# Using standardized mean differences

## 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 see http://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 itself
library(tableone)
## PS matching
library(Matching)
## Weighted analysis
library(survey)
## Reorganizing data
library(reshape2)
## plotting
library(ggplot2)

## Load data

The right heart catheterization dataset is available at http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets . This dataset was originally used in Connors et al. JAMA 1996;276:889-897, and has been made publicly available.

## Right heart cath dataset
rhc <- read.csv("http://biostat.mc.vanderbilt.edu/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 (http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3144483/#s11title ).

## Covariates
vars <- 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 table
tabUnmatched <- CreateTableOne(vars = vars, strata = "swang1", data = rhc, test = FALSE)
## Show table with SMD
print(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 imbalance
addmargins(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” (http://www.mc.vanderbilt.edu/crc/workshop_files/2008-04-11.pdf ). Predicted probabilities of being assigned to right heart catherterization, being assigned no right heart catherterization, being assigned to the true assignment, as well as the smaller of the probabilities of being assigned to right heart catherterization or no right heart catherterization are calculated for later use in propensity score matching and weighting.

## Fit model
psModel <- 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 RHC
rhc$pRhc <- predict(psModel, type = "response") ## Predicted probability of being assigned to no RHC rhc$pNoRhc <- 1 - rhc$pRhc ## Predicted probability of being assigned to the ## treatment actually assigned (either RHC or no RHC) rhc$pAssign <- NA
rhc$pAssign[rhc$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 weight
rhc$pMin <- pmin(rhc$pRhc, rhc$pNoRhc) ## Propensity score matching The Matching package can be used for propensity score matching. The logit of propensity score is often used as the matching scale, and the matchign caliper is often 0.2 $$\times$$ SD(logit(PS)). See http://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$swang1 == "RHC"),      # Need to be in 0,1
## logit of PS,i.e., log(PS/(1-PS)) as matching scale
X        = log(rhc$pRhc / rhc$pNoRhc),
## 1:1 matching
M        = 1,
## caliper = 0.2 * SD(logit(PS))
caliper  = 0.2,
replace  = FALSE,
ties     = TRUE,
version  = "fast")
## Extract matched data
rhcMatched <- rhc[unlist(listMatch[c("index.treated","index.control")]), ]

