Subgroup selection in adaptive signature designs of confirmatory clinical trials

The increasing awareness of treatment effect heterogeneity has motivated flexible designs of confirmatory clinical trials that prospectively allow investigators to test for treatment efficacy for a subpopulation of patients in addition to the entire population. If a target subpopulation is not well characterized in the design stage, it can be developed at the end of a broad eligibility trial under an adaptive signature design. The paper proposes new procedures for subgroup selection and treatment effect estimation (for the selected subgroup) under an adaptive signature design. We first provide a simple and general characterization of the optimal subgroup that maximizes the power for demonstrating treatment efficacy or the expected gain based on a specified utility function. This characterization motivates a procedure for subgroup selection that involves prediction modelling, augmented inverse probability weighting and low dimensional maximization. A cross-validation procedure can be used to remove or reduce any resubstitution bias that may result from subgroup selection, and a bootstrap procedure can be used to make inference about the treatment effect in the subgroup selected. The approach proposed is evaluated in simulation studies and illustrated with real examples

Sensitivity analysis in non-inferiority trials with residual inconstancy after covariate adjustment

A major issue in non-inferiority trials is the controversial assumption of constancy, namely that the active control has the same effect relative to placebo as in previous studies comparing the active control with placebo. The constancy assumption is often in doubt, which has motivated various methods that ‘discount’ the control effect estimate from historical data as well as methods that adjust for imbalances in observed covariates. We develop a new approach to deal with residual inconstancy, i.e. possible violations of the constancy assumption due to imbalances in unmeasured covariates after adjusting for the measured covariates. We characterize the extent of residual inconstancy under a generalized linear model framework and use the results to obtain fully adjusted estimates of the control effect in the current study based on plausible assumptions about an unmeasured covariate. Because such assumptions may be difficult to justify, we propose a sensitivity analysis approach that covers a range of situations. This approach is developed for indirect comparison with placebo and effect retention, and implemented through additive and multiplicative adjustments.The approach proposed is applied to two examples concerning benign prostate hyperplasia and human immunodeficiency virus infection, and evaluated in simulation studies.Keywords: Active control, Effect retention, Putative placebo, Discounting, Conditional effect, Constanc

Large sample theory of empirical distributions in a window censoring model for renewal processes.

In reliability or medical studies, we may only observe each ongoing renewal process for a certain period of time, and therefore, the observations are "window censored". In general, the nonparametric maximum likelihood estimator (hereafter the NPMLE) does not exist for this problem. Vardi devised the RT algorithm for finding the NPMLE restricted to a compact support (M-restricted MLE). Here a slightly different approach is proposed and the algorithm is modified to seek the NPMLE in a larger space. It is shown that the modified algorithm converges monotonically in likelihood and all its limit points are fixed points. It is also shown that for equal observation periods, the NPMLE is unique and is given by the algorithm. There are four types of observations involved in this problem: uncensored, right censored, left censored and doubly censored. The four types of observations are dependent and follow different distributions. To investigate the asymptotic properties of the estimators, first we studied the properties of the empirical processes induced by them. Some laws of large numbers are proved and some distributional properties are derived. Uniform consistency of the estimators for fixed observation periods is proved through the uniqueness of the solution for the score equation, by showing certain contraction properties of the equation. A simulation study shows that some problems with bias may occur. Specifically, the tail probability is typically inflated by the NPMLE. To correct this problem, we propose "Step estimators", which are based on the RT algorithm, but with a prescribed initial estimator to start. The uniform consistency and distributional theory are fully investigated for these estimators. Unlike the typical censored data case, the weak convergences of these estimators do not hold in uniform metric. A weight function has to be introduced.Ph.D.StatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/104707/1/9542961.pdfDescription of 9542961.pdf : Restricted to UM users only

ZhangBoPHHSSensitivityAnalysisNon-Inferiority_SupportingInformation.pdf

A major issue in non-inferiority trials is the controversial assumption of constancy, namely that the active control has the same effect relative to placebo as in previous studies comparing the active control with placebo. The constancy assumption is often in doubt, which has motivated various methods that ‘discount’ the control effect estimate from historical data as well as methods that adjust for imbalances in observed covariates. We develop a new approach to deal with residual inconstancy, i.e. possible violations of the constancy assumption due to imbalances in unmeasured covariates after adjusting for the measured covariates. We characterize the extent of residual inconstancy under a generalized linear model framework and use the results to obtain fully adjusted estimates of the control effect in the current study based on plausible assumptions about an unmeasured covariate. Because such assumptions may be difficult to justify, we propose a sensitivity analysis approach that covers a range of situations. This approach is developed for indirect comparison with placebo and effect retention, and implemented through additive and multiplicative adjustments.The approach proposed is applied to two examples concerning benign prostate hyperplasia and human immunodeficiency virus infection, and evaluated in simulation studies.Keywords: Constancy, Effect retention, Conditional effect, Putative placebo, Discounting, Active controlKeywords: Constancy, Effect retention, Conditional effect, Putative placebo, Discounting, Active controlKeywords: Constancy, Effect retention, Conditional effect, Putative placebo, Discounting, Active controlKeywords: Constancy, Effect retention, Conditional effect, Putative placebo, Discounting, Active contro

ZhangBoPHHSSensitivityAnalysisNon-Inferiority.pdf

A major issue in non-inferiority trials is the controversial assumption of constancy, namely that the active control has the same effect relative to placebo as in previous studies comparing the active control with placebo. The constancy assumption is often in doubt, which has motivated various methods that ‘discount’ the control effect estimate from historical data as well as methods that adjust for imbalances in observed covariates. We develop a new approach to deal with residual inconstancy, i.e. possible violations of the constancy assumption due to imbalances in unmeasured covariates after adjusting for the measured covariates. We characterize the extent of residual inconstancy under a generalized linear model framework and use the results to obtain fully adjusted estimates of the control effect in the current study based on plausible assumptions about an unmeasured covariate. Because such assumptions may be difficult to justify, we propose a sensitivity analysis approach that covers a range of situations. This approach is developed for indirect comparison with placebo and effect retention, and implemented through additive and multiplicative adjustments.The approach proposed is applied to two examples concerning benign prostate hyperplasia and human immunodeficiency virus infection, and evaluated in simulation studies.Keywords: Putative placebo, Conditional effect, Discounting, Active control, Effect retention, ConstancyKeywords: Putative placebo, Conditional effect, Discounting, Active control, Effect retention, Constanc