3: Stratified contrasts

In ratesci: Confidence Intervals and Tests for Comparisons of Binomial Proportions or Poisson Rates

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
options(digits = 3)

library(ratesci)

Confidence intervals for stratified comparisons of independent binomial or Poisson rates

Stratified analysis might be required for combining results from multiple studies in a meta-analysis, or adjusting clinical trial results for factors used in a stratified randomisation. Associated tests against a null hypothesis of common effects over strata (homogeneity) can also be useful for examining subgroup effects in a clinical trial. The illustration below uses data from a meta-analysis of 9 trials studying the effectiveness of graduated compression stockings for prevention of postoperative deep vein thrombosis (DVT) [from @roderick2005]:

data(compress, package = "ratesci")
strat_rd <- scoreci(x1 = compress$event.gcs, 
                   n1 = compress$n.gcs, 
                   x2 = compress$event.control, 
                   n2 = compress$n.control, 
                   contrast = "RD", 
                   stratified = TRUE)
strat_rd$estimates

strat_rd$pval

The Qtest object provides a heterogeneity test and related quantities, including an assessment of qualitative heterogeneity (indicating whether treatment effects are in opposite directions in different strata). All of which are derived using the score statistic and its estimated variance, for a consistent approach - see [@laud2017 Supplementary Appendix S4].

strat_rd$Qtest

````{=html} <!--

strat_rr <- scoreci(x1 = compress$event.gcs, 
                   n1 = compress$n.gcs, 
                   x2 = compress$event.control, 
                   n2 = compress$n.control, 
                   contrast = "RR", 
                   stratified = TRUE)
strat_rr$Qtest

--> ````

It is important to note that heterogeneity tests often have low power, so it is recommended to inspect the stratum-specific estimates as well[@greenland1982]. The stratdata object provides estimates and intervals for each stratum, along with details of stratum weights and contributions to the Q-statistic (these may be further examined using the hetplot argument).

strat_rd$stratdata

Random effects

In this instance, there is weak evidence ($p = 0.07$) that the treatment effect (on the RD scale) varies across strata. (Estimation on the RR contrast scale gives more consistency across strata.) For the sake of illustration, a random effects analysis of RD would be obtained as follows, giving a wider interval that incorporates the stratum variability. The random = TRUE option invokes the t-distribution asymptotic score (TDAS) method [@laud2017], which modifies the asymptotic score methodology using formulae from the Hartung-Knapp-Sidik-Jonkman (HKSJ) random effects meta-analysis method (with superior performance compared to the DerSimonian-Laird method).

strat_rd_rand <- scoreci(x1 = compress$event.gcs, 
                   n1 = compress$n.gcs, 
                   x2 = compress$event.control, 
                   n2 = compress$n.control, 
                   contrast = "RD", 
                   stratified = TRUE,
                   random = TRUE,
                   prediction = TRUE)
strat_rd_rand$estimates

Note that the TDAS method does not include a skewness correction, so when random = TRUE, the skew argument only affects the stratdata output element.

A prediction interval for the treatment effect in a new study [@higgins2008] can be obtained using prediction = TRUE:

strat_rd_rand$prediction

References

ratesci documentation built on June 21, 2025, 1:07 a.m.