Assessing Placebo Response Using Bayesian Hierarchical Survival Models

Achcar, J. A., and Bolfarine, H, “Constant hazard against a change-point alternative: a Bayesian approach with censored data,” Commun. Statist.-Theory Meth., vol.18(10) pp. 3801–3819, 1989. Armitage, P., Statistical Methods in Medical Research, New York, Wiley, 1971. Beecher, H.K.,”The powerful placebo effect,” Journal of the American Medical Association, vol. 159 pp. 1602–1606, 1955. Berger, J, “The robust Bayesian viewpoint”, Robustness of Bayesian AnalysesJoseph B. Kadane (ed.),North-Holland, New York, 1984. Boag, J.W., “Maximum likelihood estimation of the proportion of patients cured by cancer treatment,” Journal of the Royal Statistical Societyvol. 11 pp. 15–53, 1949. Box, G.E.P., “Sampling and Bayes' Inference in Scientific Modelling and Robustness,” Journal of the Royal Statistical SocietyA, vol. 143(4), pp. 383–430, 1980. Brown, W.A., “Placebo as a treatment for depression (with discussion),”. Neuropsychopharmacology, vol. 10 pp. 265–288, 1994. Carlin, B., Gelfand, A.E., and Smith, A.F.M., “Hierarchical Bayesian analysis of change point problems,” Applied Statisticsvol. 41(2) pp. 389–405, 1992. Casells, G., and George, E., “Explaining the Gibbs Sampler,” The American Statisticianvol. 46 pp. 167–174, 1992. Cox, D.R., “Models in statistical analysis,” Statistical Sciencevol. 5 pp. 169–174, 1990. Draper, D., “Assessment and propagation of model uncertainty (with discusssion),” Journal of the Royal Statistical SocietyB, vol. 57, pp. 45–97, 1995. Farewell, V.T., “The use of mixture models for the analysis of survival data with long-term survivors,” Biometricsvol. 38, pp. 1041–1046, 1983. Fleiss, J., “Analysis of data from multicenter clinical trials,” Controlled Clinical Trialsvol. 7 pp. 267–275, 1986. Geisser, S., “Comments on Prediction of future observations in growth curve models”. Statistical Sciencevol. 2 pp. 465–467, 1987. Geisser, S., “On hierarchical Bayes procedures for predicting simple exponential survival,” Biometricsvol. 46 pp. 225–230, 1990. Gelfand, A.E., “Model determination using sampling-based methods,” Markov Chain Monte Carlo in Practice, W.R. Gilks, S. Richardson, and D.J. Spiegelhalter (eds.) pp. 145–161.Chapman and Hall, 1996. Gelfand, A.E. and Dey, D. K., “Bayesian model choice: asymptotics and exact calculations,” J.R. Statist. Soc.B, vol. 56 pp. 501–514, 1994. Gelfand, A.E., Dey, D. K., and Chang, H., “Model determination using predictive distributions with implentation via sampling-based methods,” Bayesian Statistics 4J.M. Bernardo, J.O. Berger, A.P. Dawid and A.F.M. Smith (eds.), pp. 147–167. Oxford: Oxford University Press, 1992. Gelfand, A.E. and Smith, A.F.M., “Sampling based approaches to calculation marginal densities,” Journal of the American Statistical Associationvol. 85 pp. 398–409, 1990. Gelman, A., “Inference and monitoring convergence,” In: Gilks W., Richardson S, Spiegelhalter D eds. Practical Markov Chain Monte Carlo.New York: Chapman & Hall, pp. 131–143, 1996. Gelman, A. and Rubin, D., “Markov chain Monte Carol methods in biostatistics,” Statistical Methods in Medical Researchvol. 5 pp. 339–355, 1996. Gelman A, and Rubin D.B., “Inference from iterative simulation using multiple sequences (with discussion),” Statistical Sciencevol. 7 pp. 457–511, 1992. Gelman, A. and Meng, S.L., “Model checking and model improvement,” Markov Chain Monte Carlo in Practice, W.R. Gilks, S. Richardson and D.J. Spiegelhalter (eds.) pp. 189–201. London: Chapman & Hall, 1995. Gelman, A., Carlin, J.B., Stern, H.S., and Rubin, D.B., Bayesian Data Analysis, London: Chapman & Hall, 1995. Geman, S. and Geman, D., “Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images,” IEEE Transactions on Pattern Analysis and Machine Intelligencevol. 6 pp. 721–741, 1984. Gilks, W.R., Richardson, S., and Spiegelhalter, D.J., Markov Chain Monte Carlo in Practice, London: Chapman & Hall, 1996. Gray, R. J., “On institutional effects in multicenter clinical trials,” Biometricsvol. 50 pp. 244–253, 1994. Greenhouse J. and Wasserman L., “Robust Bayesian analysis of clinical trials,” Statistics in Medicinevol. 14 pp. 1379–1391, 1995. Greenhouse, J., Stangl, D., Kupfer, D., and Prien, R., “Methodological issues in maintenance therapy clinical trials,” Archives of General Psychiatryvol. 48 pp. 313–318, 1991. Greenhouse, J.B. and Wolfe, R.A., “A competing risks derivation of a mixture model for the analysis of survival data,” Communications in Statistics-Theory and Methodsvol.13 pp. 3133–3154, 1984. Grieve, A.P., “Some uses of predictive distributions in pharmaceutical research,” Biometry-Clinical trails and related topics, T. Okuno (ed.), pp. 83–99, 1998. Jennrich, R. I., “Some exact tests for comparing survval curves in the presence of unequal right censoring,” Biometrikavol. 