The log-odd logistic-Weibull regression model under informative censoring

Abstract

One of the main characteristics of data from survival analysis is that the random variable of interest is not always observed, so that some observations are censored. The usual methods consider that these observations do not carry information about the distribution of the response variable (non-informative censoring). In other words, it is considered that an observation is censored simply by the fact that the event of interest (failure or death) did not occur during the period of study. However, in many situations, the survival time is clearly perturbed by the censoring mechanism, so the effect produced must be included in the analysis. The question is that once informative censoring is assumed to be non-informative, the results of the analysis can mask biases and thus weakening the model’s predictive power. Therefore, we consider the informative censoring mechanism in the odd-logistic Weibull regression model, based on the method described in Huang and Wolfe (2002), to analyze the variations which occur for estimating the model parameters. We obtain maximum likelihood estimates of the parameters by considering censored data and evaluate local influence on the estimates for different perturbation schemes. In addition, we define martingale and deviance residuals to detect outliers and evaluate the model assumptions. We show that the proposed regression model is useful to the analysis of real data and may give more realistic fits than other special regression models.