Propensity Score Matching of Insurance Data
John Akwei, Data Science Specialist
Friday, September 04, 2015
Synopsis
The document performs Propensity Score Matching, in order to find balance between treatment and control groups within a sample of insurance data.
Required R language packages for Matched Sampling:
# install.packages("MatchIt")
# install.packages("Matching")
library(MatchIt)
library(Matching)
library(data.table)
require(MatchIt)
require(Matching)Import of Insurance Data, and data summary:
dt <- read.csv("Aim1.csv")
dt[1:5,]## ID birth_year chronic_meds poverty_ratio sample_type sample_weight_1
## 1 11 1982 0 198 1 218371
## 2 16 1982 0 120 1 99849
## 3 18 1982 0 0 1 96678
## 4 21 1982 0 0 1 99849
## 5 28 1983 0 82 1 110561
## mother_education daily_cigs daily_alcohol weekly_exercise
## 1 14 20 3 7
## 2 11 0 0 3
## 3 15 0 0 3
## 4 13 30 2 2
## 5 12 0 0 0
## sample_weight_15 insurance_11 routine_checkup years_insured insurance
## 1 354954 1 0 7 1
## 2 175920 0 1 7 1
## 3 0 0 0 5 0
## 4 175920 1 0 5 0
## 5 157334 1 1 8 1
## female disability NE_So_region great_health mother_college HS_grad
## 1 1 0 1 1 1 1
## 2 0 0 1 0 0 1
## 3 0 0 1 0 1 0
## 4 0 0 1 0 1 0
## 5 1 0 1 1 0 1
## low_income age_97 age_11 race_white daily_fruit daily_veg high_exercise
## 1 1 15 29 0 0 0 1
## 2 1 15 29 0 0 0 1
## 3 1 15 29 0 0 1 1
## 4 1 15 29 0 0 0 0
## 5 1 14 28 0 0 0 0
## smoker low_risk_alcohol BMI_97 BMI_11 overweight_97 obese_97
## 1 1 0 20.59570 30.20703 0 0
## 2 0 1 20.08571 21.83876 0 0
## 3 0 1 19.73223 20.52444 0 0
## 4 1 1 20.35865 25.10216 0 0
## 5 0 1 20.78205 29.53161 0 0
## overweight_11 obese_11
## 1 0 1
## 2 0 0
## 3 0 0
## 4 1 0
## 5 1 0Insurance Data variables:
names(dt)## [1] "ID" "birth_year" "chronic_meds"
## [4] "poverty_ratio" "sample_type" "sample_weight_1"
## [7] "mother_education" "daily_cigs" "daily_alcohol"
## [10] "weekly_exercise" "sample_weight_15" "insurance_11"
## [13] "routine_checkup" "years_insured" "insurance"
## [16] "female" "disability" "NE_So_region"
## [19] "great_health" "mother_college" "HS_grad"
## [22] "low_income" "age_97" "age_11"
## [25] "race_white" "daily_fruit" "daily_veg"
## [28] "high_exercise" "smoker" "low_risk_alcohol"
## [31] "BMI_97" "BMI_11" "overweight_97"
## [34] "obese_97" "overweight_11" "obese_11"attach(dt)Propensity Score Matching of Insurance Data, (Treatment & Control Groups):
dt2 <- cbind(dt[15:22], dt[25:30])
m.out <- matchit(insurance ~ great_health + mother_college + HS_grad + low_income + disability + female + NE_So_region + high_exercise + smoker + race_white + daily_veg + daily_fruit + low_risk_alcohol, data=dt2, method="subclass")
# , ratio=1
summary(m.out)##
## Call:
## matchit(formula = insurance ~ great_health + mother_college +
## HS_grad + low_income + disability + female + NE_So_region +
## high_exercise + smoker + race_white + daily_veg + daily_fruit +
## low_risk_alcohol, data = dt2, method = "subclass", sub.by = "treat")
## Summary of balance for all data:
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.5779 0.4370 0.1409 0.1578 0.1407
