Modelo de regressão chances de sobrevivência proporcionais para dados discretos com presença de censura

Abstract

Survival models, in their majority, consider continuous survival times. However, in several studies these times are discrete, and in some occasions, it is not advisable to use a continuous model to analyze discrete data. One of the most popular regression models in the analysis of survival data is the Cox proportional hazards model, whose main characteristic is to consider that the covariates have a multiplicative effect on the hazard function. However, this feature cannot be satisfied when survival times are discrete, due to the hazard function being bounded in the interval (0, 1). To solve this problem, Cox suggested a discrete alternative of his model. Another alternative regression model was presented by Bennett, which assumes that covariates have a multiplicative effect on the odds of survival. These models are referred to as proportional odds (survival) models. In this context, the present paper aims to consider proportional odds modeling as an alternative for building regression models for discrete survival data. More specifically, the objectives are: (a) to study the proportional odds model for continuous time; (b) to build the regression model for data with proportional odds of survival and discrete time; (c) to obtain point and interval estimates of the model parameters; (d) to propose procedures to verify the proportional odds assumption and the quality of the model fit; (e) to illustrate the model and proposed procedures on a real data set. The results obtained on simulated data indicated evidence of the asymptotic properties of the estimators and the proposed model showed a good fit to the real data set, proving to be a good alternative for modeling discrete survival data with covariates.