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Using standardized mean differences

Kazuki Yoshida

2022-03-27

Standardized mean difference

The standardized (mean) difference is a measure of distance between two group means in terms of one or more variables. In practice it is often used as a balance measure of individual covariates before and after propensity score matching. As it is standardized, comparison across variables on different scales is possible. For definitions seehttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3144483/#s11title.

Standardized mean differences can be easily calculated with tableone. All standardized mean differences in this package are absolute values, thus, there is no directionality.

Load packages

## tableone package itselflibrary(tableone)## PS matchinglibrary(Matching)## Weighted analysislibrary(survey)## Reorganizing datalibrary(reshape2)## plottinglibrary(ggplot2)

Load data

The right heart catheterization dataset is available athttps://biostat.app.vumc.org/wiki/Main/DataSets. This dataset was originally used in Connorset al. JAMA 1996;276:889-897, and has been made publicly available.

## Right heart cath datasetrhc<-read.csv("https://biostat.app.vumc.org/wiki/pub/Main/DataSets/rhc.csv")

Unmatched table

Out of the 50 covariates, 32 have standardized mean differences of greater than 0.1, which is often considered the sign of important covariate imbalance (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3144483/#s11title).

## Covariatesvars<-c("age","sex","race","edu","income","ninsclas","cat1","das2d3pc","dnr1","ca","surv2md1","aps1","scoma1","wtkilo1","temp1","meanbp1","resp1","hrt1","pafi1","paco21","ph1","wblc1","hema1","sod1","pot1","crea1","bili1","alb1","resp","card","neuro","gastr","renal","meta","hema","seps","trauma","ortho","cardiohx","chfhx","dementhx","psychhx","chrpulhx","renalhx","liverhx","gibledhx","malighx","immunhx","transhx","amihx")## Construct a tabletabUnmatched<-CreateTableOne(vars = vars,strata ="swang1",data = rhc,test =FALSE)## Show table with SMDprint(tabUnmatched,smd =TRUE)
                        Stratified by swang1                         No RHC          RHC             SMD     n                        3551            2184                  age (mean (SD))         61.76 (17.29)   60.75 (15.63)   0.061  sex = Male (%)           1914 (53.9)     1278 (58.5)    0.093  race (%)                                                0.036     black                  585 (16.5)      335 (15.3)              other                  213 ( 6.0)      142 ( 6.5)              white                 2753 (77.5)     1707 (78.2)           edu (mean (SD))         11.57 (3.13)    11.86 (3.16)    0.091  income (%)                                              0.142     $11-$25k               713 (20.1)      452 (20.7)              $25-$50k               500 (14.1)      393 (18.0)              > $50k                 257 ( 7.2)      194 ( 8.9)              Under $11k            2081 (58.6)     1145 (52.4)           ninsclas (%)                                            0.194     Medicaid               454 (12.8)      193 ( 8.8)              Medicare               947 (26.7)      511 (23.4)              Medicare & Medicaid    251 ( 7.1)      123 ( 5.6)              No insurance           186 ( 5.2)      136 ( 6.2)              Private                967 (27.2)      731 (33.5)              Private & Medicare     746 (21.0)      490 (22.4)           cat1 (%)                                                0.583     ARF                   1581 (44.5)      909 (41.6)              CHF                    247 ( 7.0)      209 ( 9.6)              COPD                   399 (11.2)       58 ( 2.7)              Cirrhosis              175 ( 4.9)       49 ( 2.2)              Colon Cancer             6 ( 0.2)        1 ( 0.0)              Coma                   341 ( 9.6)       95 ( 4.3)              Lung Cancer             34 ( 1.0)        5 ( 0.2)              MOSF w/Malignancy      241 ( 6.8)      158 ( 7.2)              MOSF w/Sepsis          527 (14.8)      700 (32.1)           das2d3pc (mean (SD))    20.37 (5.48)    20.70 (5.03)    0.063  dnr1 = Yes (%)            499 (14.1)      155 ( 7.1)    0.228  ca (%)                                                  0.107     Metastatic             261 ( 7.4)      123 ( 5.6)              No                    2652 (74.7)     1727 (79.1)              Yes                    638 (18.0)      334 (15.3)           surv2md1 (mean (SD))     0.61 (0.19)     0.57 (0.20)    0.198  aps1 (mean (SD))        50.93 (18.81)   60.74 (20.27)   0.501  scoma1 (mean (SD))      22.25 (31.37)   18.97 (28.26)   0.110  wtkilo1 (mean (SD))     65.04 (29.50)   72.36 (27.73)   0.256  temp1 (mean (SD))       37.63 (1.74)    37.59 (1.83)    0.021  meanbp1 (mean (SD))     84.87 (38.87)   68.20 (34.24)   0.455  resp1 (mean (SD))       28.98 (13.95)   26.65 (14.17)   0.165  hrt1 (mean (SD))       112.87 (40.94)  118.93 (41.47)   0.147  pafi1 (mean (SD))      240.63 (116.66) 192.43 (105.54)  0.433  paco21 (mean (SD))      39.95 (14.24)   36.79 (10.97)   0.249  ph1 (mean (SD))          7.39 (0.11)     7.38 (0.11)    0.120  wblc1 (mean (SD))       15.26 (11.41)   16.27 (12.55)   0.084  hema1 (mean (SD))       32.70 (8.79)    30.51 (7.42)    0.269  sod1 (mean (SD))       137.04 (7.68)   136.33 (7.60)    0.092  pot1 (mean (SD))         4.08 (1.04)     4.05 (1.01)    0.027  crea1 (mean (SD))        1.92 (2.03)     2.47 (2.05)    0.270  bili1 (mean (SD))        2.00 (4.43)     2.71 (5.33)    0.145  alb1 (mean (SD))         3.16 (0.67)     2.98 (0.93)    0.230  resp = Yes (%)           1481 (41.7)      632 (28.9)    0.270  card = Yes (%)           1007 (28.4)      924 (42.3)    0.295  neuro = Yes (%)           575 (16.2)      118 ( 5.4)    0.353  gastr = Yes (%)           522 (14.7)      420 (19.2)    0.121  renal = Yes (%)           147 ( 4.1)      148 ( 6.8)    0.116  meta = Yes (%)            172 ( 4.8)       93 ( 4.3)    0.028  hema = Yes (%)            239 ( 6.7)      115 ( 5.3)    0.062  seps = Yes (%)            515 (14.5)      516 (23.6)    0.234  trauma = Yes (%)           18 ( 0.5)       34 ( 1.6)    0.104  ortho = Yes (%)             3 ( 0.1)        4 ( 0.2)    0.027  cardiohx (mean (SD))     0.16 (0.37)     0.20 (0.40)    0.116  chfhx (mean (SD))        0.17 (0.37)     0.19 (0.40)    0.069  dementhx (mean (SD))     0.12 (0.32)     0.07 (0.25)    0.163  psychhx (mean (SD))      0.08 (0.27)     0.05 (0.21)    0.143  chrpulhx (mean (SD))     0.22 (0.41)     0.14 (0.35)    0.192  renalhx (mean (SD))      0.04 (0.20)     0.05 (0.21)    0.032  liverhx (mean (SD))      0.07 (0.26)     0.06 (0.24)    0.049  gibledhx (mean (SD))     0.04 (0.19)     0.02 (0.16)    0.070  malighx (mean (SD))      0.25 (0.43)     0.20 (0.40)    0.101  immunhx (mean (SD))      0.26 (0.44)     0.29 (0.45)    0.080  transhx (mean (SD))      0.09 (0.29)     0.15 (0.36)    0.170  amihx (mean (SD))        0.03 (0.17)     0.04 (0.20)    0.074
## Count covariates with important imbalanceaddmargins(table(ExtractSmd(tabUnmatched)>0.1))
FALSE  TRUE   Sum    18    32    50

