Application of the Weibull-Poisson long-term survival model

Red propolis effect analysis of dairy calves health based on Weibull regression model with long-term survivors

Diarrhea is the most common cause of mortality and morbidity in dairy calves during the first weeks of life. It is responsible for the majority of costs related to animal death and treatments, as well as lower productivity due to reduced weight gain. Therefore, studies that focus on strategies to reduce diarrhea incidence and to improve animal welfare are very important for the dairy industry. For that reason, the beneficial effects of red propolis on the health status of preweaned dairy calves was studied. Animal disease data usually present incomplete observations of interest time, so-called censored observations and one of the statistical techniques for this modeling type is the survival analysis, hence it is a set of methods for analyzing data where the response variable is the time until the occurrence of an event of interest. We propose among some methods of survival data analysis, the long-term models. The motivation to study these models is the fact that part of the population is not susceptible to the event of interest during the period of the study, considered as immune or cured. In this paper, we studied the Weibull distribution in a structure of long-term model, including the covariates in the proportion of cured through the logistic link function. Besides, we used the residual analysis to check the assumptions of the model. The reason for the choice of the Weibull distribution was that this model is very flexibility to model a variety of data sets, among them animal science and long-term survival data. We illustrate its application with a case study from an animal experiment, which examined the time till the occurrence of diarrhea in Holstein calves, where a proportion of the animals were not susceptible to this health condition. This experiment aimed to verify the efficiency of red propolis in disease prevention and the influence of that on the proportion of animals that are not susceptible to diarrhea.