description) Most analyses involving survival data are performed using non-parametric methods. Survival probabilities as a function of time are using the method of Kaplan and Meier; comparisons of survival curves are made using a linear test such as Gehan's test or the log rank test. This tendency results in the fact that the exponential function, which plays a central role in survival analysis, clearly fails to fit the data that is often seen. Other more complicated distribu-tions, such as the Weibull, do no better. In particular, these distributions do not allow for the horizontal asymptote or """"""""plateau"""""""" frequently observed. Such """"""""plateaus"""""""" indicate the existence of a non-zero proportion of indefinite survivors or """"""""cures. The use of non-metric alternatives, while producing unbiased estimators and valid tests, have two major shortcomings: 1) Estimates will not be as precise or tests as powerful as the corresponding parametric estimates and tests. 2) Important questions concerning the proportion cured cannot be addressed by non-parametric analyses. However, such questions can be addressed by analyses based on models having that cure rate as a parameter. This proposed research project will study a parametric model for survival that allows for cures. This model, which is defined by the Gompertz function, provides an excellent fit for data seen in pediatric oncology studies. Although it contains two parameters, their estimation requires the solution of only one equation and is easily and reliably accomplished. By using this model, researchers will be able to estimate and compare cure rates. It is expected that such estimates will be more and comparative tests more powerful than the non-parametric alternatives. In addition, a test for the goodness of this model will be developed and applied to a large number of treatment groups from studies previously conducted by the Pediatric Oncology Group. A linear rank test which should have greater power than the log rank test under the Gompertz model will also be proposed and its properties studied.
