Análise de Resíduos para o Modelo Logístico Generalizado Dependente do Tempo

ABSTRACT

Researchers from different areas of knowledge have used the Cox proportional-hazards model, due to its simplicity and easy interpretation when studying situations in which the response variable is the time until the occurrence of an event of interest. However, the traditional Cox proportional-hazards model is not suitable for modeling data sets that violate the assumption of proportionality of the risks (or failure rates) and the effects of covariates over time are not detected. The generalized time-dependent logistic (GTDL) model has been used as an alternative in the modeling of survival data, taking into account the assumption of non-proportionality of the risks. In the literature, we found a wide and relevant production in inferential procedures, but no contribution in diagnostic methods or techniques. In this paper, Cox-Snell, modified Cox-Snell, martingale, deviance, randomized quantiles, NMSP (normally-transformed modified survival probabilities) and NRSP (normally-transformed randomized survival probabilities) residuals are proposed to assess the suitability of the GTDL model to the data. A Monte Carlo simulation study is conducted in order to investigate the empirical distribution of these residuals. In summary, the obtained simulation results indicate the adequacy, for the GTDL model, of the randomized quantile and NRSP residuals, regardless of the proportion of censorship in the data. The GTDL library is built and made available in the R programming language. Finally, the methodology studied is applied to a set of real data, available in the literature, involving patients diagnosed with advanced-stage lung cancer. Codes for installing and using the GTDL library are shown in the Supplementary Material (https://github.com/carrascojalmar/GTDL-Material-Suplementar).

Keywords:
residual analysis; lung cancer; Cox proportional-hazards model; GTDL model; Monte Carlo simulation