## great_health 0.7912 0.7333 0.0579 0.0000 0.0573
## mother_college 0.5474 0.3718 0.1757 0.0000 0.1753
## HS_grad 0.8347 0.6323 0.2023 0.0000 0.2019
## low_income 0.3715 0.6330 -0.2615 0.0000 0.2619
## disability 0.1719 0.1869 -0.0150 0.0000 0.0150
## female 0.5876 0.4604 0.1272 0.0000 0.1269
## NE_So_region 0.4848 0.5484 -0.0636 0.0000 0.0641
## high_exercise 0.4789 0.4379 0.0410 0.0000 0.0409
## smoker 0.2958 0.4393 -0.1435 0.0000 0.1439
## race_white 0.6765 0.5164 0.1602 0.0000 0.1596
## daily_veg 0.3630 0.3322 0.0308 0.0000 0.0307
## daily_fruit 0.2424 0.2087 0.0337 0.0000 0.0334
## low_risk_alcohol 0.5105 0.5791 -0.0686 0.0000 0.0689
## eQQ Max
## distance 0.1796
## great_health 1.0000
## mother_college 1.0000
## HS_grad 1.0000
## low_income 1.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 1.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 1.0000
## low_risk_alcohol 1.0000
##
##
## Summary of balance by subclasses:
## , , Subclass 1
##
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.3009 0.2629 0.0380 0.0408 0.0384
## great_health 0.6640 0.6869 -0.0229 0.0000 0.0198
## mother_college 0.1858 0.1981 -0.0123 0.0000 0.0119
## HS_grad 0.4308 0.2875 0.1433 0.0000 0.1423
## low_income 0.9170 0.8962 0.0208 0.0000 0.0237
## disability 0.2411 0.1901 0.0510 0.0000 0.0514
## female 0.4229 0.2827 0.1402 0.0000 0.1423
## NE_So_region 0.5889 0.6166 -0.0277 0.0000 0.0277
## high_exercise 0.4071 0.4169 -0.0098 0.0000 0.0079
## smoker 0.5257 0.6278 -0.1021 0.0000 0.1028
## race_white 0.3478 0.3610 -0.0132 0.0000 0.0119
## daily_veg 0.3281 0.2891 0.0389 0.0000 0.0395
## daily_fruit 0.1858 0.1789 0.0069 0.0000 0.0079
## low_risk_alcohol 0.6403 0.6406 -0.0003 0.0000 0.0000
## eQQ Max
## distance 0.0663
## great_health 1.0000
## mother_college 1.0000
## HS_grad 1.0000
## low_income 1.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 1.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 1.0000
## low_risk_alcohol 0.0000
##
## , , Subclass 2
##
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.4592 0.4510 0.0082 0.0085 0.0084
## great_health 0.7154 0.6959 0.0195 0.0000 0.0198
## mother_college 0.2411 0.2978 -0.0567 0.0000 0.0553
## HS_grad 0.8261 0.8150 0.0110 0.0000 0.0119
## low_income 0.7233 0.7398 -0.0165 0.0000 0.0158
## disability 0.1462 0.2069 -0.0607 0.0000 0.0593
## female 0.5810 0.5204 0.0607 0.0000 0.0632
## NE_So_region 0.5375 0.5611 -0.0236 0.0000 0.0237
## high_exercise 0.3597 0.4389 -0.0792 0.0000 0.0791
## smoker 0.3360 0.3417 -0.0057 0.0000 0.0040
## race_white 0.4704 0.4796 -0.0093 0.0000 0.0079
## daily_veg 0.3439 0.3354 0.0085 0.0000 0.0079
## daily_fruit 0.2134 0.2100 0.0034 0.0000 0.0040
## low_risk_alcohol 0.6126 0.6019 0.0108 0.0000 0.0119
## eQQ Max
## distance 0.0147
## great_health 1.0000
## mother_college 1.0000
## HS_grad 1.0000
## low_income 1.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 1.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 1.0000
## low_risk_alcohol 1.0000
##
## , , Subclass 3
##
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.5537 0.5496 0.0042 0.0039 0.0045
## great_health 0.7945 0.7938 0.0007 0.0000 0.0000
## mother_college 0.6838 0.6134 0.0704 0.0000 0.0670
## HS_grad 0.8577 0.8660 -0.0083 0.0000 0.0103
## low_income 0.3913 0.4639 -0.0726 0.0000 0.0722
## disability 0.1739 0.1134 0.0605 0.0000 0.0567
## female 0.4308 0.5103 -0.0795 0.0000 0.0825
## NE_So_region 0.4783 0.4639 0.0143 0.0000 0.0103
## high_exercise 0.4506 0.4639 -0.0133 0.0000 0.0155
## smoker 0.4071 0.3608 0.0463 0.0000 0.0464
## race_white 0.6680 0.6031 0.0649 0.0000 0.0619
## daily_veg 0.3162 0.3608 -0.0446 0.0000 0.0464
## daily_fruit 0.2095 0.1907 0.0188 0.0000 0.0155
## low_risk_alcohol 0.5099 0.5361 -0.0262 0.0000 0.0258
## eQQ Max
## distance 0.0125
## great_health 0.0000
## mother_college 1.0000
## HS_grad 1.0000
## low_income 1.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 1.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 1.0000
## low_risk_alcohol 1.0000
##
## , , Subclass 4
##
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.6435 0.6400 0.0036 0.0023 0.0035
