Bias in estimating association parameters for longitudinal binary responses with drop-outs

This paper considers the impact of bias in the estimation of the association parameters for longitudinal binary responses when there are drop-outs. A number of different estimating equation approaches are considered for the case where drop-out cannot be assumed to be a completely random process. In particular, standard generalized estimating equations (GEE), GEE based on conditional residuals, GEE based on multivariate normal estimating equations for the covariance matrix, and second-order estimating equations (GEE2) are examined. These different GEE estimators are compared in terms of finite sample and asymptotic bias under a variety of drop-out processes. Finally, the relationship between bias in the estimation of the association parameters and bias in the estimation of the mean parameters is explored.     

Flexible implementations of group sequential stopping rules using constrained boundaries

Group sequential stopping rules are often used during the conduct of clinical trials in order to attain more ethical treatment of patients and to better address efficiency concerns. Because the use of such stopping rules materially affects the frequentist operating characteristics of the hypothesis test, it is necessary to choose an appropriate stopping rule during the planning of the study. It is often the case, however, that the number and timing of interim analyses are not precisely known at the time of trial design, and thus the implementation of a particular stopping rule must allow for flexible determination of the schedule of interim analyses. In this article, we consider the use of constrained stopping boundaries in the implementation of stopping rules. We compare this approach when used on various scales for the test statistic. When implemented on the scale of boundary crossing probabilities, this approach is identical to the error spending function approach of Lan and DeMets (1983).     

P-value adjustment in sequential clinical trials

Many randomized clinical trials utilize a group sequential monitoring procedure for assessing treatment efficacy during the course of the trial. For a group sequential trial in which the null hypothesis is ultimately rejected, the nominal p-value generally overstates the statistical significance of the result and some adjustment is required. Several orderings of the sample space have been proposed for performing this adjustment, each with unique operating characteristics. In this article, we compare four proposed methods with respect to the degree to which each captures the strength of evidence against the null hypothesis implied by the data. We conclude that the ordering of the sample space induced by the observed z-score has the most desirable operating characteristics.     

Generalized linear mixture models for handling nonignorable dropouts in longitudinal studies

This paper presents a method for analysing longitudinal data when there are dropouts. In particular, we develop a simple method based on generalized linear mixture models for handling nonignorable dropouts for a variety of discrete and continuous outcomes. Statistical inference for the model parameters is based on a generalized estimating equations (GEE) approach (Liang and Zeger, 1986). The proposed method yields estimates of the model parameters that are valid when nonresponse is nonignorable under a variety of assumptions concerning the dropout process. Furthermore, the proposed method can be implemented using widely available statistical software. Finally, an example using data from a clinical trial of contracepting women is used to illustrate the methodology.     

A homogeneity test in overviews with group sequentially monitored clinical trials

It is known that using statistical stopping rules in clinical trials can create an artificial heterogeneity of treatment effects in overviews of related trials (Hughes, Freedman, and Pocock, 1992, Biometrics 48, 41-53). If the true treatment effect being tested is small, as is often the case, the homogeneity test by DerSimonian and Laird (1986, Controlled Clinical Trials 7, 177-188) violates the size of the test very severely. This paper provides a new homogeneity test, which preserves the size of the test more accurately. The operating characteristics of the new test are examined through simulations.