(untitled) (Research, Society and Development, 2020)
Survival analysis is currently one of the fastest-growing areas in the field of statistical analysis, with a solid theory for adjusting regression models to study certain phenomena, which have, in their structure, the characteristic of having incomplete observations in the sample called censorship. Although such models can efficiently represent the phenomenon under study in many situations, some of them do not take into account the existence of an unobservable variable present in most studies, called frailty. This fragility denotes the susceptibility of the event to occur by a determined individual or object under investigation. The objective of this work was to show that in situations where frailty is present, the use of models that capture the variability of this variable is more viable for the analysis of these data when compared to conventional models in survival studies. For this purpose, a comparative analysis was performed between these models, adjusted for a set of data from patients diagnosed with Diabetic Retinopathy, and a simulation study was also carried out for the gamma fragility model with different percentages of censorship and heterogeneity. After adjusting the models, it can be seen that the fragility models performed better when compared to the Cox model, with an emphasis on the gamma fragility model, which generated the lowest value for AIC and BIC. The simulation study showed that high censorship rates impair the degree of predictability of the fragility model and that high heterogeneity rates contribute to parameter estimates.