Pocock boundary

About: Pocock boundary is a research topic. Over the lifetime, 12 publications have been published within this topic receiving 4436 citations.

A multiple testing procedure for clinical trials.

Abstract: A multiple testing procedure is proposed for comparing two treatments when response to treatment is both dichotomous (i.e., success or failure) and immediate. The proposed test statistic for each test is the usual (Pearson) chi-square statistic based on all data collected to that point. The maximum number (N) of tests and the number (m1 + m2) of observations collected between successive tests is fixed in advance. The overall size of the procedure is shown to be controlled with virtually the same accuracy as the single sample chi-square test based on N(m1 + m2) observations. The power is also found to be virtually the same. However, by affording the opportunity to terminate early when one treatment performs markedly better than the other, the multiple testing procedure may eliminate the ethical dilemmas that often accompany clinical trials.

Group sequential methods in the design and analysis of clinical trials

Abstract: SUMMARY In clinical trials with sequential patient entry, fixed sample size designs are unjustified on ethical grounds and sequential designs are often impracticable. One solution is a group sequential design dividing patient entry into a number of equal-sized groups so that the decision to stop the trial or continue is based on repeated significance tests of the accumulated data after each group is evaluated. Exact results are obtained for a trial with two treatments and a normal response with known variance. The design problem of determining the required size and number of groups is also considered. Simulation shows that these normal results may be adapted to other types of response data. An example shows that group sequential designs can sometimes be statistically superior to standard sequential designs.

Continuous Toxicity Monitoring in Phase II Trials in Oncology

Abstract: The goal of a phase II trial in oncology is to evaluate the efficacy of a new therapy The dose investigated in a phase II trial is usually an estimate of a maximum-tolerated dose obtained in a preceding phase I trial Because this estimate is imprecise, stopping rules for toxicity are used in many phase II trials We give recommendations on how to construct stopping rules to monitor toxicity continuously A table is provided from which Pocock stopping boundaries can be easily obtained for a range of toxicity rates and sample sizes Estimation of the probability of toxicity and response is also discussed

Testing a Primary and a Secondary Endpoint in a Group Sequential Design

Abstract: We consider a clinical trial with a primary and a secondary endpoint where the secondary endpoint is tested only if the primary endpoint is significant The trial uses a group sequential procedure with two stages The familywise error rate (FWER) of falsely concluding significance on either endpoint is to be controlled at a nominal level α The type I error rate for the primary endpoint is controlled by choosing any α-level stopping boundary, eg, the standard O'Brien-Fleming or the Pocock boundary Given any particular α-level boundary for the primary endpoint, we study the problem of determining the boundary for the secondary endpoint to control the FWER We study this FWER analytically and numerically and find that it is maximized when the correlation coefficient ρ between the two endpoints equals 1 For the four combinations consisting of O'Brien-Fleming and Pocock boundaries for the primary and secondary endpoints, the critical constants required to control the FWER are computed for different values of ρ An ad hoc boundary is proposed for the secondary endpoint to address a practical concern that may be at issue in some applications Numerical studies indicate that the O'Brien-Fleming boundary for the primary endpoint and the Pocock boundary for the secondary endpoint generally gives the best primary as well as secondary power performance The Pocock boundary may be replaced by the ad hoc boundary for the secondary endpoint with a very little loss of secondary power if the practical concern is at issue A clinical trial example is given to illustrate the methods

Adaptive extensions of a two-stage group sequential procedure for testing primary and secondary endpoints (I): unknown correlation between the endpoints.

Abstract: In a previous paper we studied a two-stage group sequential procedure (GSP) for testing primary and secondary endpoints where the primary endpoint serves as a gatekeeper for the secondary endpoint. We assumed a simple setup of a bivariate normal distribution for the two endpoints with the correlation coefficient ρ between them being either an unknown nuisance parameter or a known constant. Under the former assumption, we used the least favorable value of ρ = 1 to compute the critical boundaries of a conservative GSP. Under the latter assumption, we computed the critical boundaries of an exact GSP. However, neither assumption is very practical. The ρ = 1 assumption is too conservative resulting in loss of power, whereas the known ρ assumption is never true in practice. In this part I of a two-part paper on adaptive extensions of this two-stage procedure (part II deals with sample size re-estimation), we propose an intermediate approach that uses the sample correlation coefficient r from the first-stage data to adaptively adjust the secondary boundary after accounting for the sampling error in r via an upper confidence limit on ρ by using a method due to Berger and Boos. We show via simulation that this approach achieves 5–11% absolute secondary power gain for ρ ≤0.5. The preferred boundary combination in terms of high primary as well as secondary power is that of O'Brien and Fleming for the primary and of Pocock for the secondary. The proposed approach using this boundary combination achieves 72–84% relative secondary power gain (with respect to the exact GSP that assumes known ρ). We give a clinical trial example to illustrate the proposed procedure. Copyright © 2012 John Wiley & Sons, Ltd.