Repairing the efficiency loss due to varying cluster sizes in two‐level two‐armed randomized trials with heterogeneous clustering

In two-armed trials with clustered observations the arms may differ in terms of (i) the intraclass correlation, (ii) the outcome variance, (iii) the average cluster size, and (iv) the number of clusters. For a linear mixed model analysis of the treatment effect, this paper examines the expected efficiency loss due to varying cluster sizes based upon the asymptotic relative efficiency of varying versus constant cluster sizes. Simple, but nearly cost-optimal, correction factors are derived for the numbers of clusters to repair this efficiency loss. In an extensive Monte Carlo simulation, the accuracy of the asymptotic relative efficiency and its Taylor approximation are examined for small sample sizes. Practical guidelines are derived to correct the numbers of clusters calculated under constant cluster sizes (within each treatment) when planning a study. Because of the variety of simulation conditions, these guidelines can be considered conservative but safe in many realistic situations. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Gerard J P van Breukelen,et al.  Relative efficiency of unequal versus equal cluster sizes in cluster randomized and multicentre trials , 2007, Statistics in medicine.

[2]  P Jacklin,et al.  Joint teleconsultations (virtual outreach) versus standard outpatient appointments for patients referred by their general practitioner for a specialist opinion: a randomised trial , 2002, The Lancet.

[3]  Amita K. Manatunga,et al.  Sample Size Estimation in Cluster Randomized Studies with Varying Cluster Size , 2001 .

[4]  R. Grissom,et al.  Heterogeneity of variance in clinical data. , 2000, Journal of consulting and clinical psychology.

[5]  Martijn P. F. Berger,et al.  Optimality of Equal vs. Unequal Cluster Sizes in Multilevel Intervention Studies: A Monte Carlo Study for Small Sample Sizes , 2008, Commun. Stat. Simul. Comput..

[6]  H. Keselman,et al.  Consequences of Assumption Violations Revisited: A Quantitative Review of Alternatives to the One-Way Analysis of Variance F Test , 1996 .

[7]  Michal Golovner,et al.  Teleconsultation for cardiac patients: a comparison between nurses and physicians: the SHL experience in Israel. , 2006, Telemedicine journal and e-health : the official journal of the American Telemedicine Association.

[8]  Chris Roberts,et al.  Design and analysis of clinical trials with clustering effects due to treatment , 2005, Clinical trials.

[9]  D. Ashby,et al.  Sample size for cluster randomized trials: effect of coefficient of variation of cluster size and analysis method. , 2006, International journal of epidemiology.

[10]  Z. Feng,et al.  A comparison of statistical methods for clustered data analysis with Gaussian error. , 1996, Statistics in medicine.

[11]  Evangelos Evangelou,et al.  Intraclass correlation coefficients for cluster randomized trials in primary care: the cholesterol education and research trial (CEART). , 2005, Contemporary clinical trials.

[12]  G. V. van Breukelen,et al.  Varying cluster sizes in trials with clusters in one treatment arm: Sample size adjustments when testing treatment effects with linear mixed models , 2009, Statistics in medicine.

[13]  S. Spence,et al.  Cognitive-behavioural therapy versus EMG biofeedback in the treatment of chronic low back pain. , 1995, Behaviour research and therapy.

[14]  H. Keselman,et al.  Consequences of Assumption Violations Revisited: A Quantitative Review of Alternatives to the One-Way Analysis of Variance F Test , 1996 .

[15]  David M Murray,et al.  Individually randomized group treatment trials: a critical appraisal of frequently used design and analytic approaches. , 2008, American journal of public health.

[16]  Eric Stice,et al.  Statistical analysis of group-administered intervention data: Reanalysis of two randomized trials , 2008, Psychotherapy research : journal of the Society for Psychotherapy Research.

[17]  R L Kane,et al.  Primary care outcomes in patients treated by nurse practitioners or physicians: a randomized trial. , 2000, JAMA.

[18]  Mirjam Moerbeek,et al.  A priori power analysis in longitudinal three-level multilevel models: An example with therapist effects , 2010, Psychotherapy research : journal of the Society for Psychotherapy Research.

[19]  G. V. van Breukelen,et al.  Calculating sample sizes for cluster randomized trials: we can keep it simple and efficient! , 2012, Journal of clinical epidemiology.

[20]  G. V. van Breukelen,et al.  Efficiency loss because of varying cluster size in cluster randomized trials is smaller than literature suggests , 2012, Statistics in medicine.

[21]  Jacob Cohen,et al.  A power primer. , 1992, Psychological bulletin.

[22]  A. Holbrook,et al.  Comparing methods to estimate treatment effects on a continuous outcome in multicentre randomized controlled trials: A simulation study , 2011, BMC medical research methodology.

[23]  Ann Louise Kinmonth,et al.  General practice Randomised controlled trial of patient centred care of diabetes in general practice : impact on current wellbeing and future disease risk , 1998 .

[24]  P. Greenbaum,et al.  Testing for group membership effects during and after treatment: The example of group therapy for smoking cessation , 2002 .

[25]  X. Liu,et al.  Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization , 2003 .

[26]  D. Hoover.  Clinical trials of behavioural interventions with heterogeneous teaching subgroup effects , 2002, Statistics in medicine.

[27]  Chris Roberts,et al.  Therapist variation within randomised trials of psychotherapy: implications for precision, internal and external validity , 2010, Statistical methods in medical research.

[28]  B. Moser,et al.  The two-sample t test versus satterthwaite's approximate f test , 1989 .

[29]  Gerard J P Van Breukelen,et al.  Sample size adjustments for varying cluster sizes in cluster randomized trials with binary outcomes analyzed with second‐order PQL mixed logistic regression , 2010, Statistics in medicine.

[30]  S. Raudenbush.  Statistical analysis and optimal design for cluster randomized trials , 1997 .

[31]  G. V. van Breukelen,et al.  Sample size calculation for treatment effects in randomized trials with fixed cluster sizes and heterogeneous intraclass correlations and variances , 2015, Statistical methods in medical research.

[32]  Md Abu Manju,et al.  Sample size calculation in cost‐effectiveness cluster randomized trials: optimal and maximin approaches , 2014, Statistics in medicine.

[33]  Richard J. Hayes,et al.  Cluster randomised trials , 2009 .

[34]  Martijn P. F. Berger,et al.  Design Issues for Experiments in Multilevel Populations , 2000 .

[35]  D. Mant,et al.  General practice Randomised controlled trial of follow up care in general practice of patients with myocardial infarction and angina : final results of the Southampton heart integrated care project ( SHIP ) , 1999 .

[36]  J. Ogrodniczuk,et al.  Assessing and adjusting for dependent observations in group treatment research using multilevel models. , 2009 .