## great_health 0.7960 0.7791 0.0169 0.0000 0.0123
## mother_college 0.5240 0.5153 0.0087 0.0000 0.0061
## HS_grad 0.9200 0.9509 -0.0309 0.0000 0.0368
## low_income 0.1600 0.2086 -0.0486 0.0000 0.0491
## disability 0.2200 0.2331 -0.0131 0.0000 0.0123
## female 0.6000 0.6810 -0.0810 0.0000 0.0859
## NE_So_region 0.5160 0.4969 0.0191 0.0000 0.0184
## high_exercise 0.5000 0.4110 0.0890 0.0000 0.0859
## smoker 0.2640 0.3067 -0.0427 0.0000 0.0429
## race_white 0.7520 0.7178 0.0342 0.0000 0.0307
## daily_veg 0.3680 0.3804 -0.0124 0.0000 0.0123
## daily_fruit 0.2280 0.2577 -0.0297 0.0000 0.0307
## low_risk_alcohol 0.5480 0.4908 0.0572 0.0000 0.0552
## eQQ Max
## distance 0.0112
## great_health 1.0000
## mother_college 1.0000
## HS_grad 1.0000
## low_income 1.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 1.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 1.0000
## low_risk_alcohol 1.0000
##
## , , Subclass 5
##
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.7106 0.7087 0.0019 0.0014 0.0020
## great_health 0.8789 0.8627 0.0162 0.0000 0.0098
## mother_college 0.8281 0.7451 0.0830 0.0000 0.0784
## HS_grad 0.9727 1.0000 -0.0273 0.0000 0.0294
## low_income 0.0391 0.0686 -0.0296 0.0000 0.0294
## disability 0.1484 0.1961 -0.0476 0.0000 0.0490
## female 0.5781 0.6275 -0.0493 0.0000 0.0490
## NE_So_region 0.4375 0.4804 -0.0429 0.0000 0.0490
## high_exercise 0.5547 0.4902 0.0645 0.0000 0.0588
## smoker 0.2422 0.2157 0.0265 0.0000 0.0294
## race_white 0.8516 0.8529 -0.0014 0.0000 0.0098
## daily_veg 0.3750 0.3922 -0.0172 0.0000 0.0196
## daily_fruit 0.2734 0.2647 0.0087 0.0000 0.0098
## low_risk_alcohol 0.4297 0.4706 -0.0409 0.0000 0.0392
## eQQ Max
## distance 0.0093
## great_health 1.0000
## mother_college 1.0000
## HS_grad 1.0000
## low_income 1.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 1.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 1.0000
## low_risk_alcohol 1.0000
##
## , , Subclass 6
##
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.7989 0.7915 0.0074 0.0075 0.0075
## great_health 0.8972 0.8710 0.0263 0.0000 0.0161
## mother_college 0.8182 0.7581 0.0601 0.0000 0.0484
## HS_grad 1.0000 1.0000 0.0000 0.0000 0.0000
## low_income 0.0000 0.0000 0.0000 0.0000 0.0000
## disability 0.1028 0.1452 -0.0424 0.0000 0.0323
## female 0.9130 0.9355 -0.0224 0.0000 0.0323
## NE_So_region 0.3518 0.3065 0.0453 0.0000 0.0484
## high_exercise 0.6008 0.5484 0.0524 0.0000 0.0484
## smoker 0.0000 0.0000 0.0000 0.0000 0.0000
## race_white 0.9684 0.9194 0.0490 0.0000 0.0484
## daily_veg 0.4466 0.4355 0.0112 0.0000 0.0161
## daily_fruit 0.3439 0.3387 0.0052 0.0000 0.0000
## low_risk_alcohol 0.3241 0.3871 -0.0630 0.0000 0.0645
## eQQ Max
## distance 0.0172
## great_health 1.0000
## mother_college 1.0000
## HS_grad 0.0000
## low_income 0.0000
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 0.0000
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 0.0000
