IDEAS home Printed from https://ideas.repec.org/a/spr/lifeda/v31y2025i3d10.1007_s10985-025-09657-y.html
   My bibliography  Save this article

Design and analysis of individually randomized group-treatment trials with time to event outcomes

Author

Listed:
  • Sin-Ho Jung

    (Duke University)

Abstract

In a typical individually randomized group-treatment (IRGT) trial, subjects are randomized between a control arm and an experimental arm. While the subjects randomized to the control arm are treated individually, those in the experimental arm are assigned to one of clusters for group treatment. By sharing some common frailties, the outcomes of subjects in the same groups tend to be dependent, whereas those in the control arm are independent. In this paper, we consider IRGT trials with time to event outcomes. We modify the two-sample log-rank test to compare the survival data from TRGT trials, and derive its sample size formula. The proposed sample size formula requires specification of marginal survival distributions for the two arms, bivariate survival distribution and cluster size distribution for the experimental arm, and accrual period or accrual rate together with additional follow-up period. In a sample size calculation, either the cluster sizes are given and the number of clusters is calculated or the number of clusters is given at the time of study open and the required accrual period to determine the cluster sizes is calculated. Simulations and a real data example show that the proposed test statistic controls the type I error rate and the formula provides accurately powered sample sizes. Also proposed are optimal designs minimizing the total sample size or the total cost when the cost per subject is different between two treatment arms.

Suggested Citation

  • Sin-Ho Jung, 2025. "Design and analysis of individually randomized group-treatment trials with time to event outcomes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 31(3), pages 574-594, July.
    • Handle: RePEc:spr:lifeda:v:31:y:2025:i:3:d:10.1007_s10985-025-09657-y
    DOI: 10.1007/s10985-025-09657-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10985-025-09657-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10985-025-09657-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Jianghao Li & Sin-Ho Jung, 2022. "Sample size calculation for clustered survival data under subunit randomization," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 40-67, January.
    2. Pals, S.L. & Murray, D.M. & Alfano, C.M. & Shadish, W.R. & Hannan, P.J. & Baker, W.L., 2008. "Individually randomized group treatment trials: A critical appraisal of frequently used design and analytic approaches," American Journal of Public Health, American Public Health Association, vol. 98(8), pages 1418-1424.
    3. Ying, Z. & Wei, L. J., 1994. "The Kaplan-Meier Estimate for Dependent Failure Time Observations," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 17-29, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    2. Jessica R Goodkind & M Lee Van Horn & Julia Meredith Hess & David Lardier & Cirila Estela Vasquez Guzman & Janet Ramirez & Susana Echeverri Herrera & Meredith Blackwell & Alejandra Lemus & Bianca Ruiz, 2024. "Protocol of the study: Multilevel community-based mental health intervention to address structural inequities and adverse disparate consequences of COVID-19 pandemic on Latinx Immigrants and African r," PLOS ONE, Public Library of Science, vol. 19(4), pages 1-19, April.
    3. R. Dhanya Nair & E. I. Abdul Sathar, 2024. "Nonparametric estimation of extropy based measures under right censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2374-2382, June.
    4. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    5. Jianghao Li & Sin-Ho Jung, 2022. "Sample size calculation for clustered survival data under subunit randomization," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 40-67, January.
    6. Chien-Lin Su & Russell J. Steele & Ian Shrier, 2021. "The semiparametric accelerated trend-renewal process for recurrent event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 357-387, July.
    7. Trine Filges & Mette Verner & Else Ladekjær & Elizabeth Bengtsen, 2023. "PROTOCOL: Participation in organised sport to improve and prevent adverse developmental trajectories of at‐risk youth: A systematic review," Campbell Systematic Reviews, John Wiley & Sons, vol. 19(2), June.
    8. Roberto Cattivelli & Anna Guerrini Usubini & Gian Mauro Manzoni & Francesco Vailati Riboni & Giada Pietrabissa & Alessandro Musetti & Christian Franceschini & Giorgia Varallo & Chiara A. M. Spatola & , 2021. "ACTonFood. Acceptance and Commitment Therapy-Based Group Treatment Compared to Cognitive Behavioral Therapy-Based Group Treatment for Weight Loss Maintenance: An Individually Randomized Group Treatmen," IJERPH, MDPI, vol. 18(18), pages 1-19, September.
    9. Nour El Houda Rouabah & Nahima Nemouchi & Fatiha Messaci, 2019. "A rate of consistency for nonparametric estimators of the distribution function based on censored dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 259-280, June.
    10. Bernard Rosner & Camden Bay & Robert J. Glynn & Gui-shuang Ying & Maureen G. Maguire & Mei-Ling Ting Lee, 2023. "Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton–Oakes model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 854-887, October.
    11. Trine Filges & Anja Bondebjerg Mølgaard & Geir Smedslund & Malene W. Kildemoes & Elizabeth Bengtsen, 2024. "Protocol: Proactive resilience programmes for improving resilience and psychological adaptation in employees in high‐risk occupations: A systematic review," Campbell Systematic Reviews, John Wiley & Sons, vol. 20(4), December.
    12. Candel, Math J.J.M. & Van Breukelen, Gerard J.P., 2010. "D-optimality of unequal versus equal cluster sizes for mixed effects linear regression analysis of randomized trials with clusters in one treatment arm," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1906-1920, August.
    13. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    14. Trine Filges & Jens Dietrichson & Bjørn C. A. Viinholt & Nina T. Dalgaard, 2022. "Service learning for improving academic success in students in grade K to 12: A systematic review," Campbell Systematic Reviews, John Wiley & Sons, vol. 18(1), March.
    15. Trine Filges & Geir Smedslund & Tine Eriksen & Kirsten Birkefoss, 2023. "PROTOCOL: The FRIENDS preventive programme for reducing anxiety symptoms in children and adolescents: A systematic review," Campbell Systematic Reviews, John Wiley & Sons, vol. 19(4), December.
    16. Guosheng Yin & Jianwen Cai, 2005. "Quantile Regression Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 151-161, March.
    17. Trine Filges & Mette Verner & Else Ladekjær & Elizabeth Bengtsen, 2024. "Participation in organised sport to improve and prevent adverse developmental trajectories of at‐risk youth: A systematic review," Campbell Systematic Reviews, John Wiley & Sons, vol. 20(1), March.
    18. Wei Pan & Thomas A. Louis, 2000. "A Linear Mixed-Effects Model for Multivariate Censored Data," Biometrics, The International Biometric Society, vol. 56(1), pages 160-166, March.
    19. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    20. Lu Mao, 2023. "Study design for restricted mean time analysis of recurrent events and death," Biometrics, The International Biometric Society, vol. 79(4), pages 3701-3714, December.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:lifeda:v:31:y:2025:i:3:d:10.1007_s10985-025-09657-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.