Bayesian and likelihood-based interval estimation for the risk ratio using double sampling with misclassified binomial data.
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Access changed 3/18/13.
Rahardja, Dewi Gabriela.
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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.