Journal of Data Science

Abstract: Of interest in this paper is the development of a model that uses inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false positive misclassification rate may be estimated. Also, three first-order likelihood based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the score and likelihood ratio intervals are generally preferable over the Wald interval. Lastly, the model is applied to a medical data set.

Abstract: We derive three likelihood-based confidence intervals for the risk ratio of two proportion parameters using a double sampling scheme for mis classified binomial data. The risk ratio is also known as the relative risk. We obtain closed-form maximum likelihood estimators of the model parameters by maximizing the full-likelihood function. Moreover, we develop three confidence intervals: a naive Wald interval, a modified Wald interval, and a Fieller-type interval. We apply the three confidence intervals to cervical cancer data. Finally, we perform two Monte Carlo simulation studies to assess and compare the coverage probabilities and average lengths of the three interval estimators. Unlike the other two interval estimators, the modified Wald interval always produces close-to-nominal confidence intervals for the various simulation scenarios examined here. Hence, the modified Wald confidence interval is preferred in practice.

Abstract: Interval estimation for the proportion parameter in one-sample misclassified binary data has caught much interest in the literature. Re cently, an approximate Bayesian approach has been proposed. This ap proach is simpler to implement and performs better than existing frequen tist approaches. However, because a normal approximation to the marginal posterior density was used in this Bayesian approach, some efficiency may be lost. We develop a closed-form fully Bayesian algorithm which draws a posterior sample of the proportion parameter from the exact marginal posterior distribution. We conducted simulations to show that our fully Bayesian algorithm is easier to implement and has better coverage than the approximate Bayesian approach.