Rejoinder to "Efficient Statistical Inference for a Parallel Study with Missing Data by using and Exact Method"

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Letter to the Editor

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Journal of Biopharmaceutical Statistics





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In the letter, the author(s) used conditional probabilities to show why unconditional exact tests are the most appropriate ones for comparing two independent proportions. We agree with them, and we recommend that data analysis should always be aligned with data generating mechanism. Tian et al. (2018Tian, G. L., C. Zhang, and X. Jiang. 2018 Apr. Valid statistical inference methods for a casecontrol study with missing data. Statistical Methods in Medical Research 27(4):1001–1023. doi:10.1177/0962280216649619.[Crossref], [PubMed], [Web of Science ®], , [Google Scholar]) discussed three types of data generating mechanism for a study with missing data: (1) total sample size fixed; (2) sample size for each group fixed; and (3) independent sampling with sample sizes for complete data and missing data fixed. Data generating mechanisms were also discussed by Shan and Wilding (2015Shan, G., and G. Wilding. 2015 Feb. Unconditional tests for association in 2 * 2 contingency tables in the total sum fixed design. Statistica Neerlandica 69(1):67–83. doi:10.1111/stan.12047.[Crossref], [Web of Science ®], , [Google Scholar]) for a study with complete data. For a parallel randomized clinical trial, the second data generating mechanism is preferable because the sample size for each group is often pre-determined. That data generating mechanism was utilized in our article for comparing two independent proportions with missing data (Shan et al. 2019Shan, G., A. Hutson, G. E. Wilding, C. Ma, and G. L.Tian. 2019 May. Efficient statistical inference for a parallel study with missing data by using an exact method. Journal of Biopharmaceutical Statistics29(3):478–490. doi:10.1080/10543406.2019.1605782.[Taylor & Francis Online], [Web of Science ®], , [Google Scholar]). The consistency between data analysis and data generating mechanism is extremely important in contemporary clinical trials, e.g. multi-stage designs (Shan et al. 2016Shan, G., G. E. Wilding, A. D. Hutson, and S.Gerstenberger. 2016 Apr. Optimal adaptive two-stage designs for early phase II clinical trials. Statistics in Medicine 35(8):1257–1266. doi:10.1002/sim.6794.[Crossref], [PubMed], [Web of Science ®], , [Google Scholar]). The nature of designs with multiple stages needs to be considered in order to make proper statistical inference (Jennison and Turnbull 1999Jennison, C., and B. W. Turnbull. 1999. Group sequential methods(Chapman & Hall/CRC Interdisciplinary Statistics). 1 ed. Chapman and Hall/CRC.http://www.worldcat.org/isbn/0849303168. [Google Scholar]; Shan 2018aShan, G. 2018a Apr. Exact confidence limits for the response rate in two-stage designs with over- or under-enrollment in the second stage. Statistical Methods in Medical Research 27(4):1045–1055. doi:10.1177/0962280216650918.[Crossref], [PubMed], [Web of Science ®], , [Google Scholar], 2018bShan, G. 2018b Sep. Exact confidence limits for the probability of response in two-stage designs. Statistics52(5):1086–1095. doi:10.1080/02331888.2018.1469023.[Taylor & Francis Online], [Web of Science ®], , [Google Scholar]; Shan et al. 2017Shan, G., H. Zhang, and T. Jiang. 2017 Feb. Efficient confidence limits for adaptive one-arm two-stage clinical trials with binary endpoints. BMC Medical Research Methodology 17 (1).http://view.ncbi.nlm.nih.gov/pubmed/28166741.[Crossref], [PubMed], , [Google Scholar]).


Data generating mechanism; Exact test; One-sided test; Parallel study; Unconditional test


Design of Experiments and Sample Surveys | Statistical Methodology



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