New parametric model for survival fitting
S.Kulikov
National Center for Hematology, Moscow, Russia
Objectives: To introduce new class of function for survival function fitting and to increase the power of related parametric comparison testing.
Methods: It is common in oncology study publications that survival curves do not tend to the zero and reach a "plateau". For some types of events like remissions, expectation of the time to event can be infinity. That means a finite subset of subjects in whom the investigated event will not occur. In usual parametric survival analysis, only functions with S(∞)=0 are taken into account because of the second Kolmogorov's axiom. The idea of the proposed approach is to reject the demand for "S(∞)=0" . This implies new parametric functions for distribution fitting. Two simple approximation two-parametric functions which have non-zero asymptotic value are introduced. The first evaluated parameter is the "plateau" level. This also is known as cure rate. In practical usage, this value is often of interest as common endpoints of clinical trials, for example, remission rate or long-term survival rate.
Results: Two survival models were proposed:
S(t)=a + (1- a)exp(-t/t) (1) S(t)=a (1- exp(-t/t)) (2)
The first term is a typical exponential function. It describes binary heterogeneous population: with constant and zero hazard rate. The second term is easier to use in the maximum likelihood estimation procedures. It describes the object with time-dependent exponentially dropping hazard function. Geometrically, these two functions are very close but they capture two different failure processes. SAS macros which use NLIN procedure for model parameter estimation were developed to assess their performance. Two model functions were investigated and compared for fitting of simulations data, data of multicentre acute lymphoblast leukemia trials and data of multiple donation frequency.
Conclusion: A new re-parameterization of the survival function was proposed, which a specific algorithm for parameter estimation and tests for comparison. Their relevance in survival data analysis was demonstrated using empirical and simulated datasets.