Random effects survival models applied to animal breeding data

Abstract

Introduction: In the developing sub-Saharan countries, sheep and goats are kept mainly by small scale farmers for meat production. These animals graze on open natural pastures or in communal pastoral systems. Almost 30% of the animals however do not reach to maturity age due to high levels of infections from endoparasites. Although control methods that focus on reducing contamination of pastures through anthelmintic treatment are in place, their use is limited due to high cost. Due to this there is need for animals that are well adapted to the environment so as to increase productivity. The data considered in this thesis come from a breeding program conducted from 1991-1996 at the International Livestock Research Institute (ILRI). The objective of the program was to assess genetic resistance to endoparasites among the Red Masaai, Dorper and their cross breeds. In each of the years, the lambs were observed for a period of at most 12 months. The genetic resistance of the lambs has been assessed by using linear mixed models on measurements of packed cell volume (PCV), faecel egg count (FEC) and body weight (BWT) collected at arbitrarily defined time points in the animal’s life span. It has now been reported (Baker et al., 1994, 1999, 2003) that the Red Maasai has higher resilience (higher PCV) and higher resistance (lower FEC) than the Dorper. From the experimental set-up, information of any lambs that died during the follow-up time was also available. These time-to-event measurements (time to death) are the main focus of this thesis. The genetic component was considered at the sire level. Thus the times of lambs from the same sire were assumed to be correlated. Such survival times, fall in the class of multivariate time-to-event data. These are time-to-event data that are correlated within some cluster. For example the times to recurrent trypanosomiases infections for a lamb or the survival times of lambs from the same sire. In the last several years extensive research on multivariate time-to-event data has been carried out (Klein and Moeschberger, 1997, Hougaard, 2000, Therneau and Grambsch, 2000). To account for correlation in the times within a cluster or equivalently heterogeneity between clusters, a random effect term is used, resulting in what are known as frailty models. Models with one random effect per cluster are known as shared frailty models. Most shared frailty models are an extension of the semi-parametric Cox proportional hazard (PH) model (Therneau and Grambsch, 2000). On the other hand the Weibull baseline hazard has been the most widely used form for the parametric shared frailty model (Hougaard, 2000). ...