The Analysis of Labor Time and Healthcare Management via Generalized Gamma Zero-Inflated Cure-Rate Regression Model

Abstract

Standard survival models assume that time is greater than zero. However, there are several practical examples where a proportion of the data presents times equal to zero. Based on this issue, survival models including this proportion have been proposed and are called zero-inflated survival models. It is important to consider flexible distributions in this context in order to model more complex patterns. In this paper, we propose a Generalized Gamma zero-inflated cure-rate survival model, motivated by the pattern observed in the labor progression times. Based on simulation study, we show that estimation methods (maximum likelihood estimates and asymptotic confidence intervals) present a good performance even for small sample sizes. Concerning the model selection, we verified that Likelihood Ratio Test showed the best results. The proposed model was considered to analyze the labor time of pregnant women from sub-Saharan Africa. For diagnostic analysis, we used Cox-Snell residuals and Local Influence methods. In general, the model showed as an adequate tool to describe the labor and we conclude that this model can be a tool in the study of childbirth times supporting management in obstetrical healthcare. We acknowledge the World Health Organization for granting us permission to use the data set.