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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY We consider graphs, confidence procedures and tests that can be used with censored survival data to compare the hazard experience of a treatment group with that of a control group. In particular, we consider the relative change A(t) in a cumulative rate function which is used to define a generalized proportional hazard model. This model is equivalent to the model obtained by introducing a gamma distributed frailty term in the proportional hazard model. We introduce an estimate A(t) or A(t) based on the Kaplan-Meier and Nelson-Aalen estimates, and obtain the asymptotic distribution of the process A(t) -A(t) appropriately scaled. This result is used to construct asymptotic pointwise confidence intervals for A(t). Under the proportional hazard model assumption, Doob's transformation of Gaussian processes is used to derive asymptotic simultaneous confidence bands for A(t) from a general class of test statistics defined as sup norms of weighted differences between A(t) and its estimate A(t).We also consider procedures based on estimates r(u) of the relative trend function r(u) between cumulative hazards. The methods are illustrated on a data set from a study of the effect of radiation on mice, and on a data set from a study of the effect of tumour size on the survival of cancer patients.Some key words: Confidence band; Cumulative hazard function; Generalized proportional odds ratio model; Proportional hazards model.

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Mixed linear models describe the dependence via random effects in multivariate normal survival data. Recently they have received considerable attention in the biomedical literature. They model the conditional survival times, whereas the alternative frailty model uses the conditional hazard rate. We develop an inferential method for the mixed linear model via Lee and Nelder's (1996) hierarchical-likelihood (h-likelihood). Simulation and a practical example are presented to illustrate the new method.