## low_risk_alcohol 1.0000
##
##
## Sample sizes by subclasses:
## Subclass 1 Subclass 2 Subclass 3 Subclass 4 Subclass 5 Subclass 6
## Treated 253 253 253 250 256 253
## Control 626 319 194 163 102 62
## Total 879 572 447 413 358 315
##
## Summary of balance across subclasses
## Means Treated Means Control Mean Diff eQQ Med eQQ Mean
## distance 0.5779 0.5674 0.0067 0.0108 0.0107
## great_health 0.7912 0.7817 0.0077 0.0000 0.0129
## mother_college 0.5474 0.5218 0.0230 0.0000 0.0447
## HS_grad 0.8347 0.8200 0.0250 0.0000 0.0384
## low_income 0.3715 0.3959 0.0160 0.0000 0.0317
## disability 0.1719 0.1807 0.0199 0.0000 0.0436
## female 0.5876 0.5928 0.0329 0.0000 0.0758
## NE_So_region 0.4848 0.4875 0.0127 0.0000 0.0296
## high_exercise 0.4789 0.4617 0.0243 0.0000 0.0492
## smoker 0.2958 0.3086 0.0205 0.0000 0.0376
## race_white 0.6765 0.6559 0.0149 0.0000 0.0284
## daily_veg 0.3630 0.3656 0.0107 0.0000 0.0237
## daily_fruit 0.2424 0.2401 0.0062 0.0000 0.0113
## low_risk_alcohol 0.5105 0.5211 0.0164 0.0000 0.0327
## eQQ Max
## distance 0.0219
## great_health 0.8333
## mother_college 1.0000
## HS_grad 0.8333
## low_income 0.8333
## disability 1.0000
## female 1.0000
## NE_So_region 1.0000
## high_exercise 1.0000
## smoker 0.8333
## race_white 1.0000
## daily_veg 1.0000
## daily_fruit 0.8333
## low_risk_alcohol 0.8333
##
## Percent Balance Improvement:
## Mean Diff. eQQ Med eQQ Mean eQQ Max
## distance 92.5223 93.1869 92.4010 87.8202
## great_health 83.7176 0.0000 77.3994 16.6667
## mother_college 85.3827 0.0000 74.5195 0.0000
## HS_grad 92.7641 0.0000 80.9657 16.6667
## low_income 90.6808 0.0000 87.9138 16.6667
## disability 41.3094 0.0000 -190.2639 0.0000
## female 95.9345 0.0000 40.2647 0.0000
## NE_So_region 95.7670 0.0000 53.7671 0.0000
## high_exercise 58.0292 0.0000 -20.2119 0.0000
## smoker 91.0615 0.0000 73.9099 16.6667
## race_white 87.1122 0.0000 82.2246 0.0000
## daily_veg 91.5163 0.0000 22.9446 0.0000
## daily_fruit 93.2177 0.0000 66.3155 16.6667
## low_risk_alcohol 84.5596 0.0000 52.4910 16.6667Create output data table:
matchedIns <- match.data(m.out)
write.csv(matchedIns, file="MatchedData.csv")Jitter Plot of Propensity Score Matching:
plot(m.out, type="jitter")
## [1] "To identify the units, use first mouse button; to stop, use second."## integer(0)Histogram of Propensity Score Matching:
plot(m.out, type="hist")
T-tests of Predictor Group Balance
##
## Welch Two Sample t-test
##
## data: insurance by great_health
## t = -3.7301, df = 1183.2, p-value = 0.0002005
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1219875 -0.0378926
## sample estimates:
## mean in group 0 mean in group 1
## 0.4477401 0.5276801##
## Welch Two Sample t-test
##
## data: insurance by mother_college
## t = -9.7821, df = 2920.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2121013 -0.1412699
## sample estimates:
## mean in group 0 mean in group 1
## 0.4272388 0.6039244##
## Welch Two Sample t-test
##
## data: insurance by HS_grad
## t = -13.221, df = 1470.6, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.2983018 -0.2212233
## sample estimates:
## mean in group 0 mean in group 1
## 0.3177215 0.5774840##
## Welch Two Sample t-test
##
## data: insurance by low_income
## t = 14.791, df = 2981.7, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 0.2267418 0.2960464
## sample estimates:
## mean in group 0 mean in group 1
## 0.6394102 0.3780161