LOS            734.3       39.7   18.51  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2970 on 496 degrees of freedom
Multiple R-squared:  0.419, Adjusted R-squared:  0.416 
F-statistic:  179 on 2 and 496 DF,  p-value: <2e-16

Comparing Models

Data	Approach	Model Name	Detail	R2	adj R2	std err	R2 - adj R2	p-value
HospitalCosts	Ap1:significance	hospitalCostModel	signifi, all independent variables	0.554	0.549	2610	0.005	<2e-16
HospitalCosts	Ap1:significance	hcm1	-RACE	0.553	0.549	2610	0.004	<2e-16
HospitalCosts	Ap1:significance	hcm2	-RACE - FEMALE (gender)	0.551	0.548	2620	0.003	<2e-16
HospitalCosts	Ap1:significance	hcm3	AGE + LOS	0.419	0.416	2970	0.003	<2e-16

• Removing Race and gender doesn’t change the R2 value. It doesn’t impact cost
• Removing APRDRG in model hcm3 increases the standard error. Hence model hcm2 seems to be better.

Analysis Conclusion:

• As is evident in the multiple models above, health care costs is dependent on age, length of stay and the diagnosis type.

1. Healthcare cost is the most for patients in the 0-1 yrs age group category

1. Maximum expenditure for 0-1 yr is 678118

2. Length of Stay increases the hospital cost

3. All Patient Refined Diagnosis Related Groups also affects healthcare costs

1. 640 diagnosis related group had a max cost of 437978

4. Race or gender doesn’t have that much impact on hospital cost