## 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.

## 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 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


## 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


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,
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))         60.84 (17.14)   60.58 (15.72)   0.016
sex = Male (%)            891 (57.0)      892 (57.1)    0.001
race (%)                                                0.014
black                  241 (15.4)      247 (15.8)
other                   96 ( 6.1)       99 ( 6.3)
white                 1226 (78.4)     1217 (77.9)
edu (mean (SD))         11.81 (3.16)    11.78 (3.16)    0.011
income (%)                                              0.029
$11-$25k               329 (21.0)      337 (21.6)
$25-$50k               250 (16.0)      262 (16.8)
> $50k 130 ( 8.3) 124 ( 7.9) Under$11k             854 (54.6)      840 (53.7)
ninsclas (%)                                            0.019
Medicaid               157 (10.0)      152 ( 9.7)
Medicare               368 (23.5)      371 (23.7)
Medicare & Medicaid     91 ( 5.8)       94 ( 6.0)
No insurance            94 ( 6.0)       89 ( 5.7)
Private                495 (31.7)      498 (31.9)
Private & Medicare     358 (22.9)      359 (23.0)
cat1 (%)                                                0.076
ARF                    708 (45.3)      679 (43.4)
CHF                    167 (10.7)      175 (11.2)
COPD                    51 ( 3.3)       57 ( 3.6)
Cirrhosis               44 ( 2.8)       47 ( 3.0)
Colon Cancer             0 ( 0.0)        1 ( 0.1)
Coma                    90 ( 5.8)       76 ( 4.9)
Lung Cancer              4 ( 0.3)        5 ( 0.3)
MOSF w/Malignancy      131 ( 8.4)      128 ( 8.2)
MOSF w/Sepsis          368 (23.5)      395 (25.3)
das2d3pc (mean (SD))    20.50 (5.40)    20.58 (5.08)    0.014
dnr1 = Yes (%)            137 ( 8.8)      130 ( 8.3)    0.016
ca (%)                                                  0.023
Metastatic             107 ( 6.8)       98 ( 6.3)
No                    1188 (76.0)     1194 (76.4)
Yes                    268 (17.1)      271 (17.3)
surv2md1 (mean (SD))     0.58 (0.21)     0.59 (0.20)    0.027
aps1 (mean (SD))        57.06 (19.66)   57.27 (19.66)   0.011
scoma1 (mean (SD))      18.78 (28.89)   18.85 (28.26)   0.003
wtkilo1 (mean (SD))     70.09 (26.08)   70.72 (27.19)   0.024
temp1 (mean (SD))       37.63 (1.88)    37.62 (1.74)    0.006
meanbp1 (mean (SD))     73.45 (35.70)   73.07 (35.74)   0.011
resp1 (mean (SD))       28.12 (13.59)   28.05 (14.15)   0.005
hrt1 (mean (SD))       117.18 (42.14)  117.77 (40.24)   0.014
pafi1 (mean (SD))      208.31 (107.85) 211.39 (108.01)  0.028
paco21 (mean (SD))      37.79 (11.00)   37.45 (11.56)   0.031
ph1 (mean (SD))          7.39 (0.11)     7.39 (0.11)    0.010
wblc1 (mean (SD))       15.54 (12.21)   15.92 (13.00)   0.030
hema1 (mean (SD))       30.87 (8.06)    30.91 (7.55)    0.004
sod1 (mean (SD))       136.56 (7.70)   136.64 (7.43)    0.011
pot1 (mean (SD))         4.03 (1.02)     4.05 (0.99)    0.016
crea1 (mean (SD))        2.28 (2.29)     2.28 (1.96)   <0.001
bili1 (mean (SD))        2.53 (5.58)     2.55 (5.09)    0.005
alb1 (mean (SD))         3.04 (0.70)     3.04 (0.96)    0.001
resp = Yes (%)            525 (33.6)      519 (33.2)    0.008
card = Yes (%)            603 (38.6)      599 (38.3)    0.005
neuro = Yes (%)           110 ( 7.0)      109 ( 7.0)    0.003
gastr = Yes (%)           284 (18.2)      291 (18.6)    0.012
renal = Yes (%)            91 ( 5.8)       94 ( 6.0)    0.008
meta = Yes (%)             67 ( 4.3)       74 ( 4.7)    0.022
hema = Yes (%)            102 ( 6.5)       97 ( 6.2)    0.013
seps = Yes (%)            330 (21.1)      332 (21.2)    0.003
trauma = Yes (%)           13 ( 0.8)       12 ( 0.8)    0.007
ortho = Yes (%)             3 ( 0.2)        1 ( 0.1)    0.036
cardiohx (mean (SD))     0.21 (0.40)     0.20 (0.40)    0.013
chfhx (mean (SD))        0.20 (0.40)     0.20 (0.40)    0.008
dementhx (mean (SD))     0.07 (0.25)     0.07 (0.26)    0.020
psychhx (mean (SD))      0.06 (0.23)     0.05 (0.23)    0.019
chrpulhx (mean (SD))     0.15 (0.35)     0.15 (0.36)    0.023
renalhx (mean (SD))      0.06 (0.23)     0.05 (0.22)    0.029
liverhx (mean (SD))      0.06 (0.24)     0.07 (0.26)    0.031
gibledhx (mean (SD))     0.03 (0.18)     0.03 (0.17)    0.018
malighx (mean (SD))      0.23 (0.42)     0.23 (0.42)    0.011
immunhx (mean (SD))      0.28 (0.45)     0.28 (0.45)    0.007
transhx (mean (SD))      0.12 (0.33)     0.12 (0.33)    0.002
amihx (mean (SD))        0.03 (0.18)     0.03 (0.17)    0.015

