ABSTRACT
Subgroup analysis occurs naturally in personalized medicine. This chapter describes them in the setting of Randomized Controlled Trials (RCTs) for targeted therapies. To personalize medicine is to compare the efficacy of treatment versus control in subgroups and their mixtures. Naturally occurring logical relationships among efficacy in subgroups and their mixtures should be respected. However, for binary and time-to-event outcomes, there has been an oversight in current practice of analyses of efficacy stratified on a biomarker, in that they do not respect such logical relationships. Causes of the illogical analyses are as follows: (a) the use of efficacy measures such as Odds Ratio and Hazard Ratio which are not logic-respecting and (b) incorrect mixing of efficacy measure such as Relative Response (RR) even when they are logic-respecting, due to ignoring the prognostic effect. We show that the path to achieve confident logical inference on efficacy in subgroups and their mixtures is as follows: (1) choose a logic-respecting efficacy measure, (2) model the data and adjust for imbalance using the Least Squares means technique, (3) apply the Subgroup Mixable Estimation principle to infer efficacy in subgroups and their mixtures, which automatically correctly takes the prognostic effect into account.
