In biomedical research, challenges to working with multiple events are often observed while dealing with time-to-event data. Studies on prolonged survival duration are prone to having numerous possibilities. In studies on prolonged survival, patients might die of other causes. Sometimes in the survival studies, patients experienced some events (e.g. cancer relapse) before dying within the study period. In this context, the semi-competing risks framework was found useful. Similarly, the prolonged duration of follow-up studies is also affected by censored observation, especially interval censoring, and right censoring. Some conventional approaches work with time-to-event data, like the Cox-proportional hazard model. However, the accelerated failure time (AFT) model is more effective than the Cox model because it overcomes the proportionality hazard assumption. We also observed covariates impacting the time-to-event data measured as the categorical format. No established method currently exists for fitting an AFT model that incorporates categorical covariates, multiple events, and censored observations simultaneously. This work is dedicated to overcoming the existing challenges by the applications of R programming and data illustration. We arrived at a conclusion that the developed methods are suitable to run and easy to implement in R software. The selection of covariates in the AFT model can be evaluated using model selection criteria such as the Deviance Information Criteria (DIC) and Log-pseudo marginal likelihood (LPML). Various extensions of the AFT model, such as AFT-DPM and AFT-LN, have been demonstrated. The final model was selected based on minimum DIC values and larger LPML values.

censoring, illness-death models, accelerated failure time model, Bayesian Survival Analysis, semi-competing risks.

Adam Ding, A., Shi, G., Wang, W. and Hsieh, J. J., (2009). Marginal regression analysis for semi-competing risks data under dependent censoring. Scandinavian Journal of Statistics, 36(3), pp. 481–500.

Armero, C., Cabras, S., Castellanos, M. E., Perra, S., Quirós, A., Oruezábal, M.J. and Sánchez-Rubio, J., (2016). Bayesian analysis of a disability model for lung cancer survival. Statistical methods in medical research, 25(1), pp. 336–351.

Buckley, J., James, I., (1979). Linear regression with censored data.Biometrika, 66(3), pp.429-436.

Celeux, G., Forbes, F., Robert, C. P. and Titterington, D. M., (2006). Deviance information criteria for missing data models. Bayesian analysis, 1.4 (2006), pp. 651–673.

Chen, M. H., Shao, Q. M. and Ibrahim, J. G., (2012). Monte Carlo methods in Bayesian computation. Springer Science & Business Media.

Christensen, R., Johnson, W., (1988). Modelling accelerated failure time with a Dirichlet process. Biometrika, 75(4), pp. 693–704.

Ferguson, T. S., (1973). A Bayesian analysis of some nonparametric problems. The annals of statistics, pp. 209–230.

Geisser, S., Eddy, W. F., (1979). A predictive approach to model selection. Journal of the American Statistical Association, 74(365), pp. 153–160.

Ghosh, D., Taylor, J. M. and Sargent, D. J., (2012). Meta-analysis for surrogacy: Accelerated failure time models and semicompeting risks modeling. Biometrics, 68(1), pp. 226–232.

Ghosh, S. K., Ghosal, S., (2006). Semiparametric accelerated failure time models for censored data. Bayesian statistics and its applications, 15, pp. 213–229.

Haneuse, S., Lee, K.H., (2016). Semi-competing risks data analysis: accounting for death as a competing risk when the outcome of interest is nonterminal.Circulation: Cardiovascular Quality and Outcomes, 9(3), pp. 322–331.

Jiang, F., Haneuse, S., (2017). A semi-parametric transformation frailty model for semicompeting risks survival data. Scandinavian Journal of Statistics, 44(1), pp.112–129.

Kuo, L., Mallick, B., (1997). Bayesian semiparametric inference for the accelerated failuretime model. Canadian Journal of Statistics, 25(4), pp.457–472.

Lee, K.H., Haneuse, S., Schrag, D. and Dominici, F., (2015). Bayesian semi-parametric analysis of semi-competing risks data: investigating hospital readmission after a pancreatic cancer diagnosis. Journal of the Royal Statistical Society. Series C, Applied Statistics, 64(2), p. 253.

Lee, K. H., Lee, C., Alvares, D., Haneuse, S. and Lee, M. K. H., (2015). Package ‘Semi- CompRisks’.

Lee, K. H., Rondeau, V. and Haneuse, S., (2017). Accelerated failure time models for semi-competing risks data in the presence of complex censoring. Biometrics, 73(4), pp. 1401–1412.

Odell, P. M., Anderson, K. M. and D’Agostino, R. B., (1992). Maximum likelihood estimation for interval-censored data using a Weibull-based accelerated failure time model. Biometrics, pp. 951–959.

Prentice, R. L., (1992). Introduction to Cox, 1972, regression models and life-tables. Breakthroughs in Statistics: Methodology and Distribution, pp. 519–526.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Van Der Linde, A., (2002). Bayesian measures of model complexity and fit. Journal of the royal statistical society: Series b (statistical methodology), 64(4), pp. 583–639.

Xu, J., Kalbfleisch, J. D. and Tai, B., (2010). Statistical analysis of illness–death processes and semicompeting risks data. Biometrics, 66(3), pp. 716–725.