How to calculate SMD between 3 groups or more?

Question

I'm interested in calculating pairwise standardized mean differences(SMD) by one stratifying variable. Usually this is calculated between two groups, but can we make this calculation in 3 groups or more?

P.S. I'm a big fan of gtsummary package, so I attempted to do this analysis using example 2 from this amazing package as follows:

library(tidyverse)
library(gtsummary)
#> #BlackLivesMatter
add_difference_ex2 <-
  trial %>%
  mutate(trt=ifelse(age<40,"Drug C", trt)) %>% 
  select(trt, age, marker, grade, stage) %>%
  tbl_summary(
    by = trt,
    statistic = list(all_continuous() ~ "{mean} ({sd})"),
    missing = "no",
    include = c(age, marker, trt)
  ) %>%
  add_n() %>%
  add_difference(adj.vars = c(grade, stage))
#> 11 observations missing `trt` have been removed. To include these observations, use `forcats::fct_explicit_na()` on `trt` column before passing to `tbl_summary()`.
#> Error: 'tbl_summary'/'tbl_svysummary' object must have a `by=` value with exactly two levels

^{Created on 2021-10-27 by the reprex package (v2.0.1)}

Answer 1

To add the pairwise standardized mean differences (SMD), you first need to define a function that will calculate and return the pairwise SMD estimates. Once you've done that, you can add it to the gtsummary table using the generic function add_stat(). Example Below!

library(gtsummary)
library(tidyverse)

# function to calculate pairwise smd
pairwise_smd <- function(data, variable, by, ...) {
  data <- 
    dplyr::select(data, all_of(c(variable, by))) %>%
    rlang::set_names(c("variable", "by")) %>%
    dplyr::filter(complete.cases(.)) %>%
    arrange(desc(.data$by))
  
  tibble(exclude = unique(data$by)) %>%
    mutate(
      include = map_chr(.data$exclude, ~unique(data$by) %>% setdiff(.x) %>% paste(collapse = " vs. ")),
      data_subset = 
        map(
          .data$exclude, 
          ~data %>%
            filter(!.data$by  %in% .x) %>%
            mutate(by = factor(.data$by))
        ),
      smd = map_dbl(.data$data_subset, ~smd::smd(.x$variable, .x$by)$estimate)
    ) %>%
    select(include, smd) %>%
    spread(include, smd)
}

tbl <-
  trial %>%
  select(age, grade, stage) %>%
  tbl_summary(
    by = grade,
    statistic = list(all_continuous() ~ "{mean} ({sd})"),
    missing = "no"
  ) %>%
  add_stat(fns = everything() ~ pairwise_smd)

^{Created on 2021-10-27 by the reprex package (v2.0.1)}

Answer 2

UPDATE: The function is now incorporated into a package, which can be loaded with:

install.packages("devtools")
devtools::install_github("zheer-kejlberg/Z.gtsummary.addons")
library(Z.gtsummary.addons)

---

I've written some code (heavily inspired by the answer of @DanielD.Sjoberg) to do just this with gtsummary tables at https://github.com/zheer-kejlberg/gtsummary-SMDs.

With the use of %>% add_SMD() you can get pairwise SMDs between any arbitrary number of groups. With the use of the ref_group = TRUE argument, you can also limit the SMDs to just being calculated between the first group and each of the other groups.

The function works on both tbl_summary and tbl_svysummary (with weighting)

Another neat thing is that it can supply both overall SMDs (like add_difference("smd") does) and the per-level-of-categorical-variables SMD -- or even both simultaneously. This is specified via the location argument.

Se an example of its use here:

trial %>% mutate(
  w = weightit(grade ~ age + stage + trt, data = ., focal="I")$weights) %>% # create ATT weights
  survey::svydesign(~1, data = ., weights = ~w) %>% # create the svydesign object
  tbl_svysummary(by = grade, include = c(trt, age, stage)) %>%
  add_SMD(location = "both")