Testing Homogeneity of Proportion Ratios for Stratified Bilateral Correlated Data

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This article is written with many details of the example used to illustrate the performance of three MLE-based tests (likelihood ratio test, Wald-type test, and score test) when testing the homogeneity of proportion ratios in stratified bilateral correlated data. Some comments for authors to consider:

1. In the Introduction, it is mentioned that the constant R from Rosner’s R model can not reach 1 unless all response rates are equal. I would suggest providing information on the desired range of this conditional probability. Additionally, the authors mention criticisms regarding the poor fit of Rosner's R model in specific situations, it would be helpful to clarify the nature of the poor fit, such as overestimation, underestimation, or fluctuations.

2. In the Introduction, the authors demonstrate the limitations of Rosner’s R and Donner’s ρ model, and choose Dallal’s model for homogeneity testing. Including details on how the mechanism of Dallal's model solves these limitations is recommended.

3. The authors choose Fisher's scoring when getting MLE for δ, please explain the reason of this change. 

4. For Table 2-5 and Table 6-9, line graphs would be beneficial for a clear comparison of simulation results across various scenarios.

5. I would suggest discussing the limitations of the Wald-type test regarding its performance in Empirical Type I error rates.

6. For a more comprehensive illustration of the treatment effect, I would recommend adding the frequency summary of OME-free ears before treatment in Real Data Examples section.

7. The authors may discuss their choice of the likelihood ratio test, score test, and Wald-type test, despite the asymptotic methods are not flexible enough to deal with different sample sizes.

Overall, I think this article effectively compares the likelihood ratio test, score test, and Wald-type test for homogeneity testing of two proportions with stratified bilateral correlated data, providing valuable insights for researchers in this field.

 

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

This paper considers the homogeneity test of proportion ratios  for stratified bilateral correlated data, and presents 3 widely used statistics for testing homogeneity of proportion ratios. Simulation studies are conducted to assess the performance of the presented test statistics in terms of the type I error and power. Two real examples are illustrated by the presented test statistics. 

1. Page 5, line 95: What is m? Please give their definitions. 

2. For the wald-type statistics, the authors can consider the constrained estimates of parameters for I_W  

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

please see attached file

Comments for author File: Comments.pdf

Comments on the Quality of English Language

please see attached file

Author Response

Please see attached word file.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have answered all my questions and I don't have any more comments.