# 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 https://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.

## tableone package itself
library(tableone)
## PS matching
library(Matching)
## Weighted analysis
library(survey)
## Reorganizing data
library(reshape2)
## plotting
library(ggplot2)

The right heart catheterization dataset is available at https://biostat.app.vumc.org/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("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).

## 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”. 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 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,
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 the propensity score is often used as the matching scale, and the matching caliper is often 0.2 $$\times$$ SD(logit(PS)). See https://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                        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 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 (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 in https://pubmed.ncbi.nlm.nih.gov/26238958/.

## 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 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 imbalance addmargins(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 methods dataPlot <- 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 ggplot2 dataPlotMelt <- melt(data = dataPlot, id.vars = c("variable"), variable.name = "Method", value.name = "SMD") ## Order variable names by magnitude of SMD varNames <- as.character(dataPlotvariable)[order(dataPlot$Unmatched)] ## Order factor levels in the same order dataPlotMelt$variable <- factor(dataPlotMelt$variable, levels = varNames) ## Plot using ggplot2 ggplot(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 the print() method, which actually invisibly returns a matrix. ## Column bind tables resCombo <- cbind(print(tabUnmatched, printToggle = FALSE), print(tabMatched, printToggle = FALSE), print(tabWeighted, printToggle = FALSE), print(tabWeightedOw, printToggle = FALSE)) ## Add group name row, and rewrite column names resCombo <- 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. The ShowRegTable() function may come in handy. ## Unmatched model (unadjusted) 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

$Matched exp(coef) [confint] p (Intercept) 1.78 [1.61, 1.98] <0.001 swang1RHC 1.26 [1.09, 1.46] 0.002$Weighted
exp(coef) [confint] p
(Intercept) 1.70 [1.55, 1.85]   <0.001
swang1RHC   1.31 [1.14, 1.49]   <0.001