A mixture model for bovine abortion and foetal survival

The effect of spontaneous abortion on the dairy industry is substantial, costing the industry on the order of US dollars 200 million per year in California alone. We analyse data from a cohort study of nine dairy herds in Central California. A key feature of the analysis is the observation that only a relatively small proportion of cows will abort (around 10;15 per cent), so that it is inappropriate to analyse the time-to-abortion (TTA) data as if it were standard censored survival data, with cows that fail to abort by the end of the study treated as censored observations. We thus broaden the scope to consider the analysis of foetal lifetime distribution (FLD) data for the cows, with the dual goals of characterizing the effects of various risk factors on (i). the likelihood of abortion and, conditional on abortion status, on (ii). the risk of early versus late abortion. A single model is developed to accomplish both goals with two sets of specific herd effects modelled as random effects. Because multimodal foetal hazard functions are expected for the TTA data, both a parametric mixture model and a non-parametric model are developed. Furthermore, the two sets of analyses are linked because of anticipated dependence between the random herd effects. All modelling and inferences are accomplished using modern Bayesian methods.