Performance of mixed effects models and generalized estimating equations for continuous outcomes in partially clustered trials including both independent and paired data.
clinical trials
generalized estimating equations
mixed effects models
partial clustering
power
simulation study
Journal
Statistics in medicine
ISSN: 1097-0258
Titre abrégé: Stat Med
Pays: England
ID NLM: 8215016
Informations de publication
Date de publication:
04 Sep 2024
04 Sep 2024
Historique:
revised:
19
06
2024
received:
01
03
2024
accepted:
07
08
2024
medline:
5
9
2024
pubmed:
5
9
2024
entrez:
5
9
2024
Statut:
aheadofprint
Résumé
Many clinical trials involve partially clustered data, where some observations belong to a cluster and others can be considered independent. For example, neonatal trials may include infants from single or multiple births. Sample size and analysis methods for these trials have received limited attention. A simulation study was conducted to (1) assess whether existing power formulas based on generalized estimating equations (GEEs) provide an adequate approximation to the power achieved by mixed effects models, and (2) compare the performance of mixed models vs GEEs in estimating the effect of treatment on a continuous outcome. We considered clusters that exist prior to randomization with a maximum cluster size of 2, three methods of randomizing the clustered observations, and simulated datasets with uninformative cluster size and the sample size required to achieve 80% power according to GEE-based formulas with an independence or exchangeable working correlation structure. The empirical power of the mixed model approach was close to the nominal level when sample size was calculated using the exchangeable GEE formula, but was often too high when the sample size was based on the independence GEE formula. The independence GEE always converged and performed well in all scenarios. Performance of the exchangeable GEE and mixed model was also acceptable under cluster randomization, though under-coverage and inflated type I error rates could occur with other methods of randomization. Analysis of partially clustered trials using GEEs with an independence working correlation structure may be preferred to avoid the limitations of mixed models and exchangeable GEEs.
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Subventions
Organisme : National Health and Medical Research Council
ID : 1171422
Organisme : National Health and Medical Research Council
ID : 1173576
Organisme : Australian Government
Informations de copyright
© 2024 The Author(s). Statistics in Medicine published by John Wiley & Sons Ltd.
Références
Vierron E, Giraudeau B. Design effect in multicenter studies: gain or loss of power? BMC Med Res Methodol. 2009;9(1):39.
Donner A, Klar N. Design and Analysis of Cluster Randomization Trials in Health Research. Arnold: Co‐published by the Oxford University Press; 2000.
Senn SS. Cross‐Over Trials in Clinical Research. 2nd ed. New York: Wiley; 2002.
Lange KM, Kasza J, Sullivan TR, Yelland LN. Partially clustered designs for clinical trials: unifying existing designs using consistent terminology. Clin Trials. 2023;20(2):99‐110.
Collins CT, Makrides M, McPhee AJ, et al. Docosahexaenoic acid and bronchopulmonary dysplasia in preterm infants. N Engl J Med. 2017;376(13):1245‐1255.
Chew EY, Clemons TE, Jaffe GJ, et al. Effect of ciliary neurotrophic factor on retinal neurodegeneration in patients with macular telangiectasia type 2: a randomized clinical trial. Ophthalmology. 2019;126(4):540‐549.
Hjorth MH, Kold S, Søballe K, et al. Preparation of the femoral bone cavity for cementless stems: broaching vs compaction. A five‐year randomized radiostereometric analysis and dual energy x‐ray absorption study. J Arthroplasty. 2017;32(6):1894‐1901.
Roberts C, Roberts SA. Design and analysis of clinical trials with clustering effects due to treatment. Clin Trials. 2005;2(2):152‐162.
Lohr S, Schochet PZ, Sanders E. Partially nested randomized controlled trials in education research: a guide to design and analysis. NCER 2014–2000. Jessup, MD: National Center for Education Research; 2014. https://eric.ed.gov/?id=ED545532. Accessed July 26, 2021.
Walwyn R, Roberts C. Therapist variation within randomised trials of psychotherapy: implications for precision, internal and external validity. Stat Methods Med Res. 2010;19(3):291‐315.
Moerbeek M, Wong WK. Sample size formulae for trials comparing group and individual treatments in a multilevel model. Stat Med. 2008;27(15):2850‐2864.
Candel MJJM, Breukelen GJPV. Varying cluster sizes in trials with clusters in one treatment arm: sample size adjustments when testing treatment effects with linear mixed models. Stat Med. 2009;28(18):2307‐2324.
