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SMOOTHING COVARIATE EFFECTS IN CURE MODELS

ABSTRACT Cure models are a useful approach in survival analysis when a fraction of the population is not susceptible to the event of interest. A mixture model formulation allows separate consideration of whether the event will eventually occur, termed incidence, and when the event will occur given the individual is susceptible, termed latency. In this paper, we propose a flexible semi-parametric cure model. In the model the latency distribution is non-parametrically specified, and covariates can affect the incidence probability through a non-linear generalized additive model. An EM algorithm, applied to a penalized likelihood, is developed to fit the model. Likelihood ratio tests are developed to test for non-linearity. The proposed methodology is applied to a data set of tonsil cancer patients treated with radiation therapy to evaluate the effects of dose and treatment time on the probability of local recurrence. The estimation and testing procedures are evaluated in a Monte Carlo simulation study. The simulation results suggest that the procedure can estimate the non-linearity and that the likelihood ratio test is effective in detecting departures from linearity.