Regression models play a vital role in the study of data regarding survival of subjects. The Cox proportional hazards model for regression analysis has been frequently used in survival modelling. In survival studies, it is also possible that survival time may occur with multiple occurrences of event or competing risks. The situation of competing risks arises when there are more than one mutually exclusive causes of death (or failure) for the person (or subject). In this paper, we developed a parametric regression model using Gompertz distribution via the Cox proportional hazards model with competing risks. We discussed point and interval estimation of unknown parameters and cumulative cause-specific hazard function with maximum-likelihood method and Bayesian method of estimation. The Bayes estimates are obtained based on non-informative priors and symmetric as well as asymmetric loss functions. To observe the finite sample behaviour of the proposed model under both estimation procedures, we carried out a Monte Carlo simulation analysis. To demonstrate our methodology, we also included real data analysis.
We develop error-control based time integration algorithms for compressible fluid dynamics (CFD) applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime. Focusing on discontinuous spectral element semidiscretizations, we design new controllers for existing methods and for some new embedded Runge-Kutta pairs. We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice. We compare a wide range of error-control-based methods, along with the common approach in which step size control is based on the Courant-Friedrichs-Lewy (CFL) number. The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances, while additionally providing control of the temporal error at tighter tolerances. The numerical examples include challenging industrial CFD applications.