Parameter Estimation for Additive Hazard Model Recurrent Event Using Counting Process Approach

Abstract

The Cox regression model is widely used for survival data analysis. The Cox model requires a proportional hazard. If the proportional hazard assumption is doubtful, then the additive hazard model can be used, where the covariates act in an additively to the baseline hazard function. If the observed survival time is more than once for one individual during the observation, it is called a recurrent event. The additive hazard model measures risk difference to the effect of a covariate in absolutely, while the proportional hazards model measure hazard ratio in relatively. The risk coefficients estimation in the additive hazard model mimics the multiplicative hazard model, using partial likelihood methods. The derivation of these estimators, outlined in the technical notes, is based on the counting process approach. The counting process approach was first developed by Aalen on 1975 which combines elements of stochastic integration, martingale theory and counting process theory. The method is applied to study about the effect of supplementation on infant growth and development. Based on the processing results, the factors that affect the growth and development of the infant are gender, treatment and mother's education.