Gamma-Gompertz shared frailty model for analysis of the time of stay in an Anglo-Nubian goat herd

Abstract Goats, even though adapted to tropical environments, are exposed to infection by endoparasites during grazing, which can negatively affect the time a female stays in the herd, compromising the breeding efficiency. In this context, the objective of this study was to evaluate a gamma-Gompertz shared frailty model for correction of unobserved heterogeneity attributed to the effects of unmeasured factors in analyzing the time of stay in a herd of Anglo-Nubian goats, using the survival analysis technique. The method was applied using data from records of 101 does born in the period 2009 to 2013 in an experimental herd located in the municipality of Teresina, Piaui, Brazil, where the replacement was carried out over four generations, with bulls from other herds and females incorporated regardless of the value of their EPG exam, to increase the variation of sensitivity to worms in the herd. The removal of a doe due to death caused by worm infection was considered the event of interest (failure) and losses due to other causes were considered censored events. According to the model selection criteria (AIC and BIC), the shared gamma-Gompertz frailty model stood out from the gamma shared frailty models with risk functions based on the Weibull and log-logistic distributions for the proposal studied. The gamma-Gompertz shared frailty model (with and without effect of observed factors) allowed observing a significant influence of the of year-season effect, indicating as frailty effects the differentiated death tendency between years (does born in 2011 in the rainy season and 2012 in the more fragile dry season). When associating the random effect to groups formed by goats descended from the same father, a significant association was observed between the times of goats belonging to such groups, with only 2 bulls showing more fragile daughters and consequently less permanence in the herd. The use of frailty models is relevant to meet the objectives of animal husbandry, as a technique to identify frailties due to the effects of factors that are difficult or costly to measure in bulls classified as having high genetic value. The simplicity and presentation of results in the form of graphs that are easy to understand make the method attractive for this type of research.