Abstract:

Two basic formulas, for the mean and variance of the number of effects in an epidemiological cohort, are derived. The formula for variance shows “extra-binomial variation” or “overdispersion” when there is correlated uncertainty of the probability of an effect. The formulas were validated by a numerical Monte Carlo study. The method of including “epistemic” uncertainty discussed by Hofer (E. Hofer, Health Physics, 2007) is generalized to include separately uncertainty from a Bayesian posterior distribution when the prior is known, and uncertainty of the prior.