Propensity score estimation

Usually a logistic regression model is used to estimate individual propensity scores. The model here is taken from“How To Use Propensity Score Analysis”. Predicted probabilities of being assigned to right heart catheterization, being assigned no right heart catheterization, being assigned to the true assignment, as well as the smaller of the probabilities of being assigned to right heart catheterization or no right heart catheterization are calculated for later use in propensity score matching and weighting.

rhc$swang1<-factor(rhc$swang1,levels =c("No RHC","RHC"))## Fit modelpsModel<-glm(formula = swang1~ age+ sex+ race+ edu+ income+ ninsclas+                         cat1+ das2d3pc+ dnr1+ ca+ surv2md1+ aps1+ scoma1+                         wtkilo1+ temp1+ meanbp1+ resp1+ hrt1+ pafi1+                         paco21+ ph1+ wblc1+ hema1+ sod1+ pot1+ crea1+                         bili1+ alb1+ resp+ card+ neuro+ gastr+ renal+                         meta+ hema+ seps+ trauma+ ortho+ cardiohx+ chfhx+                         dementhx+ psychhx+ chrpulhx+ renalhx+ liverhx+ gibledhx+                         malighx+ immunhx+ transhx+ amihx,family  =binomial(link ="logit"),data    = rhc)## Predicted probability of being assigned to RHCrhc$pRhc<-predict(psModel,type ="response")## Predicted probability of being assigned to no RHCrhc$pNoRhc<-1- rhc$pRhc## Predicted probability of being assigned to the## treatment actually assigned (either RHC or no RHC)rhc$pAssign<-NArhc$pAssign[rhc$swang1=="RHC"]<- rhc$pRhc[rhc$swang1=="RHC"]rhc$pAssign[rhc$swang1=="No RHC"]<- rhc$pNoRhc[rhc$swang1=="No RHC"]## Smaller of pRhc vs pNoRhc for matching weightrhc$pMin<-pmin(rhc$pRhc, rhc$pNoRhc)

Propensity score matching

The Matching package can be used for propensity score matching. The logit of the propensity score is often used as the matching scale, and the matching caliper is often 0.2\(\times\) SD(logit(PS)). Seehttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC3144483/#s5title for suggestions. After matching, all the standardized mean differences are below 0.1.

