Infant and child mortality rate is still high in Bangladesh. The study of infant and child mortality in developing countries is an important issue in public health programs. This book deals with the extension of the Cox's proportional hazards model that allows for heterogeneity due to omitted covariates using frailty (random effect) approach. The covariates involve some key determinants of children's time-to-death event. At first the Cox's proportional hazards model and frailty model were fitted with the help of Bangladesh Demographic and Health Survey (BDHS) 2007 data and get the estimates and corresponding standard errors of the regression coefficients. Then the application of Bayesian techniques on Cox's proportional hazards model (Kalbfleisch 1978) and frailty model (Clayton, 1991) were proposed. The frequentist parameters' results were incorporated in the Bayesian methodology as the prior information. Also the frequentist confidence interval and the Bayesian credible interval of the regression parameters and frailty component were obtained.