Sequential Testing with Recurrent Events over Multiple Treatment Periods

Nonparametric group sequential methods for recurrent and terminal events from multiple follow-up windows

Few methods are currently available for group sequential analysis of recurrent events data subject to a terminal event in the clinical trial setting. This research helps fill this gap by developing a completely nonparametric group sequential monitoring procedure for use with the two-sample Tayob and Murray statistic. Advantages of the Tayob and Murray statistic include high power to detect treatment differences when there is correlation between recurrent event times or between recurrent and terminal events in an individual. This statistic does not suffer bias from dependent censoring, regardless of the correlation between event times in an individual. This manuscript briefly reviews the Tayob and Murray statistic, develops and describes how to use methods for its group sequential analysis, and through simulation, compares its operating characteristics with those of Cook and Lawless, which is currently in use as the only available nonparametric method for group sequential analysis of recurrent event data. The merits of our proposed approach are most clearly demonstrated when gap times between recurrent events are correlated; when gap times between events are independent, the Cook and Lawless method is difficult to beat. Simulations demonstrate that as correlation between recurrent event times grows, the reduction in power using the Cook and Lawless approach is substantial when compared to our method. Finally, we use our method to analyze recurrent acute exacerbation outcomes from the azithromycin in chronic obstructive pulmonary disease trial.

Exact group sequential designs for two-arm experiments with Poisson distributed outcome variables

We describe and compare two methods for the group sequential design of two-arm experiments with Poisson distributed data, which are based on a normal approximation and exact calculations respectively. A framework to determine near-optimal stopping boundaries is also presented. Using this framework, for a considered example, we demonstrate that a group sequential design could reduce the expected sample size under the null hypothesis by as much as 44% compared to a fixed sample approach. We conclude with a discussion of the advantages and disadvantages of the two presented procedures.

Group sequential designs with robust semiparametric recurrent event models

Robust semiparametric models for recurrent events have received increasing attention in the analysis of clinical trials in a variety of diseases including chronic heart failure. In comparison to parametric recurrent event models, robust semiparametric models are more flexible in that neither the baseline event rate nor the process inducing between-patient heterogeneity needs to be specified in terms of a specific parametric statistical model. However, implementing group sequential designs in the robust semiparametric model is complicated by the fact that the sequence of Wald statistics does not follow asymptotically the canonical joint distribution. In this manuscript, we propose two types of group sequential procedures for a robust semiparametric analysis of recurrent events. The first group sequential procedure is based on the asymptotic covariance of the sequence of Wald statistics and it guarantees asymptotic control of the type I error rate. The second procedure is based on the canonical joint distribution and does not guarantee asymptotic type I error rate control but is easy to implement and corresponds to the well-known standard approach for group sequential designs. Moreover, we describe how to determine the maximum information when planning a clinical trial with a group sequential design and a robust semiparametric analysis of recurrent events. We contrast the operating characteristics of the proposed group sequential procedures in a simulation study motivated by the ongoing phase 3 PARAGON-HF trial (ClinicalTrials.gov identifier: NCT01920711) in more than 4600 patients with chronic heart failure and a preserved ejection fraction. We found that both group sequential procedures have similar operating characteristics and that for some practically relevant scenarios, the group sequential procedure based on the canonical joint distribution has advantages with respect to the control of the type I error rate. The proposed method for calculating the maximum information results in appropriately powered trials for both procedures.

Group sequential designs for negative binomial outcomes

Count data and recurrent events in clinical trials, such as the number of lesions in magnetic resonance imaging in multiple sclerosis, the number of relapses in multiple sclerosis, the number of hospitalizations in heart failure, and the number of exacerbations in asthma or in chronic obstructive pulmonary disease (COPD) are often modeled by negative binomial distributions. In this manuscript, we study planning and analyzing clinical trials with group sequential designs for negative binomial outcomes. We propose a group sequential testing procedure for negative binomial outcomes based on Wald statistics using maximum likelihood estimators. The asymptotic distribution of the proposed group sequential test statistics is derived. The finite sample size properties of the proposed group sequential test for negative binomial outcomes and the methods for planning the respective clinical trials are assessed in a simulation study. The simulation scenarios are motivated by clinical trials in chronic heart failure and relapsing multiple sclerosis, which cover a wide range of practically relevant settings. Our research assures that the asymptotic normal theory of group sequential designs can be applied to negative binomial outcomes when the hypotheses are tested using Wald statistics and maximum likelihood estimators. We also propose two methods, one based on Student's t-distribution and one based on resampling, to improve type I error rate control in small samples. The statistical methods studied in this manuscript are implemented in the R package gscounts, which is available for download on the Comprehensive R Archive Network (CRAN).