listMatch<-Match(Tr       = (rhc$swang1=="RHC"),# Need to be in 0,1## logit of PS,i.e., log(PS/(1-PS)) as matching scaleX        =log(rhc$pRhc/ rhc$pNoRhc),## 1:1 matchingM        =1,## caliper = 0.2 * SD(logit(PS))caliper  =0.2,replace  =FALSE,ties     =TRUE,version  ="fast")## Extract matched datarhcMatched<- rhc[unlist(listMatch[c("index.treated","index.control")]), ]## Construct a tabletabMatched<-CreateTableOne(vars = vars,strata ="swang1",data = rhcMatched,test =FALSE)## Show table with SMDprint(tabMatched,smd =TRUE)
                        Stratified by swang1                         No RHC          RHC             SMD     n                        1562            1562                  age (mean (SD))         60.53 (17.61)   60.55 (15.72)   0.001  sex = Male (%)            884 (56.6)      890 (57.0)    0.008  race (%)                                                0.009     black                  245 (15.7)      247 (15.8)              other                   97 ( 6.2)      100 ( 6.4)              white                 1220 (78.1)     1215 (77.8)           edu (mean (SD))         11.87 (3.13)    11.78 (3.16)    0.029  income (%)                                              0.028     $11-$25k               324 (20.7)      335 (21.4)              $25-$50k               252 (16.1)      262 (16.8)              > $50k                 127 ( 8.1)      124 ( 7.9)              Under $11k             859 (55.0)      841 (53.8)           ninsclas (%)                                            0.026     Medicaid               163 (10.4)      152 ( 9.7)              Medicare               364 (23.3)      370 (23.7)              Medicare & Medicaid     94 ( 6.0)       95 ( 6.1)              No insurance            85 ( 5.4)       88 ( 5.6)              Private                502 (32.1)      498 (31.9)              Private & Medicare     354 (22.7)      359 (23.0)           cat1 (%)                                                0.058     ARF                    714 (45.7)      680 (43.5)              CHF                    162 (10.4)      175 (11.2)              COPD                    54 ( 3.5)       57 ( 3.6)              Cirrhosis               42 ( 2.7)       47 ( 3.0)              Colon Cancer             1 ( 0.1)        1 ( 0.1)              Coma                    84 ( 5.4)       76 ( 4.9)              Lung Cancer              4 ( 0.3)        5 ( 0.3)              MOSF w/Malignancy      121 ( 7.7)      128 ( 8.2)              MOSF w/Sepsis          380 (24.3)      393 (25.2)           das2d3pc (mean (SD))    20.58 (5.48)    20.58 (5.08)   <0.001  dnr1 = Yes (%)            125 ( 8.0)      130 ( 8.3)    0.012  ca (%)                                                  0.022     Metastatic             102 ( 6.5)       98 ( 6.3)              No                    1201 (76.9)     1193 (76.4)              Yes                    259 (16.6)      271 (17.3)           surv2md1 (mean (SD))     0.58 (0.20)     0.59 (0.20)    0.015  aps1 (mean (SD))        57.13 (19.65)   57.26 (19.66)   0.007  scoma1 (mean (SD))      19.37 (29.18)   18.88 (28.26)   0.017  wtkilo1 (mean (SD))     70.24 (26.23)   70.70 (27.20)   0.017  temp1 (mean (SD))       37.65 (1.89)    37.62 (1.74)    0.017  meanbp1 (mean (SD))     73.70 (35.75)   73.11 (35.74)   0.016  resp1 (mean (SD))       28.18 (13.87)   28.04 (14.15)   0.010  hrt1 (mean (SD))       116.49 (43.19)  117.78 (40.25)   0.031  pafi1 (mean (SD))      209.05 (106.18) 211.22 (108.06)  0.020  paco21 (mean (SD))      37.55 (10.82)   37.46 (11.56)   0.008  ph1 (mean (SD))          7.39 (0.11)     7.39 (0.11)    0.002  wblc1 (mean (SD))       15.73 (12.03)   15.92 (13.00)   0.015  hema1 (mean (SD))       30.78 (7.97)    30.88 (7.53)    0.014  sod1 (mean (SD))       136.61 (7.87)   136.63 (7.43)    0.002  pot1 (mean (SD))         4.04 (1.03)     4.05 (0.99)    0.009  crea1 (mean (SD))        2.31 (2.39)     2.29 (1.97)    0.008  bili1 (mean (SD))        2.54 (5.53)     2.55 (5.09)    0.002  alb1 (mean (SD))         3.05 (0.69)     3.04 (0.96)    0.007  resp = Yes (%)            538 (34.4)      520 (33.3)    0.024  card = Yes (%)            587 (37.6)      598 (38.3)    0.015  neuro = Yes (%)           114 ( 7.3)      109 ( 7.0)    0.012  gastr = Yes (%)           273 (17.5)      291 (18.6)    0.030  renal = Yes (%)            93 ( 6.0)       95 ( 6.1)    0.005  meta = Yes (%)             72 ( 4.6)       74 ( 4.7)    0.006  hema = Yes (%)             94 ( 6.0)       97 ( 6.2)    0.008  seps = Yes (%)            333 (21.3)      331 (21.2)    0.003  trauma = Yes (%)           15 ( 1.0)       12 ( 0.8)    0.021  ortho = Yes (%)             2 ( 0.1)        1 ( 0.1)    0.021  cardiohx (mean (SD))     0.20 (0.40)     0.20 (0.40)    0.006  chfhx (mean (SD))        0.20 (0.40)     0.20 (0.40)    0.011  dementhx (mean (SD))     0.07 (0.25)     0.07 (0.26)    0.017  psychhx (mean (SD))      0.05 (0.23)     0.05 (0.23)   <0.001  chrpulhx (mean (SD))     0.15 (0.36)     0.15 (0.36)    0.007  renalhx (mean (SD))      0.06 (0.23)     0.05 (0.22)    0.031  liverhx (mean (SD))      0.07 (0.25)     0.07 (0.26)    0.005  gibledhx (mean (SD))     0.03 (0.17)     0.03 (0.17)    0.004  malighx (mean (SD))      0.23 (0.42)     0.23 (0.42)    0.009  immunhx (mean (SD))      0.30 (0.46)     0.28 (0.45)    0.041  transhx (mean (SD))      0.13 (0.33)     0.12 (0.33)    0.014  amihx (mean (SD))        0.03 (0.17)     0.03 (0.17)    0.004
## Count covariates with important imbalanceaddmargins(table(ExtractSmd(tabMatched)>0.1))
FALSE   Sum    50    50

Propensity score matching weight

The matching weight method is a weighting analogue to the 1:1 pairwise algorithmic matching (https://pubmed.ncbi.nlm.nih.gov/23902694/). The matching weight is defined as the smaller of the predicted probabilities of receiving or not receiving the treatment over the predicted probability of being assigned to the arm the patient is actually in. After weighting, all the standardized mean differences are below 0.1. The standardized mean differences in weighted data are explained inhttps://pubmed.ncbi.nlm.nih.gov/26238958/.

