Bayesian Statistical Inference

Bayesian inference offers improved efficiency with smaller samples and enables clinically intuitive probability statements about intervention benefit that frequentist methods cannot provide. At n=450, Monte Carlo simulations project 83% Bayesian power at ICC=0.05, outperforming equivalent frequentist power of 77%. The decision threshold for recommending intervention adoption is a posterior probability greater than 0.75 that the treatment odds ratio exceeds 1.2. The study switched to Bayesian statistical inference after actual enrolment averaged only 20 patients per month, revising the expected total from 1,368 to approximately 450 patients. Intervention adoption decisions are based on the posterior distribution of effect sizes rather than p-value thresholds. Bayesian analysis combines the prior distribution of plausible parameter values with the observed data likelihood to form the posterior distribution.