{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T07:03:02Z","timestamp":1790751782402,"version":"4.1.0"},"update-to":[{"DOI":"10.12688\/f1000research.124917.1","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000}},{"DOI":"10.12688\/f1000research.124917.2","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000}}],"reference-count":18,"publisher":"F1000 Research Ltd","license":[{"start":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["f1000research.com"],"crossmark-restriction":false},"short-container-title":["F1000Res"],"abstract":"<ns3:p>Background Many randomized trials measure a continuous outcome simultaneously at baseline and after taking the drug. For a single continuous post-treatment outcome, the sample size calculation is simple, but if there are assessments at multiple time point post-treatment then this longitudinal data may give more insights by analyzing the data using the repeated measures method. Also, if the sample size is calculated using the single time-point method for longitudinal data, it may lead to a larger than required sample size, increasing the cost and time. Methods In this research, an effort is made to determine the size of the sample for repeated measures case and then compare with the single post-baseline case. The sample sizes were examined under different scenarios for the continuous type of response variable. Under \u2018Mean contrast\u2019 and \u2018Diff contrast\u2019 the sample sizes were calculated with different correlations. These two scenarios were again examined under compound symmetry as well as discrete Auto regressive of order 1 type of correlation structure in longitudinal data. The graphical presentation is given for better visualization of the scenarios. Results The sample size required for highly correlated longitudinal data using the multi-timepoint sample size derivation method led to a smaller sample size requirement compared to the single timepoint sample size calculation method. Conclusions This study will help researchers to make better decisions in choosing the right method for sample size determination which may reduce the time and cost of conducting the experiment. Additionally, it is crucial to carefully evaluate and choose the appropriate method when the correlation is weak, as this can significantly impact the accuracy of the results. More complex correlation structures are not studied in this article but can be studied in the same fashion.<\/ns3:p>","DOI":"10.12688\/f1000research.124917.3","type":"journal-article","created":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T08:54:07Z","timestamp":1779872047000},"page":"1550","update-policy":"https:\/\/doi.org\/10.12688\/f1000research.crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Sample size variation in single-time post-dose assessment vs multi-time post-dose assessment"],"prefix":"10.12688","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4322-9377","authenticated-orcid":false,"given":"Sarfaraz","family":"Sayyed","sequence":"first","affiliation":[{"name":"Analytics Hyderabad Telangana 500080 Novartis Healthcare Pvt. Ltd."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ashwini","family":"Mathur","sequence":"additional","affiliation":[{"name":"Clinical Technology & Innovation Dublin Novartis Ireland Ltd."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Asha","family":"Kamath","sequence":"additional","affiliation":[{"name":"Department of Data Science Manipal Karnataka 576104 Manipal Academy of Higher Studies"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2560","published-online":{"date-parts":[[2026,2,5]]},"reference":[{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-416632-5.00011-6","author":"R Nisbet","year":"2018","journal-title":"Handbook of Statistical Analysis and Data Mining Applications."},{"key":"ref3","doi-asserted-by":"publisher","first-page":"200-208","DOI":"10.1002\/ajh.25348","article-title":"Changes in Health-Related Quality of Life with Long-term Eltrombopag Treatment in Adults with Persistent\/Chronic Immune Thrombocytopenia: Findings from the EXTEND Study.","volume":"94","author":"A Khelif","year":"2019","journal-title":"Am. 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In the revised version, we have carefully corrected typographical errors, incomplete sentences, and improperly placed capital letters, and clarified statements that were previously unclear.  \n<b>Response to Comment 1<\/b> We thank the reviewer for this important clarification. In the revised manuscript, we have expanded the Introduction to explicitly explain why estimator precision is a critical metric for the target population of professional athletes. Specifically, we emphasize that professional athletes exhibit high inter- and intra-individual variability, and that precise estimation is essential for accurate performance assessment, monitoring, and interpretation of small but practically meaningful effects. We believe this added explanation clarifies the relevance of precision for the chosen population.  \n<b>Response to Comment 2<\/b> We thank the reviewer for this comment. We agree that there are numerous longitudinal studies in the literature. However, our intention was not to provide a comprehensive review of longitudinal research, but rather to illustrate that even in well\u2011established and prestigious journals, longitudinal studies often provide limited detail regarding sample size calculation. We have now clarified this scope in the manuscript to avoid any misunderstanding and to emphasize that references 3 and 4 were cited as illustrative examples rather than as an exhaustive review of the literature.  \n<b>Response to Comment 3<\/b> We thank the reviewer for pointing this out. The spelling has been corrected in the revised version of the manuscript  \n<b>Response to Comment 4<\/b> We thank the reviewer for this clarification. We have now explicitly stated that the normal distribution of the sample mean is an approximation that becomes increasingly accurate with larger sample sizes, as justified by the central limit theorem. This clarification has been added to the \u2018Notation and framework\u2019 section in the revised manuscript.  \n<b>Response to Comment 5<\/b> We thank the reviewer for this helpful suggestion. To improve clarity, we have revised the hypotheses to explicitly state \u201c\u201d and \u201c&nbsp;, where \n<i>,<\/i> &nbsp;and \n<i>\u03b4<\/i> represents the expected difference. This definition clarifies the role of \u03b4 in the sample size derivation and avoids ambiguous statements. The corresponding revision has been made in the Methods section and aligns with Equation (2) accordingly.  \n<b>Response to Comment 6<\/b> We thank the reviewer for pointing this out. The null and alternative hypothesis notation and the definition of the transpose operator have been corrected in the revised manuscript. &nbsp; \n<b>Response to Comment 7<\/b> We thank the reviewer for this important clarification. We agree that \u03c8_c and \u039b, as population parameters, cannot constitute a test statistic. In the revised manuscript, we have therefore replaced these quantities with their corresponding sample estimates and revised the notation accordingly. As a result, Formula (8) is now explicitly defined as a function of sample\u2011based random variables, ensuring that it represents a valid test statistic.  \n<b>Response to Comment 8<\/b> We thank the reviewer for carefully examining the derivation. We agree that the covariance expansion was incorrectly stated and that the origin of the value 4 in Equation (9) was not justified. In the revised manuscript, we have corrected the covariance expression by explicitly accounting for all relevant covariance terms and have revised Equation (9) accordingly. The incorrect constant has been removed, and the derivation is now consistent with standard covariance identities.  \n<b>Response to Comment 9<\/b> We thank the reviewer for these constructive suggestions to improve clarity. In the revised manuscript, we have explicitly defined and clarified the assumed time trend in the sample size calculation. We have also revised the wording as suggested, replacing \u201callowing\u201d with \u201cchoosing.\u201d In addition, we have added a summary table to clearly indicate the selected time points under each scenario.  \n<b>Response to Comment 10<\/b> We thank the reviewer for this important query. In the revised manuscript, we have explicitly detailed how the sample size of 287 was derived, including the expected difference under the alternative hypothesis, the corresponding null hypothesis, and the selected time point used in the sample size calculation, thereby making the derivation and underlying assumptions transparent and reproducible.  \n<b>Response to Comment 11<\/b> We thank the reviewer for this insightful comment. Our objective in choosing a mean\u2011over\u2011time contrast was to target the average treatment effect across the follow\u2011up period rather than the effect at a single time point. Accordingly, equal weights (1\/4 at each post\u2011baseline time point) were used to reflect this estimand. Although a linear time trend is assumed for the purpose of modeling and sample size calculation, the choice of an average contrast does not require linearity of the treatment effect over time. This approach is particularly relevant in chronic disease settings, where sustained control of biomarkers over time is often of greater clinical interest than the maximum effect at a specific visit, and it also provides robustness to missing data due to loss to follow\u2011up. We have clarified this rationale in the revised manuscript to better explain the choice of the equal\u2011weight contrast and its relationship to the assumed time trend.  \n<b>Response to Comment 12<\/b> We thank the reviewer for this insightful question. Under a compound symmetry correlation structure, when the within\u2011subject correlation is 0.5, the variance reduction gained from repeated measurements is exactly offset by their correlation, resulting in a required sample size equivalent to that of a single\u2011time\u2011point assessment. When the correlation is lower than 0.5, repeated observations provide less shared information across time points, leading to a reduced efficiency and consequently a larger required sample size. To provide a detailed mathematical justification of these results, we have added two appendices that explicitly derive the variance expressions and resulting sample size formulas under different correlation assumptions.  \n<b>Response to Comment 13<\/b> We thank the reviewer for this important question. When within\u2011subject correlation is low, repeated measurements provide relatively little shared information about the underlying treatment effect, as observations across time behave nearly independently. For contrasts that average treatment effects over time, this can lead to increased variability because the additional measurements contribute more noise than signal. In contrast, a single time\u2011point assessment, particularly at a clinically relevant follow\u2011up time point may yield a more efficient estimator under low-correlation settings, as it avoids the accumulation of variability from weakly correlated repeated measures. This explains why, in our framework, the single\u2011time\u2011point assessment can require a smaller sample size when the correlation is low. Appendix added can also give a mathematical glimpse.  \n<b>Response to Comment 14<\/b> We thank the reviewer for this insightful question. Under an AR(1) correlation structure, increasing the number of time points does not necessarily lead to increased efficiency when within\u2011subject correlation is moderate to high. As additional time points are included, the covariance between observations accumulates, and beyond a certain correlation threshold, the variance component associated with the mean\u2011over\u2011time contrast () increases rather than decreasing. This occurs because strongly correlated repeated measurements contribute limited new information while increasing the overall covariance contribution to the contrast variance. As a result, when the correlation exceeds approximately 0.35 in our setting, adding more time points inflates the variance of the mean\u2011over\u2011time estimator, leading to a higher required sample size. To clarify this behavior, we have added an appendix that explicitly compares variance components across different correlation levels and side by side layout for 4 timepoints and 10 timepoints case.  \n<b>Response to Comment 15<\/b> We thank the reviewer for this important clarification. We agree that, for the mean difference contrast, the comparison is based on two time points (baseline and a post\u2011baseline visit), and that it is the temporal distance between these time points, rather than the total number of visits that determines the correlation and variance under an AR(1) structure. We have revised the manuscript to clarify this wording and avoid any implication that the total number of visits alone drives the sample size. We also agree that the observed increase in required sample size when the post\u2011baseline assessment is further from baseline is not a general property but depends on the joint behaviour of the serial correlation and the mean difference at the chosen time point. This dependence is now acknowledged more explicitly in the revised text and reiterated in the conclusion.  \n<b>Response to Comment 16<\/b> We thank the reviewer for this helpful suggestion. To facilitate direct use by readers without a statistical background, the manuscript provides explicit formulas for both single and multiple time point sample size calculations, along with openly available R code (see Software Availability). Users can obtain required sample sizes by specifying interpretable inputs such as the anticipated treatment effect, the assumed variance-covariance structure, and the contrast of interest. In addition, we have added a worked example in the Appendices demonstrating how these inputs are selected and applied in a realistic clinical trial setting.","URL":"https:\/\/f1000research.com\/articles\/11-1550\/v3#referee-comment-15300","order":2,"name":"referee-comment-15300","label":"Referee Comment","group":{"name":"article-reports","label":"Article Reports"}},{"value":"10.5256\/f1000research.170509.r333804, Simon Vandekar, Vanderbilt University Medical Center, Tennessee, 21 Nov 2024, version 2, 1 approved, 2 not approved","URL":"https:\/\/f1000research.com\/articles\/11-1550\/v2#referee-response-333804","order":3,"name":"referee-response-333804","label":"Referee Report","group":{"name":"article-reports","label":"Article Reports"}},{"value":"<b>Sarfaraz Sayyed<\/b>; \n<i>Posted: 18 Jan 2026<\/i>; \n<b>Response to Comment 1<\/b> We thank the reviewer for this important and thorough comment and fully agree that there is a substantial body of literature on power and sample size calculation for longitudinal studies. Our intent was not to provide a comprehensive review or to introduce new theoretical developments in this well\u2011established area. Rather, the aim of the present paper is to provide a focused and accessible comparison between sample size calculations based on a single post\u2011baseline assessment and those incorporating multiple post\u2011baseline time points, under commonly used correlation structures. To better position our work within the existing literature, we have expanded the related work section to explicitly acknowledge classical and contemporary references on longitudinal power analysis, including Diggle et al. and the monograph by Ahn, Heo, and Zhang. We have also added references to existing R packages for longitudinal power analysis and clarified how our approach complements these tools by highlighting specific design trade\u2011offs in simple, interpretable settings. We hope that these revisions more clearly situate the contribution of this paper as illustrative and comparative rather than novel in a methodological sense, while providing practical insights for applied researchers.  \n<b>Response to Comment 2<\/b> We thank the reviewer for this detailed comment. In the revised manuscript, we have added appropriate references for the single\u2011time\u2011point sample size calculation methodology. We have also carefully reviewed the manuscript for grammatical issues and corrected several notation inconsistencies. In particular, we revised Equations (8) and (9) to avoid expressions such as Var(), as &nbsp;represents a fixed parameter, and reformulated these expressions using appropriate sample\u2011based quantities. We believe these revisions improve both the mathematical clarity and presentation of the manuscript.","URL":"https:\/\/f1000research.com\/articles\/11-1550\/v3#referee-comment-15301","order":4,"name":"referee-comment-15301","label":"Referee Comment","group":{"name":"article-reports","label":"Article Reports"}},{"value":"10.5256\/f1000research.179717.r510179, Lucas Damiani, Brazilian Clinical Research Institute, S\u00e3o Paulo, 31 Aug 2026, version 3, 1 approved, 3 not approved","URL":"https:\/\/f1000research.com\/articles\/11-1550\/v3#referee-response-510179","order":5,"name":"referee-response-510179","label":"Referee Report","group":{"name":"article-reports","label":"Article Reports"}},{"value":"<b>Sarfaraz Sayyed<\/b>; \n<i>Posted: 23 Sep 2026<\/i>; \n<b>Response to Major Comment 1:<\/b> We thank the reviewer for this valuable observation. We agree that the original presentation required readers to interpret the simulation results before all covariance structures and contrast definitions had been introduced. To improve clarity, we have revised the manuscript by moving the descriptions of the Compound Symmetry and Autoregressive of order 1 covariance structures, along with the definitions and rationale for the &quot;mean over time&quot; and &quot;mean difference&quot; contrasts, to the Methods section before the presentation of Figures 1 and 2 and the Results section. This reorganization provides the necessary context before the simulation outcomes are discussed and improves the overall readability of the manuscript.  \n<b>Response to Major Comment 2:<\/b> We thank the reviewer for this important observation. We agree that the original conclusion could be interpreted as favouring repeated-measures approaches over single-endpoint analyses. We have therefore revised both the Discussion and Conclusion sections to clarify that baseline-adjusted approaches such as ANCOVA and change-from-baseline analyses already account for the correlation between baseline and follow-up measurements. We further clarified that the primary contribution of this work is to illustrate the potential efficiency gains achieved when multiple post-baseline assessments are incorporated into sample size determination, compared with approaches relying on a single endpoint assessment. We also linked this interpretation to the examples discussed in the Introduction.  \n<b>Response to Major Comment 3<\/b>: We thank the reviewer for this important observation. We agree that the original wording could be misinterpreted as suggesting that fewer measurements should be collected in order to reduce sample size. This was not our intention. We have revised the Discussion and Conclusion sections to clarify that the observed pattern is primarily driven by the AR(1) covariance structure assumed in the illustrative examples, whereby the correlation between baseline and the final assessment decreases as additional intervals are introduced. We now explicitly state that this finding should not be interpreted as a recommendation to reduce the number of measurements, but rather as an illustration of the sensitivity of longitudinal sample size calculations to the assumed covariance structure. We further emphasize that assessment schedules should continue to be guided by the scientific and clinical objectives of the study.  \n<b>Response to Minor Comment 1: <\/b>We thank the reviewer for this suggestion. To improve clarity, we have revised the relevant sentence in the Results section to explicitly direct readers to the supplementary material. The manuscript now states that the mathematical derivation\/proof demonstrating why the multiple-assessment sample size coincides with the single-time-point sample size when the correlation equals 0.5 is provided in Appendix 1 of the Supplementary Appendices.  \n<b>Response to Minor Comment 2:<\/b> We thank the reviewer for this helpful suggestion. To improve clarity and interpretation of the figures, we have added footnotes to Figures 1 and 2 explicitly identifying the red line as the sample size estimate obtained under the single time point assessment scenario. The figure captions\/footnotes have been updated accordingly.  \n<b>Response to justify &quot;source data underlying the results available to ensure full reproducibility&quot;:<\/b> Thank you for your feedback. No empirical data were analyzed in this study. All results presented in the manuscript are figures generated from the assumptions and parameter values explicitly described in the Methods section. The R code used to generate all figures and plots is publicly available in the GitHub repository. Therefore, all information required to reproduce the presented results, including the analytical code and model assumptions, has been provided. We would appreciate any clarification regarding the aspects of reproducibility that you feel are not yet fully addressed, so that we can further improve the manuscript.  \n<b>Response to &quot;conclusions about the method and its performance being adequately supported by the findings presented in the article&quot;<\/b>: Thank you for your feedback. The concerns underlying this comment have been addressed through the revisions made in response to the second and third major comments. These changes strengthen the link between the presented findings and the conclusions regarding the proposed method and its performance.","URL":"https:\/\/f1000research.com\/articles\/11-1550\/v3#referee-comment-17232","order":6,"name":"referee-comment-17232","label":"Referee Comment","group":{"name":"article-reports","label":"Article Reports"}},{"value":"The author(s) declared that no grants were involved in supporting this work","order":7,"name":"grant-information","label":"Grant Information"},{"value":"This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.","order":0,"name":"copyright-info","label":"Copyright"}]}}