Modelo Weibull modificado de longa duração

Abstract

When a group of patients is monitored until a pre-established date for observation of the recurrence time of an event, it is possible that, at the end of the monitoring period, a parcel of such group has not yet suffered the event of interest. When that happens, even if the period is extended, there is evidence that an appropriate model for the theoretical survival function of the time until the event occurs would be one model able to bear this kind of data. This class of long duration models will be defined because the form presented by the nonparametric estimation of hazard function in this type of study indicates that the model should be flexible to allow such function to be increasing, decreasing, constant or U-shaped. In this report, we present the long duration modified Weibull model (LDMW) as a proposal to contemplate the issues in the medicine area. The LDMW model has a flexible hazard curve, which enables adjustment when the hazard is decreasing, increasing, U-shaped, unimodal, initially decreasing and posteriorly unimodal and constant. The report also particularizes models already known in the literature that contemplate long duration, such as the long duration Weibull (LDW), long duration Exponential (LDE) and short duration models, such as the modified Weibull (MW), Weibull and Exponential. The simulations showed that the odds of coverage reach the nominal probability of 95% for moderately to big sized samples, that the LDMW p model parameters estimation is costless when compared to the MW and that the selection criteria of the AIC and BIC models are not adequate to discriminate the LDMW model adjustment when compared to the LDW model adjustment for small or moderately sized samples. The LDMW model and its particular cases were adjusted into two sets of real data considering the Classic and Bayesian Inference. The first data set is about the time until the seroreversion of children born from HIV-positive mothers and the second data set is about the recurrence time of breast cancer in women.