71, pp. 57–64, 1984. Kadane, J. and Dickey, J., “Bayesian Decision Theory and the Simplification of Model,” Evaluation of Econometric Models, J. Kuenta and J. Ramsey (eds.), Academic Press, 1980. Kass, R.E. and Raftery, A., “Bayes factors,” J. Am. Statist. Soc.vol. 90 pp. 773–795, 1995. Kass, R.E. and Greenhouse, J.B., “Comment: A Bayesian perspective on Investigating therapies of potentially great benefit: ECMO, by James H. Ware”, Statistical Sciencevol. 4 pp. 298–340, 1989. Kass, R.E. and Steffey, D., “Approximate Bayesian inference in conditionally independent hierarchical models,” Journal of the American Statistical Associationvol.84 pp. 717–726, 1989. Keller, M.B., Shapiro, R.W., Lavori, P.W., and Wolfe, N., “Relapse in major depressive disorder: Analysis with the life table,” Archives of General Psychiatryvol. 39 pp. 911–915, 1982. Lehman, E.L., “Model Specification: The views of Fisher and Neyman and later developments,” Statistical Sciencevol. 5 pp. 160–168, 1990.. Lindley, D.V. and Smith, A.F.M., “Bayes estimates for the linear model (with discussion),” Journal of the Royal Statistical Society, Series Bvol. 34 pp. 1–42, 1972. Prien, R.F., Kupfer, D.J., Mansky, P.A., Small, J.G., Tuason, V.B., Voss, C.B., Johnson, W.E., “Drug therapy in prevention of recurrences in unipolar and bipolar affective disorders,” Archives of General Psychiatry, vol. 41 pp. 1096–1104, 1984. Raftery, A.E., Madigan, D., and Hoeting J., “Bayesian model averaging for linear regression models,” JASAvol. 92 pp. 179–191, 1997. Raftery, A.E., “Hypothesis testing and model selection,” Markov Chain Monte Carlo in Practice, W.R. Gilks, S. Richardson and D.J. Spiegelhalter (eds.), pp. 163–187. London: Chapman & Hall, 1995. Raftery, A.E., and Akman, V.E., “Bayesian analysis of a Poisson process with a changepoint,” Biometrikavol. 73 pp. 85–89, 1986. Skene, A.M., Shaw, J.E.H., and Lee, T.D., “Bayesian modelling and sensitivity analysis,” The Statisticianvol. 35 pp. 281–288, 1986. Skene, A.M., and Wakefield, J.C., “Hierarchical models for multicentre binary response studies,” Statistics in Medicinevol. 9 pp. 919–929, 1990. Smith, A.F.M., “A Bayesian approach to inference about a change-point in a sequence of random variables,” Biometrikavol.63 pp. 407–16, 1975. Smith, A.F.M., “Change-point problems: approaches and applications,” Bayesian Statistics, vol 1, J.M. Bernardo, M.H. DeGroot, D.V. Lindley, and A.F.M. Smith,(eds.) Oxford U.K.: Oxford University Press, pp. 83–98, 1980. Smith, A.F.M. and Spiegelhalter, D.A., ”Bayes factors and choice criteria for linear models,” Journal of the Royal Statistical SocietyB, vol.42 pp. 213–220, 1980. Stangl, D., “Modeling heterogeneity in multi-center clinical trials using Bayesian hierarchical survival models,” Ph.D. dissertation, Carnegie Mellon University, 1991. Stangl, D., “Prediction and decision making using Bayesian hierarchical models,” Statistics in Medicinevol. 14(20) pp. 2173–2190, 1995. Stangl, D., “Bayesian methods in the analysis of clincal trials: A discussion,” ASA Proceedings, American Statistical Association, 1995. Stangl, D. and Mukhopadhyay, S., “Balancing Centers and Observations in Multicenter Clinical Trials.” Technical Report 93-A13, ISDS, Duke University, 1993. Stewert, L., “Hierarchical Bayesian nnalysis using Monte Carlo integration: Computing posterior distributions when there are many possible models,” The Statisticianvol. 36 pp. 211–219, 1987. Turner, J.A, Deyo, R.A., Loeser, J.D., Von Korff, M. and Fordyce, W.E., “The importance of placebo effects in pain treatment and research,” The Journal of the American Medical Associationvol. 271 pp. 1609–1614, 1994. Yamaguchi, K., “Accelerated failure-time regression models with a regression model of surviving fraction: An application to the analysis of ’permanent employment’ in Japan,” JASAvol. 87 pp. 284–292, 1992. Wasserman, L., “Recent methodological advances in robust Bayesian inference”, Bayesian Statisticsvol 4, J.M. Bernardo, J.O. Berger, A.P. Dawid, and A.F.M. Smith (eds.), Oxford U.K.: Oxford University Press, pp. 483–502, 1992. Wells, K.B., Steward, A., Hayes, R.D., Burnam, A., Rogers, W., Daniels, M., Berry, S., Greenfield, S., and Ware, J.,” The functioning and well-being of depressed patients: Results from the Medical Outcomes Study,” Journal of the American Medical Associationvol. 262 pp. 914–919, 1989.