## Matching weightrhc$mw<- rhc$pMin/ rhc$pAssign## Weighted datarhcSvy<-svydesign(ids =~1,data = rhc,weights =~ mw)## Construct a table (This is a bit slow.)tabWeighted<-svyCreateTableOne(vars = vars,strata ="swang1",data = rhcSvy,test =FALSE)## Show table with SMDprint(tabWeighted,smd =TRUE)
                        Stratified by swang1                         No RHC           RHC              SMD     n                      1522.89          1520.27                  age (mean (SD))          60.82 (17.16)    60.77 (15.79)   0.003  sex = Male (%)           875.8 (57.5)     872.3 (57.4)    0.003  race (%)                                                  0.009     black                 238.1 (15.6)     235.8 (15.5)              other                  94.9 ( 6.2)      97.8 ( 6.4)              white                1189.9 (78.1)    1186.6 (78.1)           edu (mean (SD))          11.80 (3.17)     11.80 (3.09)    0.002  income (%)                                                0.004     $11-$25k              316.5 (20.8)     317.0 (20.9)              $25-$50k              251.7 (16.5)     250.8 (16.5)              > $50k                127.1 ( 8.3)     128.4 ( 8.4)              Under $11k            827.6 (54.3)     824.1 (54.2)           ninsclas (%)                                              0.014     Medicaid              153.7 (10.1)     151.9 (10.0)              Medicare              361.1 (23.7)     369.0 (24.3)              Medicare & Medicaid    91.5 ( 6.0)      91.2 ( 6.0)              No insurance           85.8 ( 5.6)      86.6 ( 5.7)              Private               487.0 (32.0)     482.2 (31.7)              Private & Medicare    343.7 (22.6)     339.3 (22.3)           cat1 (%)                                                  0.017     ARF                   685.8 (45.0)     679.9 (44.7)              CHF                   160.1 (10.5)     163.2 (10.7)              COPD                   56.2 ( 3.7)      57.2 ( 3.8)              Cirrhosis              45.0 ( 3.0)      47.0 ( 3.1)              Colon Cancer            0.9 ( 0.1)       1.0 ( 0.1)              Coma                   79.4 ( 5.2)      77.4 ( 5.1)              Lung Cancer             4.2 ( 0.3)       5.0 ( 0.3)              MOSF w/Malignancy     122.4 ( 8.0)     121.5 ( 8.0)              MOSF w/Sepsis         368.9 (24.2)     368.1 (24.2)           das2d3pc (mean (SD))     20.58 (5.45)     20.56 (5.05)    0.005  dnr1 = Yes (%)           131.5 ( 8.6)     129.2 ( 8.5)    0.005  ca (%)                                                    0.006     Metastatic             98.6 ( 6.5)      98.0 ( 6.4)              No                   1160.5 (76.2)    1162.3 (76.5)              Yes                   263.7 (17.3)     259.9 (17.1)           surv2md1 (mean (SD))      0.58 (0.20)      0.58 (0.20)    0.010  aps1 (mean (SD))         57.30 (19.53)    57.13 (19.73)   0.008  scoma1 (mean (SD))       19.12 (29.10)    19.10 (28.51)   0.001  wtkilo1 (mean (SD))      70.19 (26.54)    70.19 (27.30)  <0.001  temp1 (mean (SD))        37.63 (1.88)     37.64 (1.74)   <0.001  meanbp1 (mean (SD))      73.18 (35.48)    73.22 (35.50)   0.001  resp1 (mean (SD))        28.16 (13.84)    28.10 (14.09)   0.004  hrt1 (mean (SD))        116.96 (42.74)   116.71 (40.28)   0.006  pafi1 (mean (SD))       209.93 (107.48)  210.31 (108.23)  0.004  paco21 (mean (SD))       37.56 (10.80)    37.51 (11.59)   0.004  ph1 (mean (SD))           7.39 (0.11)      7.39 (0.11)    0.003  wblc1 (mean (SD))        15.82 (12.03)    15.69 (12.69)   0.010  hema1 (mean (SD))        30.90 (8.10)     30.95 (7.57)    0.007  sod1 (mean (SD))        136.54 (7.86)    136.58 (7.38)    0.005  pot1 (mean (SD))          4.04 (1.04)      4.05 (0.99)    0.004  crea1 (mean (SD))         2.27 (2.31)      2.27 (1.95)   <0.001  bili1 (mean (SD))         2.50 (5.37)      2.54 (5.15)    0.008  alb1 (mean (SD))          3.04 (0.70)      3.04 (0.97)   <0.001  resp = Yes (%)           516.6 (33.9)     512.6 (33.7)    0.004  card = Yes (%)           582.2 (38.2)     585.6 (38.5)    0.006  neuro = Yes (%)          109.6 ( 7.2)     109.0 ( 7.2)    0.001  gastr = Yes (%)          270.3 (17.8)     272.7 (17.9)    0.005  renal = Yes (%)           89.5 ( 5.9)      90.7 ( 6.0)    0.004  meta = Yes (%)            70.0 ( 4.6)      70.2 ( 4.6)    0.001  hema = Yes (%)            93.5 ( 6.1)      95.0 ( 6.2)    0.004  seps = Yes (%)           325.5 (21.4)     322.0 (21.2)    0.005  trauma = Yes (%)          14.8 ( 1.0)      14.3 ( 0.9)    0.003  ortho = Yes (%)            1.0 ( 0.1)       0.9 ( 0.1)    0.003  cardiohx (mean (SD))      0.20 (0.40)      0.20 (0.40)   <0.001  chfhx (mean (SD))         0.20 (0.40)      0.20 (0.40)    0.004  dementhx (mean (SD))      0.08 (0.26)      0.08 (0.26)    0.003  psychhx (mean (SD))       0.05 (0.23)      0.05 (0.22)    0.004  chrpulhx (mean (SD))      0.16 (0.36)      0.16 (0.36)    0.001  renalhx (mean (SD))       0.05 (0.22)      0.05 (0.22)    0.001  liverhx (mean (SD))       0.07 (0.25)      0.07 (0.25)    0.003  gibledhx (mean (SD))      0.03 (0.17)      0.03 (0.17)    0.007  malighx (mean (SD))       0.23 (0.42)      0.23 (0.42)    0.007  immunhx (mean (SD))       0.28 (0.45)      0.28 (0.45)   <0.001  transhx (mean (SD))       0.12 (0.33)      0.12 (0.33)    0.004  amihx (mean (SD))         0.03 (0.18)      0.03 (0.18)    0.006
## Count covariates with important imbalanceaddmargins(table(ExtractSmd(tabWeighted)>0.1))
FALSE   Sum    50    50

Propensity score overlap weight

The overlap weight method is another alternative weighting method (https://amstat.tandfonline.com/doi/abs/10.1080/01621459.2016.1260466). After weighting, all the standardized mean differences are below 0.1.

