Likelihood-based confidence intervals for the risk ratio using double sampling with over-reported binary data

In this article we derive likelihood-based confidence intervals for the risk ratio using over-reported two-sample binary data obtained using a double-sampling scheme. The risk ratio is defined as the ratio of two proportion parameters. By maximizing the full likelihood function, we obtain closed-form maximum likelihood estimators for all model parameters. In addition, we derive four confidence intervals: a naive Wald interval, a modified Wald interval, a Fieller-type interval, and an Agresti-Coull interval. All four confidence intervals are illustrated using cervical cancer data. Finally, we conduct simulation studies to assess and compare the coverage probabilities and average lengths of the four interval estimators. We conclude that the modified Wald interval, unlike the other three intervals, produces close-to-nominal confidence intervals under various simulation scenarios examined here and, therefore, is preferred in practice.