Propensity Score Diagnostics

Checking balance

  • Love plots (Standardized Mean Difference)
  • ECDF plots

Standardized Mean Difference (SMD)

\[\LARGE d = \frac{\bar{x}_{treatment}-\bar{x}_{control}}{\sqrt{\frac{s^2_{treatment}+s^2_{control}}{2}}}\]

SMD in R


Calculate standardized mean differences

library(halfmoon)
library(tidyverse)

smds <- tidy_smd(
  df,
  .vars = c(confounder_1, confounder_2, ...),
  .group = exposure,
  .wts = wts # weight is optional
)

SMD in R


Plot them! (in a Love plot!)

ggplot(
  data = smds,
  aes(
    x = abs(smd), 
    y = variable, 
    group = method, 
    color = method
  )
) +  
  geom_love()

Love plot

ECDF

For continuous variables, it can be helpful to look at the whole distribution pre and post-weighting rather than a single summary measure

Unweighted ECDF

ggplot(df, aes(x = wt71, color = factor(qsmk))) + 
  geom_ecdf() +
  scale_color_manual(
    "Quit smoking", 
    values = c("#5154B8", "#5DB854"),
    labels = c("Yes", "No")
  ) + 
  xlab("Weight in Kg in 1971") + 
  ylab("Proportion <= x")

Unweighted ECDF

Weighted ECDF

ggplot(df, aes(x = wt71, color = factor(qsmk))) +
  geom_ecdf(aes(weights = w_ate)) +
  scale_color_manual(
    "Quit smoking", 
    values = c("#5154B8", "#5DB854"),
    labels = c("Yes", "No")
  ) + 
  xlab("Weight in Kg in 1971") + 
  ylab("Proportion <= x (Weighted)")

Weighted ECDF

Weighted Tables in R

1. Create a “design object”

library(survey)

svy_des <- svydesign(
  ids = ~ 1,
  data = df,
  weights = ~ wts
)

2. Pass to tbl_svysummary()

library(gtsummary)
tbl_svysummary(svy_des, by = x) |>
  add_difference(everything() ~ "smd") |>
  modify_column_hide(conf.low)

Characteristic 0
N = 1,5651		 1
N = 1,5611		 Difference2
WEIGHT IN KILOGRAMS IN 1971 69 (60, 80) 69 (59, 79) 0.01
0: WHITE 1: BLACK OR OTHER IN 1971

0.01
    0 1,359 (87%) 1,352 (87%)
    1 206 (13%) 209 (13%)
AGE IN 1971 43 (33, 52) 43 (33, 53) -0.01
0: MALE 1: FEMALE

0.00
    0 764 (49%) 764 (49%)
    1 802 (51%) 797 (51%)
NUMBER OF CIGARETTES SMOKED PER DAY IN 1971 20 (10, 25) 20 (10, 30) 0.02
YEARS OF SMOKING 24 (15, 33) 24 (14, 33) 0.00
IN RECREATION, HOW MUCH EXERCISE? IN 1971, 0:much exercise,1:moderate exercise,2:little or no exercise

0.04
    0 302 (19%) 294 (19%)
    1 665 (42%) 691 (44%)
    2 599 (38%) 576 (37%)
IN YOUR USUAL DAY, HOW ACTIVE ARE YOU? IN 1971, 0:very active, 1:moderately active, 2:inactive

0.03
    0 700 (45%) 684 (44%)
    1 718 (46%) 738 (47%)
    2 147 (9.4%) 138 (8.9%)
Abbreviation: CI = Confidence Interval
1 Median (Q1, Q3); n (%)
2 Standardized Mean Difference