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Design choices for cluster randomised trials - Alan Girling

A talk on design choices for cluster randomised trials by Dr Alan Girling for the CLAHRC WM Scientific Advisory Group meeting, 9th June 2015, Birmingham, UK

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Design choices for cluster randomised trials - Alan Girling

  1. 1. Design Choices for Cluster- Randomised Trials Alan Girling University of Birmingham, UK A.J.Girling@bham.ac.uk CLAHRC Scientific Advisory Group Birmingham, June 2015
  2. 2. … a Statistical viewpoint • Ethical and Logistical concerns are suspended • RCTs and Parallel Cluster trials are well- understood; ‘Stepped Designs’ less so. Two questions: 1. How does the Stepped Wedge Design perform? …but The Genie is out of the bottle! 2. What about alternative stepped designs? Does it have to be a “Wedge”?
  3. 3. Some Alternative Designs: 8 months 4 groups of Clusters (“Arms”) Arms 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Months  Arms 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Months 
  4. 4. Assumptions • Study of fixed duration (8 months) • Constant recruitment rate in each cluster • Continuous Outcome – Additive treatment effect – Cross-sectional observations with constant ICC =  • Cross-over in one direction only (i.e. Treated to Control prohibited) • The analysis allows for a secular trend (“time effect”) – This has been questioned; but if time effects are ignored, the ‘best’ statistical design involves simple before-and-after studies in each cluster (i.e. not good at all!) Goal: To compare statistical performance of different designs under these assumptions, especially the Stepped-Wedge
  5. 5. 1. ‘Precision Factor Plots’ for Comparing Designs
  6. 6. Clusters 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Months  1. Simple Parallel Design Two groups of clusters. Treatment implemented in one group only, in month 1. Treatment Effect Estimate = (Mean difference between two groups over all months) Two Simple Candidate Designs
  7. 7. Clusters 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Months  1. Parallel Study with (multiple) baseline controls “Controlled Before-and-After Design” Two groups of clusters. Treatment implemented in one group only, in month 5. Treatment Effect Estimate = (Mean difference between two groups in months 5 – 8) minus r x (Mean difference between two groups in months 1 – 4) (r is a correlation coefficient “derived from the ICC”)
  8. 8. Performance measured by Precision of the effect estimate: Precision = 1/(Sampling Variance) = 1/(Standard Error)2 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0                R N 4 1 2 1 14 2     R N        1 14 2  Precision = Where R is the “Cluster-Mean Correlation” … and is the same for both designs    11   m m R (m = number of observations per cluster,  = ICC) CBA Parallel
  9. 9. Relative Efficiency of designs – by comparing straight lines on a Precision-Factor plot CBA design is better (“more efficient”) if R > 2/3. Otherwise the Parallel design is better. Parallel CBA
  10. 10. 2. The Cluster-Mean Correlation (CMC)
  11. 11. Cluster-Mean Correlation (CMC) • Relative efficiency of different designs depends on cluster-size (m) and ICC (), but only through the CMC (R) • The CMC (R) = proportion of the variance of the average observation in a cluster that is attributable to differences between clusters • (The ICC () = proportion of variance of a single observation attributable to differences between clusters) • CMC can be large (close to 1) even if ICC is small       m m m m R     111
  12. 12. Cluster-Mean Correlation: relation with cluster size • CMC can be large (close to 1) even if ICC is small • So CBA can be more efficient than a parallel design for reasonable values of the ICC, if the clusters are large enough      11 m R R
  13. 13. 3. Some other designs
  14. 14. 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Controlled Before & After Before & After + Parallel R 4 1 2 1  R 2 1 4 3  0 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 1 R 32 9 16 9  0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 R 16 5 8 5  + Baseline & Full Implementation Stepped Wedge Precision Factors
  15. 15. • Stepped-Wedge is best when the CMC is close to 1 • Parallel Design is best when the CMC is close to 0 – but risky if ICC is uncertain • Before & After/Parallel mixture is a possible compromise Parallel Stepped-Wedge B & A/Parallel
  16. 16. 4. Is there a ‘Best’ Design?
  17. 17. • If Cross-over from Treatment to Control is permitted, the Bi-directional Cross-Over (BCO) design has Precision Factor = 1 at every R, better than any other design. 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 R01 Precision Factor = • But this design is usually not feasible! • If ‘reverse cross-over’ is disallowed, the Precision Factor cannot exceed 2 3 1 1 RR 
  18. 18. 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 • Available design performance limited by choosing only 4 groups of clusters Some (nearly) ‘Best’ designs with 4 groups of clusters Stepped- Wedge Parallel Region Prohibited by Irreversibility of Intervention
  19. 19. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Some (nearly) ‘Best’ designs with 8 groups of clusters Stepped- Wedge Parallel
  20. 20. ‘Best’ Design for large studies: This is a mixture of Parallel and Stepped-Wedge clusters. 100R% Stepped-Wedge Clusters 100(1 – R)% Parallel Clusters • Includes Parallel and Stepped-Wedge designs as special cases • When R is close to 1 the Stepped-Wedge is the best possible design
  21. 21. 5. Conclusions • Efficiency of different cluster designs depends on the ICC () and the Cluster-size (m) but only through the CMC (R). • Precision Factor plots are useful for comparing designs – Comparisons are linear in R • The Stepped-Wedge Design is most advantageous when R is close to 1. – In studies with large clusters this can arise even if the ICC is relatively small. • The theoretically ‘best’ design choice is sensitive to R, and combines Parallel with Stepped-Wedge clusters
  22. 22. Limitations • Continuous data, simple mixed model – Natural starting point – exact results are possible – ?Applies to Binary observations through large- sample approximations • Extension to cohort designs through nested subject effects is straightforward and gives essentially the same answers

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