Unbiased Estimation of Relative Risk Using a Binomial with a Negative Binomial Plan

The use of the binomial distribution for the numerator and the negative binomial for the denominator in prospective studies leads to an unbiased estimate of relative risk and an unbiased estimate for combining experiments. Optimal sample sizes for groups are calculated and confidence intervals for the relative risk are presented. The efficiency of plans are evaluated by comparing variances and coefficients of variation.