Survival analysis estimation and testing assuming a two component exponential mixture

The test of a mixture mechanism in survival data has fundamental importance in biomedical research. While mixture models for fitting long-term survivors (LTS) have been studied extensively, the mixture model assuming a mixture of two component exponentials with finite means has not been fully examined. An algorithm to compute the MLE's for this model is developed. A simulation study is conducted to analyze the properties of the Likelihood Ratio Test (LRT). The null distribution of LRT for LTS is sensitive to censoring pattern and does not appear to converge to its asymptotic distribution for sample size 500 or less. For proportion of LTS 0.05 or 0.10, sample size 200 has power 0.95 or greater at the 0.01 level for low censoring rates (10% or less). For both exponential and uniform censoring, when censoring rate is higher, power decreases for smaller sample size. The null distribution of LRT for the mixture of two exponentials appears to be p1c20+ 1-p1c2 n1. The fraction of zero LRT's, p&d4;1 , is between 0.19 and 0.25. The mean MLE of degrees of freedom, n&d4;1 , is between 1.70 and 1.99. The 50-50 mixture with greater difference of component means has power near 1 for both censoring patterns and censoring rates. For skewed mixing proportions with greater difference of component means, the power increases with increasing sample size. For smaller difference of component means for both symmetric and skewed mixtures, the power is low for both censoring patterns and censoring rates. Stepwise multiple regression shows that the mixing proportion, difference of two component means and their interaction impact the average LRT value. The mixing proportion, difference of two component means, censoring rate and their interactions affected the power and fraction of zero LRT's. Applications of these models to the remission data from 83 participants in the Suffolk County Mental Health Project (SCMHP) who had bipolar disorder and reported taking mood-stabilizing medications (MS) are presented.