This thesis explores the association between a response variable and various regressors in dairy cattle breeding data using the various survival models in general and the partially linear single index survival model (PLSISM) in particular. In this study calf survival data and culling data were used. The calf survival data contains the following information: survival time, birth weight, weaning weight, calving ease score, average daily gain, number of disease incidences and serum total protein content. The culling data include, survival time, herd size variation, production level (milk, fat and protein), type of supervision, body condition score and age at first calving. Both data sets contain herd, year and season of calving and were analyzed using the various survival models. The Weibull model, however, was used for detailed analyses of the data sets. The nonparametric vector of PLSISM includes body weight, total serum protein and average daily gain for calf survival data and age at first calving, fat production and body condition core for culling data. The parametric vector of PLSISM consists of the rest of the covariates. The results show that the estimates of the parametric component are similar in the two models (Weibull and PLSISM). However, the estimates of the nonparametric component differ from parametric analysis. This difference may be attributed largely to the nonlinearity of the estimated function indicating the standard linear survival model does not adequately describe the underlying association between the response variable and the various covariates in this study. This is the first implementation and application of this complex model, PLSISM, with large real censored data.