Prior Distributions: Choosing and Justifying Priors
A practical and mathematical guide to choosing and justifying Bayesian prior distributions, including informative, weakly informative, skeptical, noninformative, and reference priors, prior elicitation, effective sample size, prior predictive checks, sensitivity analysis, clinical trial examples, and regulatory considerations.
Posterior Probability vs. P-Value: A Comparison
A practical and mathematical comparison of posterior probabilities and p-values, including Bayes
Markov Chain Monte Carlo (MCMC) for Clinical Statisticians
A practical and mathematical guide to Markov Chain Monte Carlo (MCMC) for clinical statisticians, including Bayesian posterior sampling, Metropolis-Hastings, Gibbs sampling, Hamiltonian Monte Carlo, convergence diagnostics, effective sample size, R implementation, and a complete clinical example.
Introduction to Bayesian Statistics for Clinical Trials
An intuitive and computational introduction to Bayesian statistics for clinical trials, including prior distributions, likelihoods, posterior probabilities, credible intervals, Bayesian decision-making, predictive probabilities, and a complete worked example using a beta-binomial model.
Credible Intervals vs. Confidence Intervals
A practical guide to credible intervals versus confidence intervals, explaining the Bayesian and frequentist interpretations, mathematical differences, worked examples, posterior probability, coverage probability, and implementation in R.
Bayesian vs. Frequentist Inference: Key Differences
A practical and mathematical guide to Bayesian versus frequentist inference, including parameters, probability, priors, likelihoods, posterior distributions, p-values, confidence intervals, credible intervals, hypothesis testing, clinical trial examples, and when each framework is useful.
Bayesian Sample Size Determination
A practical and computational guide to Bayesian sample size determination, including prior distributions, posterior probabilities, assurance, posterior precision, decision criteria, a complete binary-outcome worked example, and R implementation.
Bayesian Predictive Probability for Trial Monitoring
A practical and mathematical guide to Bayesian predictive probability for clinical trial monitoring, including posterior distributions, beta-binomial predictive probabilities, interim decision rules, early stopping for efficacy and futility, a complete worked example, and R implementation.
Bayesian Model Averaging in Clinical Research
A practical guide to Bayesian Model Averaging in clinical research, including model uncertainty, posterior model probabilities, Bayesian model averaging, clinical trial applications, variable selection, prediction, and a complete worked example.
Bayesian Meta-Analysis Methods
A practical and mathematical guide to Bayesian meta-analysis, including fixed-effect and random-effects models, prior distributions, posterior distributions, heterogeneity, predictive distributions, credible intervals, forest plots, sensitivity analysis, and R implementation.