Targeted therapies tend to have biomarker defined subgroups that derive differential efficacy from treatments. This article corrects three prevailing oversights in stratified analyses comparing treatments in randomized controlled trials (RCTs) with binary and time-to-event outcomes: 1.Using efficacy measures such as odds ratio (OR) and hazard ratio (HR) can make a prognostic biomarker appear predictive, targeting wrong patients, because the inference is affected by a confounding/covert factor even with ignorable treatment assignment in an RCT. As shown analytically and with real immunotherapy patient level data, OR and HR cannot meet the causal Estimand requirement of ICH E9R1. 2.Mixing efficacy in subgroups by prevalence, the prevailing practice, can give misleading results also, for any efficacy measured as a ratio. However, mixing relative response (RR) and ratio of median (RoM) survival times by the prognostic effect, the confounding/covert factor hiding in plain sight, will give causal inference in an RCT. 3.Effects in subgroups should not be mixed on the logarithmic scale, because it creates an artificial Estimand for the whole population which changes depending on how the population is divided into subgroups. Current computer package implementations contain all these oversights. Probabilities, including survival curve probabilities, naturally average within each treatment arm by prevalence. The subgroup mixable estimation (SME) principle fixes the oversights by first averaging probabilities (not their logarithms) within each treatment arm, then computing simultaneous confidence intervals for ratio efficacy in subgroups and their mixtures based on rigorous mathematical derivation, to finally provide causal inference in the form of apps.
Keywords: causal inference; collapsibility; logic-respecting efficacy measures; patient targeting; subgroup mixable estimation.
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