Abstract
In time to event analysis, the situation of competing risks arises when the individual (or subject) may experience p mutually exclusive causes of death (failure), where cause-specific hazard function is of great importance in this framework. For instance, in malignancy-related death, colorectal cancer is one of the leading causes of the death in the world and death due to other causes considered as competing causes. We include prognostic variables in the model through parametric Cox proportional hazards model. Mostly, in literature exponential, Weibull, etc. distributions have been used for parametric modelling of cause-specific hazard function but they are incapable to accommodate non-monotone failure rate. Therefore, in this article, we consider a modified Weibull distribution which is capable to model survival data with non-monotonic behaviour of hazard rate. For estimating the cumulative cause-specific hazard function, we utilized maximum likelihood and Bayesian methods. A class of non-informative types of prior (uniform, Jeffrey's and half-t) is introduced for Bayes estimation under squared error (symmetric) as well as LINEX (asymmetric) loss functions. A simulation study is performed for a comprehensive comparison of Bayes and maximum likelihood estimators of cumulative cause-specific hazard function. Real data on colorectal cancer is used to demonstrate the proposed model.