## Count covariates with important imbalance


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 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 imbalance addmargins(table(ExtractSmd(tabWeighted) > 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 = names(ExtractSmd(tabUnmatched)), Unmatched = ExtractSmd(tabUnmatched), Matched = ExtractSmd(tabMatched), Weighted = ExtractSmd(tabWeighted))  Error in data.frame(variable = names(ExtractSmd(tabUnmatched)), Unmatched = ExtractSmd(tabUnmatched), : arguments imply differing number of rows: 0, 50  ## Create long-format data for ggplot2 dataPlotMelt <- melt(data = dataPlot, id.vars = c("variable"), variable.name = "Method", value.name = "SMD")  Error in melt(data = dataPlot, id.vars = c("variable"), variable.name = "Method", : object 'dataPlot' not found  ## Order variable names by magnitude of SMD varNames <- as.character(dataPlotvariable)[order(dataPlot$Unmatched)]  Error in eval(expr, envir, enclos): object 'dataPlot' not found  ## Order factor levels in the same order dataPlotMelt$variable <- factor(dataPlotMelt$variable, levels = varNames)  Error in factor(dataPlotMelt$variable, levels = varNames): object 'dataPlotMelt' not found

## 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())

Error in ggplot(data = dataPlotMelt, mapping = aes(x = variable, y = SMD, : object 'dataPlotMelt' not found


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))

## Add group name row, and rewrite column names
resCombo <- rbind(Group = rep(c("No RHC","RHC"), 3), resCombo)
colnames(resCombo) <- c("Unmatched","","Matched","","Weighted","")
print(resCombo, quote = FALSE)