Heo M, Litwin AH, Blackstock O, Kim N, Arnsten JH. Sample size determinations for group‐based randomized clinical trials with different levels of data hierarchy between experimental and control arms. Stat Methods Med Res. 2017;26(1):399‐413.
Tong G, Tong J, Li F. Designing multicenter individually randomized group treatment trials. Biom J. 2024;66(1):2200307.
Wang X, Turner EL, Li F. Designing individually randomized group treatment trials with repeated outcome measurements using generalized estimating equations. Stat Med. 2024;43(2):358‐378.
Teerenstra S, Kasza J, Leontjevas R, Forbes AB. Sample size for partially nested designs and other nested or crossed designs with a continuous outcome when adjusted for baseline. Stat Med. 2023;42(19):3568‐3592.
Baldwin SA, Bauer DJ, Stice E, Rohde P. Evaluating models for partially clustered designs. Psychol Methods. 2011;16(2):149‐165.
Candlish J, Teare MD, Dimairo M, Flight L, Mandefield L, Walters SJ. Appropriate statistical methods for analysing partially nested randomised controlled trials with continuous outcomes: a simulation study. BMC Med Res Methodol. 2018;18(1):105.
Roberts C, Batistatou E, Roberts SA. Design and analysis of trials with a partially nested design and a binary outcome measure. Stat Med. 2016;35(10):1616‐1636.
Mountain G, Windle G, Hind D, et al. A preventative lifestyle intervention for older adults (lifestyle matters): a randomised controlled trial. Age Ageing. 2017;46(4):627‐634.
LeBrun DG, Tran T, Wypij D, Kocher MS. Statistical analysis of dependent observations in the orthopaedic sports literature. Orthop J Sports Med. 2019;7(1):2325967118818410.
Kahan BC, Forbes AB, Doré CJ, Morris TP. A re‐randomisation design for clinical trials. BMC Med Res Methodol. 2015;15(1):96.
Yelland LN, Sullivan TR, Price DJ, Lee KJ. Sample size calculations for randomised trials including both independent and paired data. Stat Med. 2017;36(8):1227‐1239.
Yelland LN, Sullivan TR, Collins CT, Price DJ, McPhee AJ, Lee KJ. Accounting for twin births in sample size calculations for randomised trials. Paediatr Perinat Epidemiol. 2018;32(4):380‐387.
Hibbs AM, Black D, Palermo L, et al. Accounting for multiple births in neonatal and perinatal trials: systematic review and case study. J Pediatr. 2010;156(2):202‐208.
Das A, Tyson J, Pedroza C, et al. Methodological issues in the design and analyses of neonatal research studies: experience of the NICHD neonatal research network. Semin Perinatol. 2016;40(6):374‐384.
Fitzmaurice GM, Laird NM, Ware JH. Applied Longitudinal Analysis. 2nd ed. Hoboken, NJ: Wiley; 2011.
Zhao LP, Prentice RL, Self SG. Multivariate mean parameter estimation by using a partly exponential model. J R Stat Soc Series B Method. 1992;54(3):805‐811.
Shaffer ML, Kunselman AR, Watterberg KL. Analysis of neonatal clinical trials with twin births. BMC Med Res Methodol. 2009;9(1):12.
Dell‐Kuster S, Droeser RA, Schäfer J, et al. Systematic review and simulation study of ignoring clustered data in surgical trials. Br J Surg. 2018;105(3):182‐191.
Yelland LN, Salter AB, Ryan P, Makrides M. Analysis of binary outcomes from randomised trials including multiple births: when should clustering be taken into account? Paediatr Perinat Epidemiol. 2011;25(3):283‐297.
Gates S, Brocklehurst P. How should randomised trials including multiple pregnancies be analysed? BJOG. 2004;111(3):213‐219.
Seaman S, Pavlou M, Copas A. Review of methods for handling confounding by cluster and informative cluster size in clustered data. Stat Med. 2014;33(30):5371‐5387.
Hedeker D, Gibbons RD, Flay BR. Random‐effects regression models for clustered data with an example from smoking prevention research. J Consult Clin Psychol. 1994;62(4):757‐765.
Liang KY, Zeger SL. Longitudinal data analysis using generalized linear models. Biometrika. 1986;73(1):13‐22.
Ritz J, Spiegelman D. Equivalence of conditional and marginal regression models for clustered and longitudinal data. Stat Methods Med Res. 2004;13(4):309‐323.
Morris TP, White IR, Crowther MJ. Using simulation studies to evaluate statistical methods. Stat Med. 2019;38(11):2074‐2102.
