Modelo de regressão Weibull generalizada restrita em eventos competitivos: aplicação no tempo de emprego dos funcionários do município de Simões Filho - Bahia - 2021

Abstract

In survival analysis, the primary interest is often the time until the occurrence of a single event; however, there are situations where interest lies in multiple events, and the occurrence of one event precludes the occurrence of others. In such cases, models that account for the presence of competing risks are employed.

Initially, competing events, censored data, and a regression model based on the Generalized Weibull distribution were considered. In a simulation study conducted across various parameter settings, sample sizes, and censoring proportions, it was observed that maximum likelihood estimates exhibited high variances. Consequently, a model with restrictions on the probability distribution was adopted.

Furthermore, the superior performance of this restricted model was confirmed through an additional simulation study under the aforementioned scenarios. The results indicated that the restricted model provided precise estimates with reduced variance, demonstrating significant improvement as the sample size increased. Hypothesis tests assessing the significance of regression coefficients were performed using the asymptotic distribution of the maximum likelihood estimators.

To evaluate the adequacy of the restricted model, quantile residuals were employed. Finally, the methodology was applied to a dataset concerning employment duration in private companies in Simões Filho (Bahia), Brazil, in 2021, where termination and dismissal without cause were considered competing events.

The covariates sex, age, race, and educational level influenced the duration of the bond differently depending on the competing event. The residual analysis indicated a good fit for the restricted Generalized Weibull model, with uniformly distributed residuals and no heteroscedasticity, although the presence of some outliers suggests occasional limitations. These results confirm the model's adequacy in describing the dynamics of the competing events in the study.