Sample size in cluster‐randomized trials with time to event as the primary endpoint

In cluster-randomized trials, groups of individuals (clusters) are randomized to the treatments or interventions to be compared. In many of those trials, the primary objective is to compare the time for an event to occur between randomized groups, and the shared frailty model well fits clustered time-to-event data. Members of the same cluster tend to be more similar than members of different clusters, causing correlations. As correlations affect the power of a trial to detect intervention effects, the clustered design has to be considered in planning the sample size. In this publication, we derive a sample size formula for clustered time-to-event data with constant marginal baseline hazards and correlation within clusters induced by a shared frailty term. The sample size formula is easy to apply and can be interpreted as an extension of the widely used Schoenfeld's formula, accounting for the clustered design of the trial. Simulations confirm the validity of the formula and its use also for non-constant marginal baseline hazards. Findings are illustrated on a cluster-randomized trial investigating methods of disseminating quality improvement to addiction treatment centers in the USA.

[1]  D. Gustafson,et al.  The Network for the Improvement of Addiction Treatment (NIATx): enhancing access and retention. , 2007, Drug and alcohol dependence.

[2]  Meinhard Kieser,et al.  Sample Size Recalculation in Internal Pilot Study Designs: A Review , 2006, Biometrical journal. Biometrische Zeitschrift.

[3]  A. Yashin,et al.  A bivariate survival model with compound Poisson frailty , 2010, Statistics in medicine.

[4]  G. Guyatt,et al.  TEACH: Trial of Education And Compliance in Heart dysfunction chronic disease and heart failure (HF) as an increasing problem. , 2008, Contemporary clinical trials.

[5]  David V Glidden,et al.  Modelling clustered survival data from multicentre clinical trials , 2004, Statistics in medicine.

[6]  E. Richard,et al.  Prevention of Dementia by Intensive Vascular Care (PreDIVA): A Cluster-randomized Trial in Progress , 2009, Alzheimer disease and associated disorders.

[7]  D. Schoenfeld,et al.  Sample-size formula for the proportional-hazards regression model. , 1983, Biometrics.

[8]  C. Brotons,et al.  Randomized clinical trial to assess the efficacy of a comprehensive programme of secondary prevention of cardiovascular disease in general practice: the PREseAP study. , 2011, Revista espanola de cardiologia.

[9]  James H. Ford,et al.  Disseminating quality improvement: study protocol for a large cluster-randomized trial , 2011, Implementation science : IS.

[10]  F. Hsieh.  Comparing sample size formulae for trials with unbalanced allocation using the logrank test. , 1992, Statistics in medicine.

[11]  Sin-Ho Jung,et al.  Rank Tests for Clustered Survival Data , 2003, Lifetime data analysis.

[12]  W. Klunk,et al.  Whatever happened to Pittsburgh Compound-A? , 2008, Alzheimer disease and associated disorders.

[13]  A Donner,et al.  Developments in cluster randomized trials and Statistics in Medicine , 2007, Statistics in medicine.

[14]  R. Hayes,et al.  Simple sample size calculation for cluster-randomized trials. , 1999, International journal of epidemiology.

[15]  S. Willich,et al.  Population-based intervention to reduce prehospital delays in patients with cerebrovascular events. , 2009, Archives of internal medicine.

[16]  A. Nathens,et al.  Intracluster correlation coefficient in multicenter childhood trauma studies , 2007, Injury Prevention.

[17]  L. Freedman.  Tables of the number of patients required in clinical trials using the logrank test. , 1982, Statistics in medicine.

[18]  L. J. Wei,et al.  The Robust Inference for the Cox Proportional Hazards Model , 1989 .

[19]  Michael R. Kosorok,et al.  Sample‐size formula for clustered survival data using weighted log‐rank statistics , 2004 .

[20]  H. Adèr,et al.  Faster return to work after psychiatric consultation for sicklisted employees with common mental disorders compared to care as usual. A randomized clinical trial , 2010, Neuropsychiatric disease and treatment.

[21]  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.

[22]  Jonathan L. Blitstein,et al.  Design and analysis of group-randomized trials: a review of recent methodological developments. , 2004, American journal of public health.

[23]  Tailiang Xie,et al.  Design and sample size estimation in clinical trials with clustered survival times as the primary endpoint , 2003, Statistics in medicine.

[24]  R. Wolfe,et al.  Frailty Survival Model Analysis of the National Deceased Donor Kidney Transplant Dataset Using Poisson Variance Structures , 2005 .

[25]  M. Fine,et al.  Implementation of an evidence-based guideline to reduce duration of intravenous antibiotic therapy and length of stay for patients hospitalized with community-acquired pneumonia: a randomized controlled trial. , 2003, The American journal of medicine.

[26]  Neil Klar,et al.  Sample size re‐estimation in cluster randomization trials , 2002, Statistics in medicine.

[27]  Douglas E Schaubel,et al.  Proportional Hazards Regression for the Analysis of Clustered Survival Data from Case–Cohort Studies , 2011, Biometrics.

[28]  R. Sylvester,et al.  Frailty modelling for survival data from multi‐centre clinical trials , 2011, Statistics in medicine.

[29]  M J Campbell,et al.  Cluster randomized trials in general (family) practice research , 2000, Statistical methods in medical research.

[30]  M. Gorfine,et al.  On robustness of marginal regression coefficient estimates and hazard functions in multivariate survival analysis of family data when the frailty distribution is mis‐specified , 2007, Statistics in medicine.

[31]  Dennis McCarty,et al.  Days to treatment and early retention among patients in treatment for alcohol and drug disorders. , 2011, Addictive behaviors.