## Overlap weightrhc$ow<- (rhc$pAssign* (1- rhc$pAssign))/ rhc$pAssign## Weighted datarhcSvyOw<-svydesign(ids =~1,data = rhc,weights =~ ow)## Construct a table (This is a bit slow.)tabWeightedOw<-svyCreateTableOne(vars = vars,strata ="swang1",data = rhcSvyOw,test =FALSE)## Show table with SMDprint(tabWeightedOw,smd =TRUE)
                        Stratified by swang1                         No RHC           RHC              SMD     n                      1005.82          1005.82                  age (mean (SD))          60.88 (17.19)    60.88 (15.73)  <0.001  sex = Male (%)           574.3 (57.1)     574.3 (57.1)   <0.001  race (%)                                                 <0.001     black                 157.5 (15.7)     157.5 (15.7)              other                  62.0 ( 6.2)      62.0 ( 6.2)              white                 786.3 (78.2)     786.3 (78.2)           edu (mean (SD))          11.78 (3.16)     11.78 (3.08)   <0.001  income (%)                                               <0.001     $11-$25k              208.4 (20.7)     208.4 (20.7)              $25-$50k              163.3 (16.2)     163.3 (16.2)              > $50k                 83.8 ( 8.3)      83.8 ( 8.3)              Under $11k            550.3 (54.7)     550.3 (54.7)           ninsclas (%)                                             <0.001     Medicaid              104.1 (10.4)     104.1 (10.4)              Medicare              242.5 (24.1)     242.5 (24.1)              Medicare & Medicaid    60.7 ( 6.0)      60.7 ( 6.0)              No insurance           57.1 ( 5.7)      57.1 ( 5.7)              Private               315.9 (31.4)     315.9 (31.4)              Private & Medicare    225.5 (22.4)     225.5 (22.4)           cat1 (%)                                                 <0.001     ARF                   450.0 (44.7)     450.0 (44.7)              CHF                   100.3 (10.0)     100.3 (10.0)              COPD                   43.8 ( 4.4)      43.8 ( 4.4)              Cirrhosis              32.5 ( 3.2)      32.5 ( 3.2)              Colon Cancer            0.7 ( 0.1)       0.7 ( 0.1)              Coma                   56.4 ( 5.6)      56.4 ( 5.6)              Lung Cancer             3.3 ( 0.3)       3.3 ( 0.3)              MOSF w/Malignancy      79.1 ( 7.9)      79.1 ( 7.9)              MOSF w/Sepsis         239.7 (23.8)     239.7 (23.8)           das2d3pc (mean (SD))     20.57 (5.46)     20.57 (5.02)   <0.001  dnr1 = Yes (%)            90.8 ( 9.0)      90.8 ( 9.0)   <0.001  ca (%)                                                   <0.001     Metastatic             65.7 ( 6.5)      65.7 ( 6.5)              No                    767.4 (76.3)     767.4 (76.3)              Yes                   172.7 (17.2)     172.7 (17.2)           surv2md1 (mean (SD))      0.58 (0.20)      0.58 (0.20)   <0.001  aps1 (mean (SD))         56.94 (19.78)    56.94 (19.79)  <0.001  scoma1 (mean (SD))       19.57 (29.46)    19.57 (28.78)  <0.001  wtkilo1 (mean (SD))      69.80 (26.87)    69.80 (27.65)  <0.001  temp1 (mean (SD))        37.63 (1.87)     37.63 (1.74)   <0.001  meanbp1 (mean (SD))      74.12 (36.09)    74.12 (36.18)  <0.001  resp1 (mean (SD))        28.16 (13.90)    28.16 (14.18)  <0.001  hrt1 (mean (SD))        116.54 (42.66)   116.54 (40.48)  <0.001  pafi1 (mean (SD))       211.64 (108.24)  211.64 (109.43) <0.001  paco21 (mean (SD))       37.76 (11.12)    37.76 (12.09)  <0.001  ph1 (mean (SD))           7.39 (0.11)      7.39 (0.11)   <0.001  wblc1 (mean (SD))        15.84 (12.07)    15.84 (12.94)  <0.001  hema1 (mean (SD))        30.98 (8.17)     30.98 (7.64)   <0.001  sod1 (mean (SD))        136.61 (7.82)    136.61 (7.31)   <0.001  pot1 (mean (SD))          4.05 (1.04)      4.05 (1.00)   <0.001  crea1 (mean (SD))         2.25 (2.30)      2.25 (1.95)   <0.001  bili1 (mean (SD))         2.50 (5.37)      2.50 (5.05)   <0.001  alb1 (mean (SD))          3.05 (0.70)      3.05 (1.05)   <0.001  resp = Yes (%)           347.3 (34.5)     347.3 (34.5)   <0.001  card = Yes (%)           378.1 (37.6)     378.1 (37.6)   <0.001  neuro = Yes (%)           81.0 ( 8.1)      81.0 ( 8.1)   <0.001  gastr = Yes (%)          177.6 (17.7)     177.6 (17.7)   <0.001  renal = Yes (%)           58.3 ( 5.8)      58.3 ( 5.8)   <0.001  meta = Yes (%)            46.3 ( 4.6)      46.3 ( 4.6)   <0.001  hema = Yes (%)            62.9 ( 6.2)      62.9 ( 6.2)   <0.001  seps = Yes (%)           208.1 (20.7)     208.1 (20.7)   <0.001  trauma = Yes (%)           9.4 ( 0.9)       9.4 ( 0.9)   <0.001  ortho = Yes (%)            0.7 ( 0.1)       0.7 ( 0.1)   <0.001  cardiohx (mean (SD))      0.20 (0.40)      0.20 (0.40)   <0.001  chfhx (mean (SD))         0.20 (0.40)      0.20 (0.40)   <0.001  dementhx (mean (SD))      0.08 (0.27)      0.08 (0.27)   <0.001  psychhx (mean (SD))       0.06 (0.23)      0.06 (0.23)   <0.001  chrpulhx (mean (SD))      0.16 (0.37)      0.16 (0.37)   <0.001  renalhx (mean (SD))       0.05 (0.22)      0.05 (0.22)   <0.001  liverhx (mean (SD))       0.07 (0.25)      0.07 (0.25)   <0.001  gibledhx (mean (SD))      0.03 (0.17)      0.03 (0.17)   <0.001  malighx (mean (SD))       0.23 (0.42)      0.23 (0.42)   <0.001  immunhx (mean (SD))       0.28 (0.45)      0.28 (0.45)   <0.001  transhx (mean (SD))       0.12 (0.33)      0.12 (0.33)   <0.001  amihx (mean (SD))         0.03 (0.18)      0.03 (0.18)   <0.001
## Count covariates with important imbalanceaddmargins(table(ExtractSmd(tabWeightedOw)>0.1))
FALSE   Sum    50    50

Assessing balance before and after matching/weighting

A plot showing covariate balance is often constructed to demonstrate the balancing effect of matching and/or weighting. Given the same propensity score model, the matching weight method often achieves better covariate balance than matching.

## Construct a data frame containing variable name and SMD from all methodsdataPlot<-data.frame(variable   =rownames(ExtractSmd(tabUnmatched)),Unmatched  =as.numeric(ExtractSmd(tabUnmatched)),Matched    =as.numeric(ExtractSmd(tabMatched)),Weighted   =as.numeric(ExtractSmd(tabWeighted)),WeightedOw =as.numeric(ExtractSmd(tabWeightedOw)))## Create long-format data for ggplot2dataPlotMelt<-melt(data          = dataPlot,id.vars       =c("variable"),variable.name ="Method",value.name    ="SMD")## Order variable names by magnitude of SMDvarNames<-as.character(dataPlot$variable)[order(dataPlot$Unmatched)]## Order factor levels in the same orderdataPlotMelt$variable<-factor(dataPlotMelt$variable,levels = varNames)## Plot using ggplot2ggplot(data = dataPlotMelt,mapping =aes(x = variable,y = SMD,group = Method,color = Method))+geom_line()+geom_point()+geom_hline(yintercept =0.1,color ="black",size =0.1)+coord_flip()+theme_bw()+theme(legend.key =element_blank())

To construct a side-by-side table, data can be extracted as a matrix and combined using theprint() method, which actually invisibly returns a matrix.

