Efficient design and inference for multistage randomized trials of individualized treatment policies.

Clinical demand for individualized "adaptive" treatment policies in diverse fields has spawned development of clinical trial methodology for their experimental evaluation via multistage designs, building upon methods intended for the analysis of naturalistically observed strategies. Because often there is no need to parametrically smooth multistage trial data (in contrast to observational data for adaptive strategies), it is possible to establish direct connections among different methodological approaches. We show by algebraic proof that the maximum likelihood (ML) and optimal semiparametric (SP) estimators of the population mean of the outcome of a treatment policy and its standard error are equal under certain experimental conditions. This result is used to develop a unified and efficient approach to design and inference for multistage trials of policies that adapt treatment according to discrete responses. We derive a sample size formula expressed in terms of a parametric version of the optimal SP population variance. Nonparametric (sample-based) ML estimation performed well in simulation studies, in terms of achieved power, for scenarios most likely to occur in real studies, even though sample sizes were based on the parametric formula. ML outperformed the SP estimator; differences in achieved power predominately reflected differences in their estimates of the population mean (rather than estimated standard errors). Neither methodology could mitigate the potential for overestimated sample sizes when strong nonlinearity was purposely simulated for certain discrete outcomes; however, such departures from linearity may not be an issue for many clinical contexts that make evaluation of competitive treatment policies meaningful.