Semiparametric Transformation Models for Survival Data with a Cure Fraction

We propose a class of transformation models for survival data with a cure fraction. The class of transformation models is motivated by biological considerations, and it includes both the proportional hazards and the proportional odds cure models as two special cases. An efficient recursive algorithm is proposed to calculate the maximum likelihood estimators. Furthermore, the maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal, and their asymptotic variances attain the semiparametric efficiency bound. Simulation studies are conducted to examine the finite sample properties of the proposed estimators. The method is illustrated on data from a clinical trial involving the treatment of melanoma.