CAPITAL: Optimal Subgroup Identification via Constrained Policy Tree Search

Personalized medicine, a paradigm of medicine tailored to a patient's characteristics, is an increasingly attractive field in health care. An important goal of personalized medicine is to identify a subgroup of patients, based on baseline covariates, that benefits more from the targeted treatment than other comparative treatments. Most of the current subgroup identification methods only focus on obtaining a subgroup with an enhanced treatment effect without paying attention to subgroup size. Yet, a clinically meaningful subgroup learning approach should identify the maximum number of patients who can benefit from the better treatment. In this paper, we present an optimal subgroup selection rule (SSR) that maximizes the number of selected patients, and in the meantime, achieves the pre-specified clinically meaningful mean outcome, such as the average treatment effect. We derive two equivalent theoretical forms of the optimal SSR based on the contrast function that describes the treatment-covariates interaction in the outcome. We further propose a ConstrAined PolIcy Tree seArch aLgorithm (CAPITAL) to find the optimal SSR within the interpretable decision tree class. The proposed method is flexible to handle multiple constraints that penalize the inclusion of patients with negative treatment effects, and to address time to event data using the restricted mean survival time as the clinically interesting mean outcome. Extensive simulations, comparison studies, and real data applications are conducted to demonstrate the validity and utility of our method

Principal Stratum Strategy: Potential Role in Drug Development

A randomized trial allows estimation of the causal effect of an intervention compared to a control in the overall population and in subpopulations defined by baseline characteristics. Often, however, clinical questions also arise regarding the treatment effect in subpopulations of patients, which would experience clinical or disease related events post-randomization. Events that occur after treatment initiation and potentially affect the interpretation or the existence of the measurements are called {\it intercurrent events} in the ICH E9(R1) guideline. If the intercurrent event is a consequence of treatment, randomization alone is no longer sufficient to meaningfully estimate the treatment effect. Analyses comparing the subgroups of patients without the intercurrent events for intervention and control will not estimate a causal effect. This is well known, but post-hoc analyses of this kind are commonly performed in drug development. An alternative approach is the principal stratum strategy, which classifies subjects according to their potential occurrence of an intercurrent event on both study arms. We illustrate with examples that questions formulated through principal strata occur naturally in drug development and argue that approaching these questions with the ICH E9(R1) estimand framework has the potential to lead to more transparent assumptions as well as more adequate analyses and conclusions. In addition, we provide an overview of assumptions required for estimation of effects in principal strata. Most of these assumptions are unverifiable and should hence be based on solid scientific understanding. Sensitivity analyses are needed to assess robustness of conclusions

CauchyCP: a powerful test under non-proportional hazards using Cauchy combination of change-point Cox regressions

Non-proportional hazards data are routinely encountered in randomized clinical trials. In such cases, classic Cox proportional hazards model can suffer from severe power loss, with difficulty in interpretation of the estimated hazard ratio since the treatment effect varies over time. We propose CauchyCP, an omnibus test of change-point Cox regression models, to overcome both challenges while detecting signals of non-proportional hazards patterns. Extensive simulation studies demonstrate that, compared to existing treatment comparison tests under non-proportional hazards, the proposed CauchyCP test 1) controls the type I error better at small $\alpha$ levels ($< 0.01$); 2) increases the power of detecting time-varying effects; and 3) is more computationally efficient. The superior performance of CauchyCP is further illustrated using retrospective analyses of two randomized clinical trial datasets and a pharmacogenetic biomarker study dataset. The R package $\textit{CauchyCP}$ is publicly available on CRAN

On power and sample size computation for multiple testing procedures

Power and sample size determination has been a challenging issue for multiple testing procedures, especially stepwise procedures, mainly because (1) there are several power definitions, (2) power calculation usually requires multivariate integration involving order statistics, and (3) expansion of these power expressions in terms of ordinary statistics, instead of order statistics, is generally a difficult task. Traditionally power and sample size calculations rely on either simulations or some recursive algorithm; neither is straightforward and computationally economic. In this paper we develop explicit formulas for minimal power and r-power of stepwise procedures as well as complete power of single-step procedures for exchangeable and non-exchangeable bivariate and trivariate test statistics. With the explicit power expressions, we were able to directly calculate the desired power, given sample size and correlation. Numerical examples are presented to illustrate the relationship among power, sample size and correlation.Power Sample size Correlation Multiple tests Order statistics