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unconstrained. A simultaneous confidence region for the two median survival times, adjusted to any selected value, z, of the covariate vector is generated using a test-based approach analogous to Brookrneyer and Crowley 's for the one-sample case. This region is, in turn, used to derive a confidence interval for the difference in median survival times between the two treatment groups at the selected value of z. A procedure suggested by Aitchison (1964) is employed to set the level of the simultaneous region to a value that should yield, at least approximately, the desired confidence coefficient for the difference in medians. Simulation studies indicate that the method provides reasonably accurate coverage probabilities. The methods are illustrated using data from a clinical trial conducted by the Radiation Therapy Oncology Group in cancer of the mouth and throat.

29A THE USE O F POISSON R E G R E S S I O N M E T H O D S IN C L I N I C A L TRIALS

Desmond Thompson Merck and Company Rahway, New Jersey

In clinical trials, patients are normally seen at specific times and hence the events of interest are usually assumed to occur at these visit times. Standard lifetable methods are used to compare the treatment groups, and the logrank statistic is reported. In many cases however, the interest is in the relative risk or the reduction of the absolute risk as a function of time or some other covariate. These "discrete" data lend themselves to grouped data analyses. Discrete model regression models that can be employed in this context include logistic regression, complementary log-log link and Poisson regression models. The use of Poisson regression methods for cohort data has been discussed by Breslow & Day (1986), Preston et al (1984), Frome (1983), Laird and Oliver (1981). Most of the basic models can be fitted using SAS or BMDP. However, we will describe a program (AMFIT) that was designed to model rates for grouped survival data. Risks may be modeled directly (absolute risk models) or relative to some baseline (relative risk model). Models included are the product additive model, the additive model and the geometric mixture model. AMFIT is fundamentally a Poisson regression program although its design is based upon the use of these models for analyses of grouped cohort follow-up data. The approach is based on approximation of the underlying hazard function as piecewise constant of fixed time intervals. The analysis is closely related to the partial likelihood method. We will describe methods in which the full hazard function can be modeled directly. These methods of analyses allows for analyses different from those based on partial likelihood methods. The method can be viewed as a convenient approximation to Cox regression when the original data are grouped into discrete intervals. For grouped data, the cohort experience is normally summarized in a cross-classification with one factor being intervals of time and the other factors determined from a cross classification over covariates values. While such tables usually involve complex calculations, we will describe a program (DATAB) in which they can be carried out easily an effectively.