## Construct a table
tabMatched <- CreateTableOne(vars = vars, strata = "swang1", data = rhcMatched, test = FALSE)
## Show table with SMD
print(tabMatched, smd = TRUE)
                        Stratified by swang1
No RHC          RHC             SMD
n                        1563            1563
age (mean (sd))         60.96 (17.21)   60.57 (15.70)   0.024
sex = Male (%)            901 (57.6)      891 (57.0)    0.013
race (%)                                                0.020
black                  238 (15.2)      248 (15.9)
other                  103 ( 6.6)       99 ( 6.3)
white                 1222 (78.2)     1216 (77.8)
edu (mean (sd))         11.82 (3.13)    11.78 (3.16)    0.013
income (%)                                              0.043
$11-$25k               320 (20.5)      335 (21.4)
$25-$50k               247 (15.8)      262 (16.8)
> $50k 121 ( 7.7) 124 ( 7.9) Under$11k             875 (56.0)      842 (53.9)
ninsclas (%)                                            0.018
Medicaid               155 ( 9.9)      152 ( 9.7)
Medicare               371 (23.7)      370 (23.7)
Medicare & Medicaid     93 ( 6.0)       94 ( 6.0)
No insurance            83 ( 5.3)       89 ( 5.7)
Private                500 (32.0)      498 (31.9)
Private & Medicare     361 (23.1)      360 (23.0)
cat1 (%)                                                0.074
ARF                    715 (45.7)      680 (43.5)
CHF                    157 (10.0)      176 (11.3)
COPD                    66 ( 4.2)       57 ( 3.6)
Cirrhosis               46 ( 2.9)       47 ( 3.0)
Colon Cancer             0 ( 0.0)        1 ( 0.1)
Coma                    78 ( 5.0)       76 ( 4.9)
Lung Cancer              5 ( 0.3)        5 ( 0.3)
MOSF w/Malignancy      123 ( 7.9)      128 ( 8.2)
MOSF w/Sepsis          373 (23.9)      393 (25.1)
das2d3pc (mean (sd))    20.48 (5.43)    20.58 (5.08)    0.019
dnr1 = Yes (%)            124 ( 7.9)      130 ( 8.3)    0.014
ca (%)                                                  0.008
Metastatic             101 ( 6.5)       98 ( 6.3)
No                    1191 (76.2)     1194 (76.4)
Yes                    271 (17.3)      271 (17.3)
surv2md1 (mean (sd))     0.58 (0.20)     0.59 (0.20)    0.021
aps1 (mean (sd))        57.52 (19.36)   57.23 (19.67)   0.015
scoma1 (mean (sd))      18.77 (28.63)   18.87 (28.25)   0.004
wtkilo1 (mean (sd))     70.48 (25.86)   70.72 (27.19)   0.009
temp1 (mean (sd))       37.64 (1.89)    37.62 (1.74)    0.011
meanbp1 (mean (sd))     72.39 (35.04)   73.11 (35.72)   0.020
resp1 (mean (sd))       28.15 (14.15)   28.06 (14.16)   0.006
hrt1 (mean (sd))       117.08 (42.59)  117.73 (40.26)   0.016
pafi1 (mean (sd))      208.38 (107.24) 211.22 (108.00)  0.026
paco21 (mean (sd))      37.87 (11.25)   37.47 (11.56)   0.036
ph1 (mean (sd))          7.39 (0.11)     7.39 (0.11)    0.007
wblc1 (mean (sd))       15.67 (12.19)   15.92 (12.99)   0.020
hema1 (mean (sd))       30.89 (8.05)    30.89 (7.54)    0.001
sod1 (mean (sd))       136.77 (8.02)   136.63 (7.42)    0.017
pot1 (mean (sd))         4.02 (1.03)     4.05 (0.99)    0.024
crea1 (mean (sd))        2.28 (2.32)     2.28 (1.97)    0.001
bili1 (mean (sd))        2.62 (5.76)     2.55 (5.09)    0.013
alb1 (mean (sd))         3.04 (0.70)     3.04 (0.96)    0.006
resp = Yes (%)            547 (35.0)      519 (33.2)    0.038
card = Yes (%)            577 (36.9)      599 (38.3)    0.029
neuro = Yes (%)           101 ( 6.5)      109 ( 7.0)    0.020
gastr = Yes (%)           288 (18.4)      291 (18.6)    0.005
renal = Yes (%)            91 ( 5.8)       94 ( 6.0)    0.008
meta = Yes (%)             66 ( 4.2)       74 ( 4.7)    0.025
hema = Yes (%)             90 ( 5.8)       97 ( 6.2)    0.019
seps = Yes (%)            329 (21.0)      331 (21.2)    0.003
trauma = Yes (%)           15 ( 1.0)       13 ( 0.8)    0.014
ortho = Yes (%)             1 ( 0.1)        1 ( 0.1)   <0.001
cardiohx (mean (sd))     0.20 (0.40)     0.20 (0.40)    0.008
chfhx (mean (sd))        0.20 (0.40)     0.20 (0.40)    0.018
dementhx (mean (sd))     0.08 (0.26)     0.07 (0.26)    0.005
psychhx (mean (sd))      0.05 (0.22)     0.05 (0.23)    0.006
chrpulhx (mean (sd))     0.16 (0.37)     0.15 (0.36)    0.016
renalhx (mean (sd))      0.05 (0.23)     0.05 (0.22)    0.020
liverhx (mean (sd))      0.07 (0.26)     0.07 (0.26)    0.007
gibledhx (mean (sd))     0.03 (0.18)     0.03 (0.17)    0.015
malighx (mean (sd))      0.23 (0.42)     0.23 (0.42)    0.002
immunhx (mean (sd))      0.29 (0.45)     0.28 (0.45)    0.016
transhx (mean (sd))      0.12 (0.33)     0.12 (0.33)    0.002
amihx (mean (sd))        0.03 (0.18)     0.03 (0.17)    0.022
## Count covariates with important imbalance
addmargins(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 (http://www.ncbi.nlm.nih.gov/pubmed/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 in http://onlinelibrary.wiley.com/doi/10.1002/sim.6607/full .

