Sample size calculation for the augmented logrank test in randomized clinical trials.
covariate adjustment
cox proportional hazards model
disease registry
martingale residuals
power calculation
Journal
Statistics in medicine
ISSN: 1097-0258
Titre abrégé: Stat Med
Pays: England
ID NLM: 8215016
Informations de publication
Date de publication:
30 06 2022
30 06 2022
Historique:
revised:
14
02
2022
received:
13
06
2021
accepted:
23
02
2022
pubmed:
24
3
2022
medline:
22
6
2022
entrez:
23
3
2022
Statut:
ppublish
Résumé
In randomized clinical trials, incorporating baseline covariates can improve the power in hypothesis testing for treatment effects. For survival endpoints, the Cox proportional hazards model with baseline covariates as explanatory variables can improve the standard logrank test in power. Although this has long been recognized, this adjustment is not commonly used as the primary analysis and instead the logrank test followed by the estimation of the hazard ratio between treatment groups is often used. By projecting the score function for the Cox proportional hazards model onto a space of covariates, the logrank test can be more powerful. We derive a power formula for this augmented logrank test under the same setting as the widely used power formula for the logrank test and propose a simple strategy for sizing randomized clinical trials utilizing historical data of the control treatment. Through numerical studies, the proposed procedure was found to have the potential to reduce the sample size substantially as compared to the standard logrank test. A concern to utilize historical data is that those might not reflect well the data structure of the study to design and then the sample size calculated might not be accurate. Since our power formula is applicable to datasets pooled across the treatment arms, the validity of the power calculation at the design stage can be checked in blind reviews.
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
2627-2644Informations de copyright
© 2022 John Wiley & Sons Ltd.
Références
Cox DR. Regression models and life tables (with discussion). J Royal Stat Soc Ser B. 1972;34:187-220.
Horiguchi M, Uno H. A flexible and coherent test/estimation procedure based on restricted mean survival times for censored time-to-event data in randomized clinical trials. Stat Med. 2018;37:2307-2320.
Fleming TR, Harrington D. Counting Processes and Survival Analysis. New York, NY: John Wiley & Son, Inc; 1991.
Pocock SJ, Assmann SE, Enos LE, Kasten LE. Subgroup analysis, covariate adjustment and baseline comparisons in clinical trial reporting: current practice and problems. Stat Med. 2002;21:2917-2930.
Committee for Proprietary Medicinal Products (CPMP). Points to consider on adjustment for baseline covariates. Stat Med. 2003;23:701-709.
Tsiatis AA, Rosner GL, Tritchler DL. Group sequential tests with censored survival data adjusting for covariates. Biometrika. 1985;72:365-373.
Anderson GL, LeBlanc M, Liu PY, Crowley J. On use of covariates in randomization and analysis of clinical trials. In: Crowley J, Ankerst DP, eds. Handbook of Statistics in Clinical Oncology. 2nd ed. Boca Raton, FL: Chapman and Hall/CRC Press; 2006:167-179.
Lin DY, Wei LJ. The robust inference for the Cox proportional hazards model. J Am Stat Assoc. 1989;84:1074-1078.
Kong FH, Slud E. Robust covariate-adjusted log-rank tests. Biometrika. 1997;84:847-862.
DiRienzo AG, Lagakos SW. Effects of model misspecification on tests of no randomized treatment effect arising from Cox's proportional hazards model. J R Stat Soc Ser B. 2001;63:745-757.
Piccart-Gebhart MJ, Procter M, Leyland-Jones GA, et al. Trastuzumab after adjuvant chemotherapy in HER2-positive breast cancer. N Engl J Med. 2005;353:1659-1672.
Bang YJ, Cutsem EV, Feyereislova A, et al. Trastuzumab in combination with chemotherapy versus chemotherapy alone for treatment of HER2-positive advanced gastric or gatro-oesophageal junction cancer (ToGA): a phase 3, open-label, randomized controlled trial. Lancet. 2010;376:687-697.
Lu X, Tsiatis AA. Improving the efficiency of the log-rank test using auxiliary covariates. Biometrika. 2008;95:679-694.
Tsiatis AA. Semiparametric Theory and Missing Data. New York, NY: Springer Scientific+Business, LCC; 2006.
Collett D. Modelling Survival Data in Medical Research. Boca Raton, FL: Chapman and Hall/CRC Press; 2004.
Schoenfeld D. The asymptotic properties of nonparametric tests for comparing survival distributions. Biometrika. 1981;68:316-319.
Struthers CA, Kalbleisch JD. Misspecified proportional hazard models. Biometrika. 1986;73:363-369.
Laurie JA, Moertel CG, Fleming TR, et al. Surgical adjuvant therapy of large-bowel carcinoma: an evaluationof levamisole and the combination of levamisole and fluorouracil: the north central cancer treatment group and the mayo clinic. J Clin Oncol. 1989;7:1447-1456.
Moertel CG, Fleming TR, MacDonald JS, et al. Levamisole and fluorouracil for adjuvant therapy of resected colon carcinoma. N Engl J Med. 1990;332:352-358.
Tsiatis AA, Davidian M, Zhang M, Lin X. Covariate adjustment for two-sample treatment comparisons in randomized clinical trials: a principled yet flexible approach. Stat Med. 2008;27:4658-4677.
Zhang M, Tsiatis AA, Davidian M. Improving efficiency of inferences in randomized clinical trials using auxiliary covariates. Biometrics. 2008;64:707-715.
Tian L, Cai T, Zhao L, Wei LJ. On the covariate-adjusted estimation for an overall treatment difference with data from a randomized comparative clinical trail. Biostatistics. 2012;13:256-273.
Zhang M. Robust methods to improve efficiency and reduce bias in estimating survival curves in randomized clinical trials. Lifetime Data Anal. 2015;21:119-137.
Jiang F, Tian L, Fu H, Hasegawa T, Wei LJ. Robust alternatives to ANCOVA for estimating the treatment effect via a randomized comparative study. J Am Stat Assoc. 2019;114:1854-1864.
Friede T, Pohlmann H, Schmidli H. Blinded sample size reestimation in event-driven clinical trials: Methods and an application in multiple sclersis. Pharm Stat. 2019;18:351-365.
Mütze T, Salem S, Benda N, Schmidli H, Friede T. Blinded continuous information monitoring of recurrent event endpoints with time trends in clinical trials. Stat Med. 2020;39:3968-3985.
Lan KK, DeMets DL. Discrete sequential boundaries for clinical trials. Biomerika. 1983;70:659-663.
Lan KK, Zucker DM. Sequential monitoring of clinical trials: the role of information and Brownian motion. Stat Med. 1993;12:753-765.
Proschan MA, Leifer E, Liu Q. Adaptive regression. J Biopharm Stat. 2005;15:593-603.
Mehrotra DV, Marceau WR. Survival analysis using a 5-step stratified testing and amalgamation routine (5-STAR) in randomized clinical trials. Stat Med. 2020;39:4724-4744.
Hattori S, Henmi M. Estimation of treatment effects based on possibly misspecified Cox regression. Lifetime Data Anal. 2012;18:408-433.