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Full-Text Articles in Statistics and Probability
Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari
Assessing Noninferiority In A Three-Arm Trial Using The Bayesian Approach, Pulak Ghosh, Farouk S. Nathoo, Mithat Gonen, Ram C. Tiwari
Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series
Non-inferiority trials, which aim to demonstrate that a test product is not worse than a competitor by more than a pre-specified small amount, are of great importance to the pharmaceutical community. As a result, methodology for designing and analyzing such trials is required, and developing new methods for such analysis is an important area of statistical research. The three-arm clinical trial is usually recommended for non-inferiority trials by the Food and Drug Administration (FDA). The three-arm trial consists of a placebo, a reference, and an experimental treatment, and simultaneously tests the superiority of the reference over the placebo along with …
Estimating The Integrated Likelihood Via Posterior Simulation Using The Harmonic Mean Identity, Adrian E. Raftery, Michael A. Newton, Jaya M. Satagopan, Pavel N. Krivitsky
Estimating The Integrated Likelihood Via Posterior Simulation Using The Harmonic Mean Identity, Adrian E. Raftery, Michael A. Newton, Jaya M. Satagopan, Pavel N. Krivitsky
Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series
The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison and Bayesian testing is a ratio of integrated likelihoods, and the model weights in Bayesian model averaging are proportional to the integrated likelihoods. We consider the estimation of the integrated likelihood from posterior simulation output, aiming at a generic method that uses only the likelihoods from the posterior simulation iterations. The key is the …
The Bayesian Two-Sample T-Test, Mithat Gonen, Wesley O. Johnson, Yonggang Lu, Peter H. Westfall
The Bayesian Two-Sample T-Test, Mithat Gonen, Wesley O. Johnson, Yonggang Lu, Peter H. Westfall
Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series
In this article we show how the pooled-variance two-sample t-statistic arises from a Bayesian formulation of the two-sided point null testing problem, with emphasis on teaching. We identify a reasonable and useful prior giving a closed-form Bayes factor that can be written in terms of the distribution of the two-sample t-statistic under the null and alternative hypotheses respectively. This provides a Bayesian motivation for the two-sample t-statistic, which has heretofore been buried as a special case of more complex linear models, or given only roughly via analytic or Monte Carlo approximations. The resulting formulation of the Bayesian test is easy …