## Column bind tablesresCombo<-cbind(print(tabUnmatched,printToggle =FALSE),print(tabMatched,printToggle =FALSE),print(tabWeighted,printToggle =FALSE),print(tabWeightedOw,printToggle =FALSE))## Add group name row, and rewrite column namesresCombo<-rbind(Group =rep(c("No RHC","RHC"),4), resCombo)colnames(resCombo)<-c("Unmatched","","Matched","","MW","","OW","")print(resCombo,quote =FALSE)
                       Unmatched                       Matched                         MW                               Group                  No RHC          RHC             No RHC          RHC             No RHC           RHC             n                        3551            2184            1562            1562          1522.89          1520.27         age (mean (SD))         61.76 (17.29)   60.75 (15.63)   60.53 (17.61)   60.55 (15.72)    60.82 (17.16)    60.77 (15.79) sex = Male (%)           1914 (53.9)     1278 (58.5)      884 (56.6)      890 (57.0)     875.8 (57.5)     872.3 (57.4)  race (%)                                                                                                                   black                  585 (16.5)      335 (15.3)      245 (15.7)      247 (15.8)     238.1 (15.6)     235.8 (15.5)     other                  213 ( 6.0)      142 ( 6.5)       97 ( 6.2)      100 ( 6.4)      94.9 ( 6.2)      97.8 ( 6.4)     white                 2753 (77.5)     1707 (78.2)     1220 (78.1)     1215 (77.8)    1189.9 (78.1)    1186.6 (78.1)  edu (mean (SD))         11.57 (3.13)    11.86 (3.16)    11.87 (3.13)    11.78 (3.16)     11.80 (3.17)     11.80 (3.09)  income (%)                                                                                                                 $11-$25k               713 (20.1)      452 (20.7)      324 (20.7)      335 (21.4)     316.5 (20.8)     317.0 (20.9)     $25-$50k               500 (14.1)      393 (18.0)      252 (16.1)      262 (16.8)     251.7 (16.5)     250.8 (16.5)     > $50k                 257 ( 7.2)      194 ( 8.9)      127 ( 8.1)      124 ( 7.9)     127.1 ( 8.3)     128.4 ( 8.4)     Under $11k            2081 (58.6)     1145 (52.4)      859 (55.0)      841 (53.8)     827.6 (54.3)     824.1 (54.2)  ninsclas (%)                                                                                                               Medicaid               454 (12.8)      193 ( 8.8)      163 (10.4)      152 ( 9.7)     153.7 (10.1)     151.9 (10.0)     Medicare               947 (26.7)      511 (23.4)      364 (23.3)      370 (23.7)     361.1 (23.7)     369.0 (24.3)     Medicare & Medicaid    251 ( 7.1)      123 ( 5.6)       94 ( 6.0)       95 ( 6.1)      91.5 ( 6.0)      91.2 ( 6.0)     No insurance           186 ( 5.2)      136 ( 6.2)       85 ( 5.4)       88 ( 5.6)      85.8 ( 5.6)      86.6 ( 5.7)     Private                967 (27.2)      731 (33.5)      502 (32.1)      498 (31.9)     487.0 (32.0)     482.2 (31.7)     Private & Medicare     746 (21.0)      490 (22.4)      354 (22.7)      359 (23.0)     343.7 (22.6)     339.3 (22.3)  cat1 (%)                                                                                                                   ARF                   1581 (44.5)      909 (41.6)      714 (45.7)      680 (43.5)     685.8 (45.0)     679.9 (44.7)     CHF                    247 ( 7.0)      209 ( 9.6)      162 (10.4)      175 (11.2)     160.1 (10.5)     163.2 (10.7)     COPD                   399 (11.2)       58 ( 2.7)       54 ( 3.5)       57 ( 3.6)      56.2 ( 3.7)      57.2 ( 3.8)     Cirrhosis              175 ( 4.9)       49 ( 2.2)       42 ( 2.7)       47 ( 3.0)      45.0 ( 3.0)      47.0 ( 3.1)     Colon Cancer             6 ( 0.2)        1 ( 0.0)        1 ( 0.1)        1 ( 0.1)       0.9 ( 0.1)       1.0 ( 0.1)     Coma                   341 ( 9.6)       95 ( 4.3)       84 ( 5.4)       76 ( 4.9)      79.4 ( 5.2)      77.4 ( 5.1)     Lung Cancer             34 ( 1.0)        5 ( 0.2)        4 ( 0.3)        5 ( 0.3)       4.2 ( 0.3)       5.0 ( 0.3)     MOSF w/Malignancy      241 ( 6.8)      158 ( 7.2)      121 ( 7.7)      128 ( 8.2)     122.4 ( 8.0)     121.5 ( 8.0)     MOSF w/Sepsis          527 (14.8)      700 (32.1)      380 (24.3)      393 (25.2)     368.9 (24.2)     368.1 (24.2)  das2d3pc (mean (SD))    20.37 (5.48)    20.70 (5.03)    20.58 (5.48)    20.58 (5.08)     20.58 (5.45)     20.56 (5.05)  dnr1 = Yes (%)            499 (14.1)      155 ( 7.1)      125 ( 8.0)      130 ( 8.3)     131.5 ( 8.6)     129.2 ( 8.5)  ca (%)                                                                                                                     Metastatic             261 ( 7.4)      123 ( 5.6)      102 ( 6.5)       98 ( 6.3)      98.6 ( 6.5)      98.0 ( 6.4)     No                    2652 (74.7)     1727 (79.1)     1201 (76.9)     1193 (76.4)    1160.5 (76.2)    1162.3 (76.5)     Yes                    638 (18.0)      334 (15.3)      259 (16.6)      271 (17.3)     263.7 (17.3)     259.9 (17.1)  surv2md1 (mean (SD))     0.61 (0.19)     0.57 (0.20)     0.58 (0.20)     0.59 (0.20)      0.58 (0.20)      0.58 (0.20)  aps1 (mean (SD))        50.93 (18.81)   60.74 (20.27)   57.13 (19.65)   57.26 (19.66)    57.30 (19.53)    57.13 (19.73) scoma1 (mean (SD))      22.25 (31.37)   18.97 (28.26)   19.37 (29.18)   18.88 (28.26)    19.12 (29.10)    19.10 (28.51) wtkilo1 (mean (SD))     65.04 (29.50)   72.36 (27.73)   70.24 (26.23)   70.70 (27.20)    70.19 (26.54)    70.19 (27.30) temp1 (mean (SD))       37.63 (1.74)    37.59 (1.83)    37.65 (1.89)    37.62 (1.74)     37.63 (1.88)     37.64 (1.74)  meanbp1 (mean (SD))     84.87 (38.87)   68.20 (34.24)   73.70 (35.75)   73.11 (35.74)    73.18 (35.48)    73.22 (35.50) resp1 (mean (SD))       28.98 (13.95)   26.65 (14.17)   28.18 (13.87)   28.04 (14.15)    28.16 (13.84)    28.10 (14.09) hrt1 (mean (SD))       112.87 (40.94)  118.93 (41.47)  116.49 (43.19)  117.78 (40.25)   116.96 (42.74)   116.71 (40.28) pafi1 (mean (SD))      240.63 (116.66) 192.43 (105.54) 209.05 (106.18) 211.22 (108.06)  209.93 (107.48)  210.31 (108.23)paco21 (mean (SD))      39.95 (14.24)   36.79 (10.97)   37.55 (10.82)   37.46 (11.56)    37.56 (10.80)    37.51 (11.59) ph1 (mean (SD))          7.39 (0.11)     7.38 (0.11)     7.39 (0.11)     7.39 (0.11)      7.39 (0.11)      7.39 (0.11)  wblc1 (mean (SD))       15.26 (11.41)   16.27 (12.55)   15.73 (12.03)   15.92 (13.00)    15.82 (12.03)    15.69 (12.69) hema1 (mean (SD))       32.70 (8.79)    30.51 (7.42)    30.78 (7.97)    30.88 (7.53)     30.90 (8.10)     30.95 (7.57)  sod1 (mean (SD))       137.04 (7.68)   136.33 (7.60)   136.61 (7.87)   136.63 (7.43)    136.54 (7.86)    136.58 (7.38)  pot1 (mean (SD))         4.08 (1.04)     4.05 (1.01)     4.04 (1.03)     4.05 (0.99)      4.04 (1.04)      4.05 (0.99)  crea1 (mean (SD))        1.92 (2.03)     2.47 (2.05)     2.31 (2.39)     2.29 (1.97)      2.27 (2.31)      2.27 (1.95)  bili1 (mean (SD))        2.00 (4.43)     2.71 (5.33)     2.54 (5.53)     2.55 (5.09)      2.50 (5.37)      2.54 (5.15)  alb1 (mean (SD))         3.16 (0.67)     2.98 (0.93)     3.05 (0.69)     