Standardization for Subgroup Analysis in Randomized Controlled Trials

Abstract

Randomized controlled trials (RCTs) emphasize the average or overall effect of a treatment (ATE) on the primary endpoint. Even though the ATE provides the best summary of treatment efficacy, it is of critical importance to know whether the treatment is similarly efficacious in important, predefined subgroups. This is why the RCTs, in addition to the ATE, also present the results of subgroup analysis for preestablished subgroups. Typically, these are marginal subgroup analysis in the sense that treatment effects are estimated in mutually exclusive subgroups defined by only one baseline characteristic at a time (e.g., men versus women, young versus old). Forest plot is a popular graphical approach for displaying the results of subgroup analysis. These plots were originally used in meta-analysis for displaying the treatment effects from independent studies. Treatment effect estimates of different marginal subgroups are, however, not independent. Correlation between the subgrouping variables should be addressed for proper interpretation of forest plots, especially in large effectiveness trials where one of the goals is to address concerns about the generalizability of findings to various populations. Failure to account for the correlation between the subgrouping variables can result in misleading (confounded) interpretations of subgroup effects. Here we present an approach called standardization, a commonly used technique in epidemiology, that allows for valid comparison of subgroup effects depicted in a forest plot. We present simulations results and a subgroup analysis from parallel-group, placebo-controlled randomized trials of antibiotics for acute otitis media.

Key Words:

• Confounding
• Consistency of treatment effect
• Forest plot
• Heterogeneity of treatment effects
• Interaction
• Marginal structural model

Notes

^a Naive approach using equation.

^b Standardization approach using equation.

^c Rejecting the hypothesis of no interaction at α = 0.05.

^d Root mean-squared error (RMSE).

^a Naive approach using equation.

^b Standardization approach using equation.

^c Rejecting the hypothesis of no interaction at α =.05.

^d Root mean-squared error (RMSE).

Note. Correlation between row and column variables ρ = −0.29 (p-value <.0001).