The importance of "shrinkage" in subgroup analyses

Abstract

Study objective: Subgroup analyses examine associations (eg, between treatment and outcome) within subsets of a larger study sample. The traditional approach evaluates the data in each of the subgroups independently. More accurate answers, however, may be expected when the rest of the data are considered in the analysis of each subgroup, provided there are 3 or more subgroups.

Methods: We present a conceptual introduction to subgroup analysis that makes use of all the available data and then illustrate the technique by applying it to a previously published study of pediatric airway management. Using WinBUGS, freely available computer software, we perform an empirical Bayesian analysis of the treatment effect in each of the subgroups. This approach corrects the original subgroup treatment estimates toward a weighted average treatment effect across all subjects.

Results: The revised estimates of the subgroup treatment effects demonstrate markedly less variability than the original estimates. Further, using these estimates will reduce our total expected error in parameter estimation compared with using the original, independent subgroup estimates. Although any particular estimate may be adjusted inappropriately, adopting this strategy will, on average, lead to results that are more accurate.

Conclusion: When multiple subgroups are considered, it is often inadvisable to ignore the rest of the study data. Authors or readers who wish to examine associations within subgroups are encouraged to use techniques that reduce the total expected error.

Figure 1

Two-level, Hierarchical Model of Individual Baseball Players (Level 1) and the Players as a Group (Level 2). Note that in keeping with standard notation, we have labeled the individual level ‘1’ and the group level ‘2.’ If the parameters for the group 2 distribution were sampled from a distribution above it, that higher distribution would be labeled ‘3.’

Figure 2

Application of Shrinkage to Odds Ratios by Subgroup. The y-axis has a log scale. ETI – endotracheal intubation; BVM – bag-valve-mask; Card – cardiopulmonary; SIDS – sudden infant death syndrome; RAD – reactive airway disease; Asp – aspiration.