3.04 (0.96)      3.04 (0.70)      3.04 (0.97)  resp = Yes (%)           1481 (41.7)      632 (28.9)      538 (34.4)      520 (33.3)     516.6 (33.9)     512.6 (33.7)  card = Yes (%)           1007 (28.4)      924 (42.3)      587 (37.6)      598 (38.3)     582.2 (38.2)     585.6 (38.5)  neuro = Yes (%)           575 (16.2)      118 ( 5.4)      114 ( 7.3)      109 ( 7.0)     109.6 ( 7.2)     109.0 ( 7.2)  gastr = Yes (%)           522 (14.7)      420 (19.2)      273 (17.5)      291 (18.6)     270.3 (17.8)     272.7 (17.9)  renal = Yes (%)           147 ( 4.1)      148 ( 6.8)       93 ( 6.0)       95 ( 6.1)      89.5 ( 5.9)      90.7 ( 6.0)  meta = Yes (%)            172 ( 4.8)       93 ( 4.3)       72 ( 4.6)       74 ( 4.7)      70.0 ( 4.6)      70.2 ( 4.6)  hema = Yes (%)            239 ( 6.7)      115 ( 5.3)       94 ( 6.0)       97 ( 6.2)      93.5 ( 6.1)      95.0 ( 6.2)  seps = Yes (%)            515 (14.5)      516 (23.6)      333 (21.3)      331 (21.2)     325.5 (21.4)     322.0 (21.2)  trauma = Yes (%)           18 ( 0.5)       34 ( 1.6)       15 ( 1.0)       12 ( 0.8)      14.8 ( 1.0)      14.3 ( 0.9)  ortho = Yes (%)             3 ( 0.1)        4 ( 0.2)        2 ( 0.1)        1 ( 0.1)       1.0 ( 0.1)       0.9 ( 0.1)  cardiohx (mean (SD))     0.16 (0.37)     0.20 (0.40)     0.20 (0.40)     0.20 (0.40)      0.20 (0.40)      0.20 (0.40)  chfhx (mean (SD))        0.17 (0.37)     0.19 (0.40)     0.20 (0.40)     0.20 (0.40)      0.20 (0.40)      0.20 (0.40)  dementhx (mean (SD))     0.12 (0.32)     0.07 (0.25)     0.07 (0.25)     0.07 (0.26)      0.08 (0.26)      0.08 (0.26)  psychhx (mean (SD))      0.08 (0.27)     0.05 (0.21)     0.05 (0.23)     0.05 (0.23)      0.05 (0.23)      0.05 (0.22)  chrpulhx (mean (SD))     0.22 (0.41)     0.14 (0.35)     0.15 (0.36)     0.15 (0.36)      0.16 (0.36)      0.16 (0.36)  renalhx (mean (SD))      0.04 (0.20)     0.05 (0.21)     0.06 (0.23)     0.05 (0.22)      0.05 (0.22)      0.05 (0.22)  liverhx (mean (SD))      0.07 (0.26)     0.06 (0.24)     0.07 (0.25)     0.07 (0.26)      0.07 (0.25)      0.07 (0.25)  gibledhx (mean (SD))     0.04 (0.19)     0.02 (0.16)     0.03 (0.17)     0.03 (0.17)      0.03 (0.17)      0.03 (0.17)  malighx (mean (SD))      0.25 (0.43)     0.20 (0.40)     0.23 (0.42)     0.23 (0.42)      0.23 (0.42)      0.23 (0.42)  immunhx (mean (SD))      0.26 (0.44)     0.29 (0.45)     0.30 (0.46)     0.28 (0.45)      0.28 (0.45)      0.28 (0.45)  transhx (mean (SD))      0.09 (0.29)     0.15 (0.36)     0.13 (0.33)     0.12 (0.33)      0.12 (0.33)      0.12 (0.33)  amihx (mean (SD))        0.03 (0.17)     0.04 (0.20)     0.03 (0.17)     0.03 (0.17)      0.03 (0.18)      0.03 (0.18)                         OW                               Group                  No RHC           RHC             n                      1005.82          1005.82         age (mean (SD))          60.88 (17.19)    60.88 (15.73) sex = Male (%)           574.3 (57.1)     574.3 (57.1)  race (%)                                                   black                 157.5 (15.7)     157.5 (15.7)     other                  62.0 ( 6.2)      62.0 ( 6.2)     white                 786.3 (78.2)     786.3 (78.2)  edu (mean (SD))          11.78 (3.16)     11.78 (3.08)  income (%)                                                 $11-$25k              208.4 (20.7)     208.4 (20.7)     $25-$50k              163.3 (16.2)     163.3 (16.2)     > $50k                 83.8 ( 8.3)      83.8 ( 8.3)     Under $11k            550.3 (54.7)     550.3 (54.7)  ninsclas (%)                                               Medicaid              104.1 (10.4)     104.1 (10.4)     Medicare              242.5 (24.1)     242.5 (24.1)     Medicare & Medicaid    60.7 ( 6.0)      60.7 ( 6.0)     No insurance           57.1 ( 5.7)      57.1 ( 5.7)     Private               315.9 (31.4)     315.9 (31.4)     Private & Medicare    225.5 (22.4)     225.5 (22.4)  cat1 (%)                                                   ARF                   450.0 (44.7)     450.0 (44.7)     CHF                   100.3 (10.0)     100.3 (10.0)     COPD                   43.8 ( 4.4)      43.8 ( 4.4)     Cirrhosis              32.5 ( 3.2)      32.5 ( 3.2)     Colon Cancer            0.7 ( 0.1)       0.7 ( 0.1)     Coma                   56.4 ( 5.6)      56.4 ( 5.6)     Lung Cancer             3.3 ( 0.3)       3.3 ( 0.3)     MOSF w/Malignancy      79.1 ( 7.9)      79.1 ( 7.9)     MOSF w/Sepsis         239.7 (23.8)     239.7 (23.8)  das2d3pc (mean (SD))     20.57 (5.46)     20.57 (5.02)  dnr1 = Yes (%)            90.8 ( 9.0)      90.8 ( 9.0)  ca (%)                                                     Metastatic             65.7 ( 6.5)      65.7 ( 6.5)     No                    767.4 (76.3)     767.4 (76.3)     Yes                   172.7 (17.2)     172.7 (17.2)  surv2md1 (mean (SD))      0.58 (0.20)      0.58 (0.20)  aps1 (mean (SD))         56.94 (19.78)    56.94 (19.79) scoma1 (mean (SD))       19.57 (29.46)    19.57 (28.78) wtkilo1 (mean (SD))      69.80 (26.87)    69.80 (27.65) temp1 (mean (SD))        37.63 (1.87)     37.63 (1.74)  meanbp1 (mean (SD))      74.12 (36.09)    74.12 (36.18) resp1 (mean (SD))        28.16 (13.90)    28.16 (14.18) hrt1 (mean (SD))        116.54 (42.66)   116.54 (40.48) pafi1 (mean (SD))       211.64 (108.24)  211.64 (109.43)paco21 (mean (SD))       37.76 (11.12)    37.76 (12.09) ph1 (mean (SD))           7.39 (0.11)      7.39 (0.11)  wblc1 (mean (SD))        15.84 (12.07)    15.84 (12.94) hema1 (mean (SD))        30.98 (8.17)     30.98 (7.64)  sod1 (mean (SD))        136.61 (7.82)    136.61 (7.31)  pot1 (mean (SD))          4.05 (1.04)      4.05 (1.00)  crea1 (mean (SD))         2.25 (2.30)      2.25 (1.95)  bili1 (mean (SD))         2.50 (5.37)      2.50 (5.05)  alb1 (mean (SD))          3.05 (0.70)      3.05 (1.05)  resp = Yes (%)           347.3 (34.5)     347.3 (34.5)  card = Yes (%)           378.1 (37.6)     378.1 (37.6)  neuro = Yes (%)           81.0 ( 8.1)      81.0 ( 8.1)  gastr = Yes (%)          177.6 (17.7)     177.6 (17.7)  renal = Yes (%)           58.3 ( 5.8)      58.3 ( 5.8)  meta = Yes (%)            46.3 ( 4.6)      46.3 ( 4.6)  hema = Yes (%)            62.9 ( 6.2)      62.9 ( 6.2)  seps = Yes (%)           208.1 (20.7)     208.1 (20.7)  trauma = Yes (%)           9.4 ( 0.9)       9.4 ( 0.9)  ortho = Yes (%)            0.7 ( 0.1)       0.7 ( 0.1)  cardiohx (mean (SD))      0.20 (0.40)      0.20 (0.40)  chfhx (mean (SD))         0.20 (0.40)      0.20 (0.40)  dementhx (mean (SD))      0.08 (0.27)      0.08 (0.27)  psychhx (mean (SD))       0.06 (0.23)      0.06 (0.23)  chrpulhx (mean (SD))      0.16 (0.37)      0.16 (0.37)  renalhx (mean (SD))       0.05 (0.22)      0.05 (0.22)  liverhx (mean (SD))       0.07 (0.25)      0.07 (0.25)  gibledhx (mean (SD))      0.03 (0.17)      0.03 (0.17)  malighx (mean (SD))       0.23 (0.42)      0.23 (0.42)  immunhx (mean (SD))       0.28 (0.45)      0.28 (0.45)  transhx (mean (SD))       0.12 (0.33)      0.12 (0.33)  amihx (mean (SD))         0.03 (0.18)      0.03 (0.18)

