Penalized Splines in the Time Varying Coefficient Rates Model

Methods have been proposed to explore the functional form of effects using splines with moderate number of knots, with parameters being estimated using penalized partial likelihoods in survival models. Research has also been conducted for development of estimation methods of means/rates of recurrent events. We propose a method that uses B-splines with small to moderate number of knots to estimate time-varying effects in the marginal rates model with estimation based on penalized partial likelihood. The proposed method is used to describe the functional form of the effect of vitamin A supplementation on the rate of recurrent diarrheal episodes and acute respiratory infections in small chidren from Brazil. Simulation studies examined the finite-sample properties of the proposed parameter estimators.