Extending the Quandt Ramsey Modeling to Survival Analysis

The mixture of two regression regimes has been extensively studied in economics. The test of a mixture of regimes in hazard modeling would be seen to have fundamental importance in biostatistical research but has not been studied. A two-regime parametric mixture is proposed to model the effect of a single covariate on the event time. Typically, the Cox proportional hazards model is applied to estimate a single regime survival regression function. The mixture of two regimes model contains five parameters to be estimated; namely, two parameters to describe each regime, and one to describe the mixing proportion. A software program developed for this research finds the maximum likelihood estimates of the parameters and the likelihood ratio test of the null hypothesis of a single regime against the alternative of a mixture of two regimes. A simulation study finds an approximation to the null distribution of the test and its approximate power.