Group Sequential Analysis Incorporating Covariate Information

In this paper we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is tted to accumulating data and we provide a uniied theory which 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 non-sequential case and they hold as long as these non-sequential 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.