Multiplicity adjustments for the Dunnett procedure under heterokcedasticity.

We give a simulation-based method for computing the multiplicity adjusted p-values and critical constants for the Dunnett procedure for comparing treatments with a control under heteroskedasticity. The Welch-Satterthwaite test statistics used in this procedure do not have a simple multivariate t-distribution because their denominators are mixtures of chi-squares and are correlated because of the common control treatment sample variance present in all denominators. The joint distribution of the denominators of the test statistics is approximated by correlated chi-square variables and is generated using a novel algorithm proposed in this paper.

Group sequential Holm and Hochberg procedures.

The problem of testing multiple hypotheses using a group sequential procedure often arises in clinical trials. We review several group sequential Holm (GSHM) type procedures proposed in the literature and clarify the relationships between them. In particular, we show which procedures are equivalent or, if different, which are more powerful and what are their pros and cons.

Advances in p-Value Based Multiple Test Procedures.

In this article we review recent advances in [Formula: see text]-value-based multiple test procedures (MTPs). We begin with a brief review of the basic tests of Bonferroni and Simes. Standard stepwise MTPs derived from them using the closure method of Marcus et al.

A gatekeeping procedure to test a primary and a secondary endpoint in a group sequential design with multiple interim looks.

Glimm et al. (2010) and Tamhane et al. (2010) studied the problem of testing a primary and a secondary endpoint, subject to a gatekeeping constraint, using a group sequential design (GSD) with K=2 looks.

Allocating recycled significance levels in group sequential procedures for multiple endpoints.

Graphical approaches have been proposed in the literature for testing hypotheses on multiple endpoints by recycling significance levels from rejected hypotheses to unrejected ones. Recently, they have been extended to group sequential procedures (GSPs). Our focus in this paper is on the allocation of recycled significance levels from rejected hypotheses to the stages of the GSPs for unrejected hypotheses.

On generalized Simes critical constants.

We consider the problem treated by Simes of testing the overall null hypothesis formed by the intersection of a set of elementary null hypotheses based on ordered p-values of the associated test statistics. The Simes test uses critical constants that do not need tabulation. Cai and Sarkar gave a method to compute generalized Simes critical constants which improve upon the power of the Simes test when more than a few hypotheses are false.

A general multistage procedure for k-out-of-n gatekeeping.

We generalize a multistage procedure for parallel gatekeeping to what we refer to as k-out-of-n gatekeeping in which at least k out of n hypotheses ( 1 ⩽ k ⩽ n) in a gatekeeper family must be rejected in order to test the hypotheses in the following family. This gatekeeping restriction arises in certain types of clinical trials; for example, in rheumatoid arthritis trials, it is required that efficacy be shown on at least three of the four primary endpoints. We provide a unified theory of multistage procedures for arbitrary k, with k = 1 corresponding to parallel gatekeeping and k = n to serial gatekeeping.

General theory of mixture procedures for gatekeeping.

The paper introduces a general approach to constructing mixture-based gatekeeping procedures in multiplicity problems with two or more families of hypotheses. Mixture procedures serve as extensions of and overcome limitations of some previous gatekeeping approaches such as parallel gatekeeping and tree-structured gatekeeping. This paper offers a general theory of mixture procedures constructed from nonparametric (p-value based) to parametric (normal theory based) procedures and studies their properties.

Adaptive extensions of a two-stage group sequential procedure for testing primary and secondary endpoints (II): sample size re-estimation.

In this part II of the paper on adaptive extensions of a two-stage group sequential procedure (GSP) for testing primary and secondary endpoints, we focus on the second stage sample size re-estimation based on the first stage data. First, we show that if we use the Cui-Huang-Wang statistics at the second stage, then we can use the same primary and secondary boundaries as for the original procedure (without sample size re-estimation) and still control the type I familywise error rate. This extends their result for the single endpoint case.

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

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.

A mixture gatekeeping procedure based on the Hommel test for clinical trial applications.

