Abstract
In personalized medicine, it is often desired to determine if all patients or only a subset of them benefit from a treatment. We consider estimation in two-stage adaptive designs that in stage 1 recruit patients from the full population. In stage 2, patient recruitment is restricted to the part of the population, which, based on stage 1 data, benefits from the experimental treatment. Existing estimators, which adjust for using stage 1 data for selecting the part of the population from which stage 2 patients are recruited, as well as for the confirmatory analysis after stage 2, do not consider time to event patient outcomes. In this work, for time to event data, we have derived a new asymptotically unbiased estimator for the log hazard ratio and a new interval estimator with good coverage probabilities and probabilities that the upper bounds are below the true values. The estimators are appropriate for several selection rules that are based on a single or multiple biomarkers, which can be categorical or continuous.
Highlights
Clinical trials in personalized medicine involve assessing whether a patient's characteristic(s), known as biomarkers, can be used to determine their best care
As we expect the same conclusion if the three estimators are extended to time to event data, in this article, we have only extended the uniformly minimum variance conditional unbiased estimator (UMVCUE)
For j ∈ where it is not concluded that θj > 0, the lower bound for θj is θj,L = I⊆{m1,...in,K}{θjI,L}. Note that in this case where at the end of the trial, for some j ∈, it is not concluded that θj > 0, the confidence intervals for the effects in the partitions where it is concluded that the log hazard ratio (HR) are greater than 0 are not informative
Summary
Clinical trials in personalized medicine involve assessing whether a patient's characteristic(s), known as biomarkers, can be used to determine their best care. Time to event patient outcomes are considered in several clinical trials assessing predictive biomarkers.[7,8,9,10] For two-stage adaptive trials, methods for controlling type I error rate and/or increasing power have been developed.[2,3,7] existing point estimators and confidence intervals that adjust for subpopulation selection do not consider time to event data.[4,5,6,11] Li et al[12] quantify the bias of the naive estimator for time to event data but do not derive unbiased estimators. There is a need to develop point and interval estimators for time to event data in two-stage adaptive trials with subpopulation selection. Our point and interval estimators are appropriate for different selection rules and biomarkers of many forms
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