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

Virological and Immunological Effects of Combination Antiretroviral Therapy with Zidovudine, Lamivudine, and Indinavir during Primary Human Immunodeficiency Virus Type 1 Infection

Forty-seven patients presenting with primary human immunodeficiency virus (HIV) infection were treated with zidovudine 200 mg 3 times a day, lamivudine 150 mg 2 times a day, and indinavir 800 mg 3 times a day for 1 year. From a mean pretreatment viral RNA level of 4.93 log10 copies/mL, the proportions of patients having <500 copies/mL at 24 and 52 weeks were 92.0% and 89.2%, respectively. For the 35 patients with data available at 24 and 52 weeks, the corresponding proportions for the <50 copies/mL analysis were 86.6% and 79.3%, respectively. The change in virus load was −2.19 and −2.41 log10 copies/mL at weeks 8 and 52, respectively. CD4 cell counts increased, from a mean of 546 cells/mm3, by 142 cells/mm3 at week 24 and by 210 cells/mm3 at week 52. Three patients discontinued the study because of drug-related toxicity. Six (12.8%) patients had adverse experiences associated with nephrolithiasis. Combination therapy with zidovudine, lamivudine, and indinavir during primary HIV infection results in a profound and sustained reduction in virus load with concurrent recovery of the CD4 cell populatio

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