Outcome analysis

The final analysis can be conducted using matched and weighted data. The results from the matching and matching weight are similar. TheShowRegTable() function may come in handy.

## Unmatched model (unadjusted)glmUnmatched<-glm(formula = (death=="Yes")~ swang1,family  =binomial(link ="logit"),data    = rhc)## Matched modelglmMatched<-glm(formula = (death=="Yes")~ swang1,family  =binomial(link ="logit"),data    = rhcMatched)## Weighted modelglmWeighted<-svyglm(formula = (death=="Yes")~ swang1,family  =binomial(link ="logit"),design  = rhcSvy)## Show results togetherresTogether<-list(Unmatched =ShowRegTable(glmUnmatched,printToggle =FALSE),Matched   =ShowRegTable(glmMatched,printToggle =FALSE),Weighted  =ShowRegTable(glmWeighted,printToggle =FALSE))print(resTogether,quote =FALSE)
$Unmatched            exp(coef) [confint] p     (Intercept) 1.70 [1.59, 1.82]   <0.001swang1RHC   1.25 [1.12, 1.40]   <0.001$Matched            exp(coef) [confint] p     (Intercept) 1.78 [1.61, 1.98]   <0.001swang1RHC   1.26 [1.09, 1.46]    0.002$Weighted            exp(coef) [confint] p     (Intercept) 1.70 [1.55, 1.85]   <0.001swang1RHC   1.31 [1.14, 1.49]   <0.001
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