Partial Verification Bias Correction Using Inverse Probability Bootstrap Sampling for Binary Diagnostic Tests

Round 1

Reviewer 1 Report

The work is publishable, need to address some comments as below

2.      Improve the introduction part and add more recent literature

3.      At the end of each equation there must be full stop or comma

4.      Remove the grammatical mistakes, typo mistakes etc.

5.      Need to write the conclusion section with a little more details.

After addressing the minor comments, the paper can be published in the journal.

Author Response

Response to Reviewer 1 Comments

Thank you to the reviewer for the constructive comments. We provided the responses for each of the comments below.

Point 1: Improve the introduction part and add more recent literature

Response 1: More recent literature were added; Kohn 2022, Day 2022, Robles 2022, El Chamieh 2022 and Faisal 2021. Kohn was cited in the context of explaining PVB issue (Introduction), Faisal 2021 on MI performance (Discussion), while the rest were cited to give recent implementations of PVB correction methods (Introduction)

Point 2: At the end of each equation there must be full stop or comma

Response 2: Full stops and commas were added to the equations. In addition, equation numbers were added for some equations without numbers in the first draft.

Point 3: Remove the grammatical mistakes, typo mistakes etc.

Response 3: We went through the manuscript again and corrected the mistakes.

Point 4: Need to write the conclusion section with a little more details.

Response 4:The conclusion was rewritten and improved to better describe the study and conclusion as a whole.

Reviewer 2 Report

In this manuscript, the authors propose inverse probability bootstrap (IPB) method in sense to correct partial verification bias (PVB) under missing-at-random (MAR) assumptions for binary diagnostic tests. To this end, they compare the performance of the IBP method with other existing methods, using bias and standard error statistics. The results were obtained by observing two datasets, simulated as well as clinical data.

The manuscript is generally correctly and well written, with all the necessary supporting elements. Therefore, in that sense, the manuscript seems really interesting and I have nothing against accepting it. However, the main problem is that, as the authors themselves state, "the IPB method serves as a flexible alternative to (other) PVB corrections..." and "the IPB had a low bias even though its SE was slightly higher than other correction methods". Based on the results presented in Tables 1 and 2, this claim is not the most clearly visible, so the question arises as to what the advantages of the bootstrap technique proposed here really are. In this context, I suggest the authors (only) to explain with more effort the advantage of the proposed methods.

Author Response

Response to Reviewer 2 Comments

Thank you to the reviewer for the constructive comments. We provided the responses for the comments below.

Point 1: However, the main problem is that, as the authors themselves state, "the IPB method serves as a flexible alternative to (other) PVB corrections..." and "the IPB had a low bias even though its SE was slightly higher than other correction methods". Based on the results presented in Tables 1 and 2, this claim is not the most clearly visible, so the question arises as to what the advantages of the bootstrap technique proposed here really are. In this context, I suggest the authors (only) to explain with more effort the advantage of the proposed methods.

Response 1: Table 1 and 2 represents the results fro the simulated data sets. From Table 1, the differences between the methods in terms of bias were very minimal, while IPB showed higher SE as compared to other comparison methods, especially at smaller sample size N = 200. The differences essentially disappeared at the large sample size N = 1000. Table 2 showed more prominent patterns at a low prevalence of p = 0.1, where IPB consistently showed small bias, which is comparable to BG and IPWE, and in most cases smaller than MI. Again, when N was small at 200, the SE was larger than other methods. The SE for IPB improved, showing smaller relative SE as compared to other methods at N = 1000. In the text, the reason for this was explained (paragraph 2, discussion section), as it is generally known that smaller sample size leads to larger standard error. We noted IPB was more sensitive to the other comparison methods in this respect.

Despite the disadvantage in terms of SE, we found that it is less biased than MI, especially at smaller disease prevalence. It is also comparable in terms of bias to BG and IPWE. The advantage of IPB over BG and IPWE is that IPB allows the use of any full data analytic methods without needing to develop specific method to account for the bias. This is also the advantage shared with MI. While MI restores full data N (observed + unobserved outcome), IPB restores the distribution of the observed data only n (with observed outcome). This explains why IPB has larger SE than MI. To make things clear n in IPB and N in general, this information was further clarified in the revised version (esp. 2.1, 2.2 and results).

Although some of the points were present in the first draft, as pointed out by the reviewer, the sentences were not clear. Therefore, we began with "Based on the results from the simulated/clinical data sets" in the discussion to make the paragraphs clear. We also made clear the differences between N and n as used in this paper, so as to highlight why IPB has larger SE, as the bootstrapped sample size is n < N. The second and last paragraphs in the Discussion were rewritten to clarify this explanation. The conclusion was also rewritten and improved accordingly.

Again we thank the reviewer for the constructive comments.

Reviewer 3 Report

Inverse probability bootstrap (IPB) sampling was proposed by authors.

 

1. The authors should explain the purpose or aim of the research, with the explicit identification of the research question.

2.  The abstract should be revised to reflect the paper's contribution and the importance of the study. 

3. The Conclusion section should be improved based on the studied aspects and the future work.

Author Response

Response to Reviewer 3 Comments

Thank you to the reviewer for the constructive comments. We provided the responses for each of the comments below.

Point 1: The authors should explain the purpose or aim of the research, with the explicit identification of the research question.

Response 1: The last paragraph in Introduction was rewritten, and the research question and objective were aligned and rephrased.

Point 2: The abstract should be revised to reflect the paper's contribution and the importance of the study. 

Response 2: The abstract was revised accordingly to better reflect the paper's contribution and the importance of the study. 

Point 3: The Conclusion section should be improved based on the studied aspects and the future work.

Response 3: The conclusion was rewritten and improved to better describe the study and conclusion as a whole.