Subgroup mixable inference on treatment efficacy in mixture populations, with an application to time-to-event...

In tailored drug development, the patient population is thought of as a mixture of two or more subgroups that may derive differential treatment efficacy. To find the right patient population for the drug to target, it is necessary to infer treatment efficacy in subgroups and combinations of subgroups. A fundamental consideration in this inference process is that the logical relationships between treatment efficacy in subgroups and their combinations should be respected (for otherwise the assessment of treatment efficacy may become paradoxical). We show that some commonly used efficacy measures are not suitable for a mixture population. We also show that the current practice of over-simply extending the least squares means concept when estimating the efficacy in a mixture population is inappropriate. Proposing a new principle called subgroup mixable estimation, we establish the logical relationships among parameters that represent efficacy and develop a simultaneous inference procedure to confidently infer efficacy in subgroups and their combinations. Using oncology studies with time-to-event outcomes as an example, we show that the hazard ratio is not suitable for measuring treatment efficacy in a mixture population and provide appropriate efficacy measures with a rigorous inference procedure.