Accuracy of Asymptotic Interval Estimation Methods for Comparing Two Risks

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Abstract
In 1985, Miettinen and Nurminen proposed asymptotic likelihood‐based methods for the interval estimation of risk differences, risk ratios and risk‐odds ratios. In the present study, with the use of simulated coverage probabilities in small samples, the actual confidence coefficients of all three of the proposed interval estimates for unstratified data were determined in a comparison with the usual ones. Rated against the 95% coverage probability, the likelihood methods that use restricted maximum likelihood estimators accurately attained the nominal level. The recommended limits also apportioned fairly equal error rates for both tails. The customary intervals performed less successfully. For simple risk differences the estimated confidence probabilities failed to reach the 95% level. For the differences in log‐transformed risks, the tail probabilities of the confidence intervals were disparately allocated, and the method was occasionally incomputable. For the difference in logit‐transformed risks, the uncorrected Woolf intervals were at times fallible and somewhat conservative in comparison to the likelihood ratio‐based intervals. Modification of the conservative Cornfield limits for the risk‐odds ratio greatly improved the accuracy of the likelihood score‐based procedure. With sparse‐stratified data the likelihood score approach produced a biased estimate of the risk‐odds ratio, which for matched pairs equals the square of the exact, conditional maximum likelihood estimate.

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