## Matching weight
rhc$mw <- rhc$pMin / rhc$pAssign ## Weighted data rhcSvy <- 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 SMD print(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 2081 (58.6) 1145 (52.4) 875 (56.0) 842 (53.9) 827.6 (54.3) 824.1 (54.2) ninsclas (%) Medicaid 454 (12.8) 193 ( 8.8) 155 ( 9.9) 152 ( 9.7) 153.7 (10.1) 151.9 (10.0) Medicare 947 (26.7) 511 (23.4) 371 (23.7) 370 (23.7) 361.1 (23.7) 369.0 (24.3) Medicare & Medicaid 251 ( 7.1) 123 ( 5.6) 93 ( 6.0) 94 ( 6.0) 91.5 ( 6.0) 91.2 ( 6.0) No insurance 186 ( 5.2) 136 ( 6.2) 83 ( 5.3) 89 ( 5.7) 85.8 ( 5.6) 86.6 ( 5.7) Private 967 (27.2) 731 (33.5) 500 (32.0) 498 (31.9) 487.0 (32.0) 482.2 (31.7) Private & Medicare 746 (21.0) 490 (22.4) 361 (23.1) 360 (23.0) 343.7 (22.6) 339.3 (22.3) cat1 (%) ARF 1581 (44.5) 909 (41.6) 715 (45.7) 680 (43.5) 685.8 (45.0) 679.9 (44.7) CHF 247 ( 7.0) 209 ( 9.6) 157 (10.0) 176 (11.3) 160.1 (10.5) 163.2 (10.7) COPD 399 (11.2) 58 ( 2.7) 66 ( 4.2) 57 ( 3.6) 56.2 ( 3.7) 57.2 ( 3.8) Cirrhosis 175 ( 4.9) 49 ( 2.2) 46 ( 2.9) 47 ( 3.0) 45.0 ( 3.0) 47.0 ( 3.1) Colon Cancer 6 ( 0.2) 1 ( 0.0) 0 ( 0.0) 1 ( 0.1) 0.9 ( 0.1) 1.0 ( 0.1) Coma 341 ( 9.6) 95 ( 4.3) 78 ( 5.0) 76 ( 4.9) 79.4 ( 5.2) 77.4 ( 5.1) Lung Cancer 34 ( 1.0) 5 ( 0.2) 5 ( 0.3) 5 ( 0.3) 4.2 ( 0.3) 5.0 ( 0.3) MOSF w/Malignancy 241 ( 6.8) 158 ( 7.2) 123 ( 7.9) 128 ( 8.2) 122.4 ( 8.0) 121.5 ( 8.0) MOSF w/Sepsis 527 (14.8) 700 (32.1) 373 (23.9) 393 (25.1) 368.9 (24.2) 368.1 (24.2) das2d3pc (mean (sd)) 20.37 (5.48) 20.70 (5.03) 20.48 (5.43) 20.58 (5.08) 20.58 (5.45) 20.56 (5.05) dnr1 = Yes (%) 499 (14.1) 155 ( 7.1) 124 ( 7.9) 130 ( 8.3) 131.5 ( 8.6) 129.2 ( 8.5) ca (%) Metastatic 261 ( 7.4) 123 ( 5.6) 101 ( 6.5) 98 ( 6.3) 98.6 ( 6.5) 98.0 ( 6.4) No 2652 (74.7) 1727 (79.1) 1191 (76.2) 1194 (76.4) 1160.5 (76.2) 1162.3 (76.5) Yes 638 (18.0) 334 (15.3) 271 (17.3) 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) 57.52 (19.36) 57.23 (19.67) 57.30 (19.53) 57.13 (19.73) scoma1 (mean (sd)) 22.25 (31.37) 18.97 (28.26) 18.77 (28.63) 18.87 (28.25) 19.12 (29.10) 19.10 (28.51) wtkilo1 (mean (sd)) 65.04 (29.50) 72.36 (27.73) 70.48 (25.86) 70.72 (27.19) 70.19 (26.54) 70.19 (27.30) temp1 (mean (sd)) 37.63 (1.74) 37.59 (1.83) 37.64 (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) 72.39 (35.04) 73.11 (35.72) 73.18 (35.48) 73.22 (35.50) resp1 (mean (sd)) 28.98 (13.95) 26.65 (14.17) 28.15 (14.15) 28.06 (14.16) 28.16 (13.84) 28.10 (14.09) hrt1 (mean (sd)) 112.87 (40.94) 118.93 (41.47) 117.08 (42.59) 117.73 (40.26) 116.96 (42.74) 116.71 (40.28) pafi1 (mean (sd)) 240.63 (116.66) 192.43 (105.54) 208.38 (107.24) 211.22 (108.00) 209.93 (107.48) 210.31 (108.23) paco21 (mean (sd)) 39.95 (14.24) 36.79 (10.97) 37.87 (11.25) 37.47 (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) 15.67 (12.19) 15.92 (12.99) 15.82 (12.03) 15.69 (12.69) hema1 (mean (sd)) 32.70 (8.79) 30.51 (7.42) 30.89 (8.05) 30.89 (7.54) 30.90 (8.10) 30.95 (7.57) sod1 (mean (sd)) 137.04 (7.68) 136.33 (7.60) 136.77 (8.02) 136.63 (7.42) 136.54 (7.86) 136.58 (7.38) pot1 (mean (sd)) 4.08 (1.04) 4.05 (1.01) 4.02 (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) 2.28 (2.32) 2.28 (1.97) 2.27 (2.31) 2.27 (1.95) bili1 (mean (sd)) 2.00 (4.43) 2.71 (5.33) 2.62 (5.76) 2.55 (5.09) 2.50 (5.37) 2.54 (5.15) alb1 (mean (sd)) 3.16 (0.67) 2.98 (0.93) 3.04 (0.70) 3.04 (0.96) 3.04 (0.70) 3.04 (0.97) resp = Yes (%) 1481 (41.7) 632 (28.9) 547 (35.0) 519 (33.2) 516.6 (33.9) 512.6 (33.7) card = Yes (%) 1007 (28.4) 924 (42.3) 577 (36.9) 599 (38.3) 582.2 (38.2) 585.6 (38.5) neuro = Yes (%) 575 (16.2) 118 ( 5.4) 101 ( 6.5) 109 ( 7.0) 109.6 ( 7.2) 109.0 ( 7.2) gastr = Yes (%) 522 (14.7) 420 (19.2) 288 (18.4) 291 (18.6) 270.3 (17.8) 272.7 (17.9) renal = Yes (%) 147 ( 4.1) 148 ( 6.8) 91 ( 5.8) 94 ( 6.0) 89.5 ( 5.9) 90.7 ( 6.0) meta = Yes (%) 172 ( 4.8) 93 ( 4.3) 66 ( 4.2) 74 ( 4.7) 70.0 ( 4.6) 70.2 ( 4.6) hema = Yes (%) 239 ( 6.7) 115 ( 5.3) 90 ( 5.8) 97 ( 6.2) 93.5 ( 6.1) 95.0 ( 6.2) seps = Yes (%) 515 (14.5) 516 (23.6) 329 (21.0) 331 (21.2) 325.5 (21.4) 322.0 (21.2) trauma = Yes (%) 18 ( 0.5) 34 ( 1.6) 15 ( 1.0) 13 ( 0.8) 14.8 ( 1.0) 14.3 ( 0.9) ortho = Yes (%) 3 ( 0.1) 4 ( 0.2) 1 ( 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) 0.08 (0.26) 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 (0.22) 0.05 (0.23) 0.05 (0.23) 0.05 (0.22) chrpulhx (mean (sd)) 0.22 (0.41) 0.14 (0.35) 0.16 (0.37) 0.15 (0.36) 0.16 (0.36) 0.16 (0.36) renalhx (mean (sd)) 0.04 (0.20) 0.05 (0.21) 0.05 (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 (0.26) 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 (0.18) 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) 0.29 (0.45) 0.28 (0.45) 0.28 (0.45) 0.28 (0.45) transhx (mean (sd)) 0.09 (0.29) 0.15 (0.36) 0.12 (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 (0.18) 0.03 (0.17) 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. ShowRegTable() function may come in handly. ## Unmatched model (unadjsuted) glmUnmatched <- glm(formula = (death == "Yes") ~ swang1, family = binomial(link = "logit"), data = rhc) ## Matched model glmMatched <- glm(formula = (death == "Yes") ~ swang1, family = binomial(link = "logit"), data = rhcMatched) ## Weighted model glmWeighted <- svyglm(formula = (death == "Yes") ~ swang1, family = binomial(link = "logit"), design = rhcSvy) ## Show results together resTogether <- 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]   <0.001
swang1RHC   1.25 [1.12, 1.40]   <0.001

$Matched exp(coef) [confint] p (Intercept) 1.75 [1.58, 1.94] <0.001 swang1RHC 1.29 [1.11, 1.49] 0.001$Weighted
exp(coef) [confint] p
(Intercept) 1.70 [1.56, 1.85]   <0.001
swang1RHC   1.31 [1.14, 1.49]   <0.001