Group-Sequential Analysis Incorporating Covariate Information

Abstract

In this article we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is fitted to accumulating data and provide a unified theory that explains the “independent increments” structure commonly seen in group-sequential test statistics. Our theory covers normal linear models, including the case of correlated observations, and asymptotic results extend to generalized linear models and the proportional hazards regression model for survival data. The asymptotic results are derived using standard methods for the nonsequential case, and they hold as long as these nonsequential techniques are applicable at each individual analysis. In all cases, the joint distribution of the sequence of parameter estimates has the same form, exactly or asymptotically, as that of the sequence of means of an increasing number of independent, identically distributed normal variables. Thus our results provide the formal basis for extending the scope of standard group-sequential methods to a wide range of problems.

Key Words:

• Censored survival data
• Clinical trials
• Counting processes
• General linear model
• Generalized linear model
• Group-sequential testing
• Longitudinal data
• Martingales
• Mixed-effects model
• Proportional hazards regression model
• Repeated measurements
• Score statistics.