Graph Based, Adaptive, Multiarm, Multiple Endpoint, Two-Stage Designs

Abstract

The graph-based approach to multiple testing is an intuitive method that enables a study team to represent clearly, through a directed graph, its priorities for hierarchical testing of multiple hypotheses, and for propagating the available type-1 error from rejected or dropped hypotheses to hypotheses yet to be tested. Although originally developed for single-stage nonadaptive designs, we show how it may be extended to two-stage designs that permit early identification of efficacious treatments, adaptive sample size re-estimation, dropping of hypotheses, and changes in the hierarchical testing strategy at the end of stage one. Two approaches are available for preserving the familywise error rate in the presence of these adaptive changes, the $p$ value combination method, and the conditional error rate method. In this investigation, we will present the statistical methodology underlying each approach and will compare the operating characteristics of the two methods in a large simulation experiment.

Keywords: MAMS design; adaptive design; combining p $$ p $$ values; conditional error rate; graphs; group sequential; hierarchical testing; multiple endpoints.

FIGURE 1

Example of graph‐based weighting strategy proposed by [8].

FIGURE 2

Impact of selective removal of $H_1$ and $H_2$ from original graph.

FIGURE 3

Graph of Stage Two Testing Strategy for Schizophrenia Trial using CER Method.

FIGURE 4

Graphical representation of design for comparing PVcombo and CER in a trial with four treatment arms and two endpoints. The black arrow indicates the proportion of weight that is reallocated from the primary to the respective secondary hypotheses once the primary hypothesis is rejected. The blue dashed arrows indicate that the remaining weight is re‐allocated to the other primary hypotheses. The orange arrows define that after the rejection of a secondary hypothesis, its weight is reallocated to the other primary hypotheses.

FIGURE 5

Graphical representation of the effect size scenarios considered in the simulation study.

FIGURE 6

Disjunctive power of CER vs Combo by treatment dropping rule and scenario.

FIGURE 7

Conjunctive power of the CER vs Combo method by treatment dropping rule and scenario. For the Ultra Aggressive rule, that selects only a single arm for the second stage, no conjunctive power is reported.