Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample

Abstract

We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

Multiple Comparison Procedures for the Differences of Proportion Parameters in Over-Reported Multiple-Sample Binomial Data

“…In the second stage (Section 6), to account for the multiplicity effect in the MCP, we prescribed three adjustment methods (Bonferroni, Šidák, and Dunn) to the differences of proportions parameters in the presence of either under/over-reported multiple-sample binomial data, into the adjusted CIs calculation. Note that unlike those difficult non-closed-form algorithms proposed in the previously reviewed literature in Rahardja of 2019 [6], this second stage (MCP stage) is easily attainable because of our closed-form algorithm, which is easy to implement, and subsequently, doable to directly invert the adjusted CI methods (Bonferroni, Šidák, and Dunn).…”

“…Stats 2020, 3 57 However, the above MCP-pioneer references are MCP methods without any presence of misclassifications (i.e., false-positive, false-negative, nor both). On the hand, there are literatures which discussed misclassified binomial data, for one-sample and two-sample binomial data, with one-type or both-type of misclassifications, Bayesian or frequentist (i.e., likelihood-based) methods, but none of them are with the multiplicity adjustments for (pairwise) MCPs, either; for example, Rahardja in 2019 [6] reviewed such literature. Additionally, there are past papers which studied various ways to analyze binomial data, but they did not include misclassifications nor multiplicity adjustments for (pairwise) MCPs; for example, among many papers, Gianinetti in 2020 [7], Giles and Fiori in 2019 [8], Hodge and Vieland in 2017 [9].…”

“…Previous literature recommends the merits of using a double sample (Rahardja et al in 2015 [14]; Rahardja & Yang in 2015 [13]; Tenenbein in 1970 [15]. To incorporate such double sample merit into the MCP problem, using maximum likelihood estimation approach, basically, the Rahardja of 2019 [6] paper has summarized the concept (in Section 1) using a Bayesian approach. Numerous literatures in past studies have previously been listed in Rahardja of 2019 [6] manuscript and hence are not re-listed here.…”

“…The pairwise proportion difference (First Stage, Sections 2-5) method is just an intermediate step. The methods proposed in the past literature reviews (Rahardja of 2019 [6]) were not able to easily reach MCP adjustment (Second/Final Stage) due to difficult, complex, and non-closed-form algorithms. However, since our closed-form algorithm is easy to implement, consequently, we are able to easily apply MCP adjustment methods (e.g., Bonferroni, Šidák, and Dunn) to address the multiplicity issue.…”