Applied Bayesian Modelling - Free

396 SURVIVAL AND EVENT HISTORY MODELSRolin, J. (1993) Bayesian survival analysis. In: Encyclopedia of Biostatistics. New York: Wiley, pp.271±286.Sahu, S., Dey, D., Aslanidou, H. and Sinha, D. (1997) A Weibull regression model with gammafrailties for multivariate survival data. Lifetime Data Anal 3(2), 123±137.Sargent, D. (1997) A flexible approach to time-varying coefficients in the Cox regression setting.Lifetime Data Anal. 3, 13±25.Sastry, N. (1997) A nested frailty model for survival data, with an application to the study of childsurvival in Northeast Brazil. J. Am. Stat. Assoc. 92, 426±435.Singer, J. and Willett, J. (1993) It's about time: using discrete-time survival analysis to studyduration and timing of events. J. Educ. Stat. 18, 155±195.Sinha, D. and Dey, D. (1997) Semiparametric Bayesian analysis of survival data. J. Am. Stat.Assoc. 92(439), 1195±1121.Spiegelhalter, D., Best, N., Carlin, B. and van der Linde, A. (2001) Bayesian measures of modelcomplexity and fit. Research Report 2001±013, Division of Biostatistics, University of Minnesota.Tanner, M. (1996) Tools for Statistical Inference: Methods for the Exploration of PosteriorDistributions and Likelihood Functions, 3rd ed. Springer Series in Statistics. New York, NY:Springer-Verlag.Thompson, R. (1977) On the treatment of grouped observations in survival analysis. Biometrics33, 463±470.Volinsky, C. and Raftery, A. (2000) Bayesian Information Criterion for censored survival models.Biometrics 56, 256±262.Weiss, R. (1994) Pediatric pain, predictive inference and sensitivity analysis. Evaluation Rev. 18,651±678.EXERCISES1. In Example 9.2, apply multiple chains with diverse (i.e. overdispersed) starting points± which may be judged in relation to the estimates in Table 9.3. Additionally, assessvia the DIC, cross-validation or AIC criteria whether the linear or quadratic modelin temperature is preferable.2. In Example 9.4, consider the impact on the covariate effects on length of stay andgoodness of fit (e.g. in terms of penalised likelihoods or DIC) of simultaneously (a)amalgamating health states 3 and 4 so that the health (category) factor has only twolevels, and (b) introducing frailty by adding a Normal error in the log(mu[i]) equation.3. In Example 9.6, repeat the Kaplan±Meier analysis with the control group. Suggesthow differences in the survival profile (e.g. probabilities of higher survival undertreatment) might be assessed, e.g. at 2 and 4 years after the start of the trial.4. In Program 9.8, try a logit rather than complementary log-log link (see Thompson,1977) and assess fit using the pseudo Bayes factor or other method.5. In Program 9.9 under the varying unemployment coefficient model, try a more informativeGamma prior (or set of priors) on 1=s 2 b with mean 100. For instance try G(1, 0.01),G(10, 0.1) and G(0.1, 0.001) priors and assess sensitivity of posterior inferences.6. In Example 9.12, apply a discrete mixture frailty model at cluster level with twogroups. How does this affect the regression parameters, and is there an improvementas against a single group model without frailty?7. In Example 9.14, try a Normal frailty model in combination with the non-parametrichazard. Also, apply a two group discrete mixture model in combination with the nonparametrichazard; how does this compare in terms of the DIC with the Normal frailtymodel?