The Variance of the Number of Effects in an Epidemiological Cohort - The Role of Dose Uncertainty

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.