When conducting clinical trials with hierarchically ordered objectives, it is essential to use multiplicity adjustment methods that control the familywise error rate in the strong sense while taking into account the logical relations among the null hypotheses. This paper proposes a gatekeeping procedure based on the Hommel (1988) test, which offers power advantages compared to other p value-based tests proposed in the literature. A general description of the procedure is given and details are presented on how it can be applied to complex clinical trial designs.

Multistage and mixture parallel gatekeeping procedures in clinical trials.

Gatekeeping procedures have been developed to solve multiplicity problems arising in clinical trials with hierarchical objectives where the null hypotheses that address these objectives are grouped into ordered families. A general method for constructing multistage parallel gatekeeping procedures was proposed by Dmitrienko et al. (2008).

Mixtures of multiple testing procedures for gatekeeping applications in clinical trials.

This paper proposes a general framework for constructing gatekeeping procedures for clinical trials with hierarchical objectives. Such problems frequently exhibit complex structures including multiple families of hypotheses and logical restrictions. The proposed framework is based on combining multiple procedures across families.

Testing a primary and a secondary endpoint in a group sequential design.

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.

Superiority inferences on individual endpoints following noninferiority testing in clinical trials.

We consider the problem of drawing superiority inferences on individual endpoints following non-inferiority testing. Röhmel et al. (2006) pointed out this as an important problem which had not been addressed by the previous procedures that only tested for global superiority.

General multistage gatekeeping procedures.

A general multistage (stepwise) procedure is proposed for dealing with arbitrary gatekeeping problems including parallel and serial gatekeeping. The procedure is very simple to implement since it does not require the application of the closed testing principle and the consequent need to test all nonempty intersections of hypotheses. It is based on the idea of carrying forward the Type I error rate for any rejected hypotheses to test hypotheses in the next ordered family.

A note on tree gatekeeping procedures in clinical trials.

Dmitrienko et al. (Statist. Med.

Gatekeeping procedures with clinical trial applications.

The objective of this paper is to give an overview of a relatively new area of multiplicity research that deals with the analysis of hierarchically ordered multiple objectives. Testing procedures for this problem are known as gatekeeping procedures and have found a variety of applications in clinical trials. This paper reviews main classes of these procedures, including serial and parallel gatekeeping procedures, and tree gatekeeping procedures that account for logical restrictions among multiple objectives.

Stepwise gatekeeping procedures in clinical trial applications.

This paper discusses multiple testing problems in which families of null hypotheses are tested in a sequential manner and each family serves as a gatekeeper for the subsequent families. Gatekeeping testing strategies of this type arise frequently in clinical trials with multiple objectives, e.g.

Tree-structured gatekeeping tests in clinical trials with hierarchically ordered multiple objectives.

This paper discusses a new class of multiple testing procedures, tree-structured gatekeeping procedures, with clinical trial applications. These procedures arise in clinical trials with hierarchically ordered multiple objectives, for example, in the context of multiple dose-control tests with logical restrictions or analysis of multiple endpoints. The proposed approach is based on the principle of closed testing and generalizes the serial and parallel gatekeeping approaches developed by Westfall and Krishen (J.

Finding the maximum safe dose level for heteroscedastic data.

In this article we extend to the heteroscedastic setting the multiple stepwise test procedures proposed in Tamhane et al. [Tamhane. A.

Accurate critical constants for the one-sided approximate likelihood ratio test of a normal mean vector when the covariance matrix is estimated.

Tang, Gnecco, and Geller (1989, Biometrika 76, 577-583) proposed an approximate likelihood ratio (ALR) test of the null hypothesis that a normal mean vector equals a null vector against the alternative that all of its components are nonnegative with at least one strictly positive. This test is useful for comparing a treatment group with a control group on multiple endpoints, and the data from the two groups are assumed to follow multivariate normal distributions with different mean vectors and a common covariance matrix (the homoscedastic case). Tang et al.