Blondel B, Macfarlane A, Gissler M, Breart G, Zeitlin J. General obstetrics: preterm birth and multiple pregnancy in European countries participating in the PERISTAT project. BJOG. 2006;113(5):528‐535.
Karakosta A, Vassilaki M, Plainis S, Elfadl NH, Tsilimbaris M, Moschandreas J. Choice of analytic approach for eye‐specific outcomes: one eye or two? Am J Ophthalmol. 2012;153(3):571‐579.e1.
Park MS, Kim SJ, Chung CY, Choi IH, Lee SH, Lee KM. Statistical consideration for bilateral cases in orthopaedic research. J Bone Joint Surg Am. 2010;92(8):1732‐1737.
R Core Team. R: A Language and Environment for Statistical Computing. 2020. http://www.R‐project.org/
Bates D, Mächler M, Bolker B, Walker S. Fitting linear mixed‐effects models using lme4. J Stat Softw. 2015;67(1):1‐48.
Højsgaard S, Halekoh U, Yan J. The R package geepack for generalized estimating equations. J Stat Softw. 2006;15:1‐11.
Gasparini A. Rsimsum: summarise results from Monte Carlo simulation studies. J Open Source Softw. 2018;3(26):739.
Gedde SJ, Schiffman JC, Feuer WJ, Parrish RK, Heuer DK, Brandt JD. The tube versus trabeculectomy study: design and baseline characteristics of study patients. Am J Ophthalmol. 2005;140(2):275.e1‐275.e14.
Gedde SJ, Schiffman JC, Feuer WJ, Herndon LW, Brandt JD, Budenz DL. Treatment outcomes in the tube versus trabeculectomy study after one year of follow‐up. Am J Ophthalmol. 2007;143(1):9‐22.e2.
Katz J. Two eyes or one? The data analyst's dilemma. Ophthalmic Surg Lasers Imaging Retina. 1988;19(8):585‐589.
Bengtsson B, Lindén C, Heijl A, Andersson‐Geimer S, Aspberg J, Jóhannesson G. The glaucoma intensive treatment study: interim results from an ongoing longitudinal randomized clinical trial. Acta Ophthalmol. 2022;100(2):e455‐e462.
Yang Y, Jiang Y, Huang S, et al. Laser in glaucoma and ocular hypertension trial (LIGHT) in China – a randomized controlled trial: design and baseline characteristics. Am J Ophthalmol. 2021;230:143‐150.
Leyrat C, Morgan KE, Leurent B, Kahan BC. Cluster randomized trials with a small number of clusters: which analyses should be used? Int J Epidemiol. 2018;47(1):321‐331.
Li P, Redden DT. Small sample performance of bias‐corrected sandwich estimators for cluster‐randomized trials with binary outcomes. Stat Med. 2015;34(2):281‐296.
Thompson J, Hemming K, Forbes A, Fielding K, Hayes R. Comparison of small‐sample standard‐error corrections for generalised estimating equations in stepped wedge cluster randomised trials with a binary outcome: a simulation study. Stat Methods Med Res. 2021;30(2):425‐439.
Kahan BC, Forbes G, Ali Y, et al. Increased risk of type I errors in cluster randomised trials with small or medium numbers of clusters: a review, reanalysis, and simulation study. Trials. 2016;17(1):438.
Huang S, Fiero MH, Bell ML. Generalized estimating equations in cluster randomized trials with a small number of clusters: review of practice and simulation study. Clin Trials. 2016;13(4):445‐449.
Kahan BC, Li F, Copas AJ, Harhay MO. Estimands in cluster‐randomized trials: choosing analyses that answer the right question. Int J Epidemiol. 2023;52(1):107‐118.
Yelland LN, Sullivan TR, Pavlou M, Seaman SR. Analysis of randomised trials including multiple births when birth size is informative. Paediatr Perinat Epidemiol. 2015;29(6):567‐575.
Bernardo J, Nowacki A, Martin R, Fanaroff JM, Hibbs AM. Multiples and parents of multiples prefer same arm randomization of siblings in neonatal trials. J Perinatol. 2015;35(3):208‐213.
Mancl LA, Leroux BG. Efficiency of regression estimates for clustered data. Biometrics. 1996;52(2):500.
Dahmen G, Ziegler A. Generalized estimating equations in controlled clinical trials: hypotheses testing. Biom J. 2004;46(2):214‐232.
Williamson JM, Datta S, Satten GA. Marginal analyses of clustered data when cluster size is informative. Biometrics. 2003;59(1):36‐42.