                       Unmatched                       Matched                         Weighted
Group                  No RHC          RHC             No RHC          RHC             No RHC           RHC
n                        3551            2184            1563            1563          1522.89          1520.27
age (mean (SD))         61.76 (17.29)   60.75 (15.63)   60.84 (17.14)   60.58 (15.72)    60.82 (17.16)    60.77 (15.79)
sex = Male (%)           1914 (53.9)     1278 (58.5)      891 (57.0)      892 (57.1)     875.8 (57.5)     872.3 (57.4)
race (%)
black                  585 (16.5)      335 (15.3)      241 (15.4)      247 (15.8)     238.1 (15.6)     235.8 (15.5)
other                  213 ( 6.0)      142 ( 6.5)       96 ( 6.1)       99 ( 6.3)      94.9 ( 6.2)      97.8 ( 6.4)
white                 2753 (77.5)     1707 (78.2)     1226 (78.4)     1217 (77.9)    1189.9 (78.1)    1186.6 (78.1)
edu (mean (SD))         11.57 (3.13)    11.86 (3.16)    11.81 (3.16)    11.78 (3.16)     11.80 (3.17)     11.80 (3.09)
income (%)
$11-$25k               713 (20.1)      452 (20.7)      329 (21.0)      337 (21.6)     316.5 (20.8)     317.0 (20.9)
$25-$50k               500 (14.1)      393 (18.0)      250 (16.0)      262 (16.8)     251.7 (16.5)     250.8 (16.5)
> $50k 257 ( 7.2) 194 ( 8.9) 130 ( 8.3) 124 ( 7.9) 127.1 ( 8.3) 128.4 ( 8.4) Under$11k            2081 (58.6)     1145 (52.4)      854 (54.6)      840 (53.7)     827.6 (54.3)     824.1 (54.2)
ninsclas (%)
Medicaid               454 (12.8)      193 ( 8.8)      157 (10.0)      152 ( 9.7)     153.7 (10.1)     151.9 (10.0)
Medicare               947 (26.7)      511 (23.4)      368 (23.5)      371 (23.7)     361.1 (23.7)     369.0 (24.3)
Medicare & Medicaid    251 ( 7.1)      123 ( 5.6)       91 ( 5.8)       94 ( 6.0)      91.5 ( 6.0)      91.2 ( 6.0)
No insurance           186 ( 5.2)      136 ( 6.2)       94 ( 6.0)       89 ( 5.7)      85.8 ( 5.6)      86.6 ( 5.7)
Private                967 (27.2)      731 (33.5)      495 (31.7)      498 (31.9)     487.0 (32.0)     482.2 (31.7)
Private & Medicare     746 (21.0)      490 (22.4)      358 (22.9)      359 (23.0)     343.7 (22.6)     339.3 (22.3)
cat1 (%)
ARF                   1581 (44.5)      909 (41.6)      708 (45.3)      679 (43.4)     685.8 (45.0)     679.9 (44.7)
CHF                    247 ( 7.0)      209 ( 9.6)      167 (10.7)      175 (11.2)     160.1 (10.5)     163.2 (10.7)
COPD                   399 (11.2)       58 ( 2.7)       51 ( 3.3)       57 ( 3.6)      56.2 ( 3.7)      57.2 ( 3.8)
Cirrhosis              175 ( 4.9)       49 ( 2.2)       44 ( 2.8)       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)       90 ( 5.8)       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)      131 ( 8.4)      128 ( 8.2)     122.4 ( 8.0)     121.5 ( 8.0)
MOSF w/Sepsis          527 (14.8)      700 (32.1)      368 (23.5)      395 (25.3)     368.9 (24.2)     368.1 (24.2)
das2d3pc (mean (SD))    20.37 (5.48)    20.70 (5.03)    20.50 (5.40)    20.58 (5.08)     20.58 (5.45)     20.56 (5.05)
dnr1 = Yes (%)            499 (14.1)      155 ( 7.1)      137 ( 8.8)      130 ( 8.3)     131.5 ( 8.6)     129.2 ( 8.5)
ca (%)
Metastatic             261 ( 7.4)      123 ( 5.6)      107 ( 6.8)       98 ( 6.3)      98.6 ( 6.5)      98.0 ( 6.4)
No                    2652 (74.7)     1727 (79.1)     1188 (76.0)     1194 (76.4)    1160.5 (76.2)    1162.3 (76.5)
Yes                    638 (18.0)      334 (15.3)      268 (17.1)      271 (17.3)     263.7 (17.3)     259.9 (17.1)
