Interval Estimation of the Risk Ratio between a Secondary Infection, Given a Primary Infection, and the Primary Infection

This paper discusses interval estimation of the risk ratio (RR) between a secondary infection, given a primary infection, and the primary infection. Three asymptotic closed-form interval estimators are developed using Wald's test statistic, the logarithmic transformation, and Fieller's theorem. The performance of these interval estimators is compared with respect to the coverage probability and the expected length of the resulting confidence intervals. When the underlying probability of a primary infection is high (say, 0.80), all three estimators perform reasonably well. In fact, in this case, they are all essentially equivalent when the number of subjects n > or = 100. When the probability of a primary infection is small (say, 0.20) or moderate (say, 0.30 to 0.50), the interval estimator using the logarithmic transformation outperforms the other two estimators when n < or = 100. In fact, the coverage probability of the former estimator is consistently greater than or equal to the desired confidence level in all the situations considered in this paper and hence is recommended for general use.