Bayesian and likelihood-based interval estimation for the risk ratio using double sampling with misclassified binomial data.

Abstract

We consider the problem of point and interval estimation for the risk ratio using double sampling with two-sample misclassified binary data. For such data, it is well-known that the actual data model is unidentifiable. To achieve model identifiability, then, we obtain additional data via a double-sampling scheme. For the Bayesian paradigm, we devise a parametric, straight-forward algorithm for sampling from the joint posterior density for the parameters, given the data. We then obtain Bayesian point and interval estimators of the risk ratio of two-proportion parameters. We illustrate our algorithm using a real data example and conduct two Monte Carlo simulation studies to demonstrate that both the point and interval estimators perform well. Additionally, we derive three likelihood-based confidence intervals (CIs) for the risk ratio. Specifically, we first obtain closed-form maximum likelihood estimators (MLEs) for all parameters. We then derive three CIs for the risk ratio: a naive Wald interval, a modified Wald interval, and a Fieller-type interval. For illustration purposes, we apply the three CIs to a real data example. We also perform various Monte Carlo simulation studies to assess and compare the coverage probabilities and average lengths of the three CIs. A modified Wald CI performs the best of the three CIs and has near-nominal coverage probabilities.