surv2md1 (mean (SD))     0.61 (0.19)     0.57 (0.20)     0.58 (0.21)     0.59 (0.20)      0.58 (0.20)      0.58 (0.20)
aps1 (mean (SD))        50.93 (18.81)   60.74 (20.27)   57.06 (19.66)   57.27 (19.66)    57.30 (19.53)    57.13 (19.73)
scoma1 (mean (SD))      22.25 (31.37)   18.97 (28.26)   18.78 (28.89)   18.85 (28.26)    19.12 (29.10)    19.10 (28.51)
wtkilo1 (mean (SD))     65.04 (29.50)   72.36 (27.73)   70.09 (26.08)   70.72 (27.19)    70.19 (26.54)    70.19 (27.30)
temp1 (mean (SD))       37.63 (1.74)    37.59 (1.83)    37.63 (1.88)    37.62 (1.74)     37.63 (1.88)     37.64 (1.74)
meanbp1 (mean (SD))     84.87 (38.87)   68.20 (34.24)   73.45 (35.70)   73.07 (35.74)    73.18 (35.48)    73.22 (35.50)
resp1 (mean (SD))       28.98 (13.95)   26.65 (14.17)   28.12 (13.59)   28.05 (14.15)    28.16 (13.84)    28.10 (14.09)
hrt1 (mean (SD))       112.87 (40.94)  118.93 (41.47)  117.18 (42.14)  117.77 (40.24)   116.96 (42.74)   116.71 (40.28)
pafi1 (mean (SD))      240.63 (116.66) 192.43 (105.54) 208.31 (107.85) 211.39 (108.01)  209.93 (107.48)  210.31 (108.23)
paco21 (mean (SD))      39.95 (14.24)   36.79 (10.97)   37.79 (11.00)   37.45 (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)   15.54 (12.21)   15.92 (13.00)    15.82 (12.03)    15.69 (12.69)
hema1 (mean (SD))       32.70 (8.79)    30.51 (7.42)    30.87 (8.06)    30.91 (7.55)     30.90 (8.10)     30.95 (7.57)
sod1 (mean (SD))       137.04 (7.68)   136.33 (7.60)   136.56 (7.70)   136.64 (7.43)    136.54 (7.86)    136.58 (7.38)
pot1 (mean (SD))         4.08 (1.04)     4.05 (1.01)     4.03 (1.02)     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 (2.29)     2.28 (1.96)      2.27 (2.31)      2.27 (1.95)
bili1 (mean (SD))        2.00 (4.43)     2.71 (5.33)     2.53 (5.58)     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)      525 (33.6)      519 (33.2)     516.6 (33.9)     512.6 (33.7)
card = Yes (%)           1007 (28.4)      924 (42.3)      603 (38.6)      599 (38.3)     582.2 (38.2)     585.6 (38.5)
neuro = Yes (%)           575 (16.2)      118 ( 5.4)      110 ( 7.0)      109 ( 7.0)     109.6 ( 7.2)     109.0 ( 7.2)
gastr = Yes (%)           522 (14.7)      420 (19.2)      284 (18.2)      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)       67 ( 4.3)       74 ( 4.7)      70.0 ( 4.6)      70.2 ( 4.6)
hema = Yes (%)            239 ( 6.7)      115 ( 5.3)      102 ( 6.5)       97 ( 6.2)      93.5 ( 6.1)      95.0 ( 6.2)
seps = Yes (%)            515 (14.5)      516 (23.6)      330 (21.1)      332 (21.2)     325.5 (21.4)     322.0 (21.2)
trauma = Yes (%)           18 ( 0.5)       34 ( 1.6)       13 ( 0.8)       12 ( 0.8)      14.8 ( 1.0)      14.3 ( 0.9)
ortho = Yes (%)             3 ( 0.1)        4 ( 0.2)        3 ( 0.2)        1 ( 0.1)       1.0 ( 0.1)       0.9 ( 0.1)
cardiohx (mean (SD))     0.16 (0.37)     0.20 (0.40)     0.21 (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)     0.06 (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 (0.35)     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)     0.06 (0.24)     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)     0.28 (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,
data    = rhc)
## Matched model
glmMatched <- glm(formula = (death == "Yes") ~ swang1,
data    = rhcMatched)
## Weighted model
glmWeighted <- svyglm(formula = (death == "Yes") ~ swang1,
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) 1.73 [1.56, 1.92]   <0.001
swang1RHC   1.30 [1.12, 1.51]    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