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Power Considerations in the “Quality Initiative in Rectal Cancer” Trial Design

Power Considerations in the “Quality Initiative in Rectal Cancer” Trial Design. by Eddy Rempel May 13, 2005 SOSGSSD 2005. Presentation Outline. Research on TME QIRC Trial Factors impacting power Sample Size Calculations. Motivation for Total Mesorectal Excision (TME) Research .

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Power Considerations in the “Quality Initiative in Rectal Cancer” Trial Design

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  1. Power Considerations in the “Quality Initiative in Rectal Cancer” Trial Design by Eddy Rempel May 13, 2005 SOSGSSD 2005

  2. Presentation Outline • Research on TME • QIRC Trial • Factors impacting power • Sample Size Calculations

  3. Motivation for Total Mesorectal Excision (TME) Research • Refinement of rectal cancer surgery • Removal of lymph node bearing tissue • Retains autonomic nerves • preserving bowel, bladder, and sexual function • Reduces need for radiation and chemotherapy • Great patient outcomes in Europe • 5000 rectal cancers diagnosed in Ontario per year

  4. Rectal Cancer Patient Back View

  5. TME – Total Mesorectal Excision x-ray Seminal Vesicles  ParietalFascia  VisceralFascia 

  6. TME Recurrence Rates in Europe: TME versus Conventional Surgery • MacFarlane JK, Ryall RD, Heald RJ. Mesorectal excision for rectal cancer. Lancet 1993; 341(8843):457-460. • SRCT. N Engl J Med 1997; 336(14):980-7. • Kapiteijn E, et al. Preoperative radiotherapy combined with total mesorectal excision for resectable rectal cancer. N Engl J Med 2001; 345(9): 638-46.

  7. Outcome Measures for Radiation Groups in English Hospital Simonovic M, Sexton R, Rempel E, Moran BJ, Heald BJ. Optimal preoperative assessment and surgery for rectal cancer may greatly limit the need for radiotherapy. British Journal of Surgery (August 2003) Volume: 90 , Issue: 8 , Date: August 2003

  8. TME Pilot Study at Three Hospitals in Ontario

  9. The QIRC Trial • CIHR funding – October 2001 • Randomized Control Trial • Experimental arm surgeons trained in TME by workshop, operative demonstrations, post operative questionnaires • Control arm surgeons learn as usual – no limitation on learning and practicing new techniques including TME • Primary outcomes – rates of permanent colostomy, local recurrence, long-term survival

  10. QIRC Trial Randomization • Clustered design – Patients within Hospitals • Hospitals randomized to experimental or control arm • Surgeons in experimental arm hospitals trained in TME • No training of control arm surgeons • Consecutive patients – no randomization of patients • Clinically relevant difference from experimental to control arm outcome proportions

  11. Approximating Binomial with Normal Distribution • CLT the binomial approaches the normal asymptotically • Good approximation when • p+/- (p(1-p) / n)½ in (0,1) • Even small n is close to normal • e.g. p=.3 requires only n=10 and p=.08 requires n=46. Mendenhall W, Wackerly D, Scheaffer RL. Mathematical Statistics with Applications, 4th ed. p. 326, PWS-KENT Publishing Company, 1990.

  12. Approximating Binomial with Normal Distribution p+/- (p(1-p) / n)½ in (0,1)

  13. Hypothesis Test Test that there is a clinical relevant difference between the outcome proportions in the two arms. H0: pe – pc = 0 vs. Ha: |pe – pc| >= d where pe is the proportion with outcome in the experimental arm pc is the proportion with outcome in the control arm

  14. Test Level and Power a= P(D>k under H0: d=0) = P(Z>za), Z~N(0,1) g=1-b= P(D<k under Ha: d>d) = P(Z<=-zb)

  15. Test Statistic X ~N(np,np(1-p)) P=X/n ~N(p,p(1-p)/n) Assume pooled variance Var[D] = {pe(1-pe)+pc(1-pc)}/n k=za {pe(1-pe)+pc(1-pc)}½n-½ k=zg {pe(1-pe)+pc(1-pc)}½n-½

  16. Sample Size in Clustered Randomized Control Trial The sample size of each arm n = (za+zg)2sp2 / d2 where ais the level of the test g=1-b, and bis the power of the test sp2 =(pe(1-pe) + pc(1-pc))*k the variance of a single case d=pe–pc the difference between arm proportions Donner A, Klar N. Methods for comparing event rates in intervention studies when the unit of allocation is a cluster. Am J Epid 1994; 140:279-89.

  17. Intra-Class Correlation • ICC proportion of total variance that is attributed to between clusters variation • r = S nipi(1-pi) • (m-1)p(1-p) • where ni andpiare the cluster sizeand proportion, and m and p are the average cluster size and proportion when cluster sizes are not too variable • Then inflation factor k = [1-(1-m)r]

  18. Power sensitivity to variables • Differences in Proportions • Intra-class correlation • One or Two-sided Tests • Sample Size

  19. Power of Clinically Relevant Difference Test

  20. Effect of Difference in Proportions d= pe – pc .01 .20 .60 Power .063 .634 1.000

  21. Effect of Intra-Class Correlation on Power r .02 .04 .10 Power .792 .634 .381

  22. Effect of One or Two Sided Tests Test 2-sided 1-sided Power .634 .745

  23. Sample Size Effect on Power n 42 168 336 Power .209 .634 .903

  24. Power function of Difference The Power(d) function of selected sample size, n d= pe – pc The units in the experimental and control arms are considered independent the variance of d is the sum the I estimated the overestimated the variance using p=.5 in the variance calculation

  25. Some Power (d) curves

  26. Permanent Colostomy Rates • Colostomy rates • vary widely (0 to 68%) in Ontario Hosp 10+ cases • average 32.5% • icc calculated icc=.039989 based on our sample

  27. Colostomy Rates in Ontario

  28. Local Recurrence Rates • found to range from 10 to 45% by surgeon in Edmonton • we estimate to be 20% in Ontario • no way to estimate icc • use 4% – consistent with the icc of other colorectal cancer surgery outcomes in Ontario • i.e. operative mortality and long-term survival Theriault M, Simonovic M. Hierarchical Modeling in Cancer Outcomes. CIHR Annual Research Conference, 2003.

  29. Long-term Survival Rate • surprisingly survival rates are not known • estimated to be about 35% • no way to estimate icc • use 4% – consistent with the icc of other colorectal cancer surgery outcomes in Ontario • i.e. operative mortality and long-term survival • Cox proportional modelling is much more efficient than modeling of fixed term survival binomial outcome Theriault M, Simonovic M. Hierarchical Modeling in Cancer Outcomes. CIHR Annual Research Conference, 2003.

  30. Samples Size Inputs • icc r= .04 • cluster size m=42 • Test level a=05 is standard • Reviewers demand 2-sided test • Power g=.8 to .9 is standard, we use .8 • We selected the calculated sample size of local recurrence: n=336 and k=8 hospitals in each arm

  31. Sample Size Requirements

  32. Summary • ICC has a huge impact on Power and hence on required sample size • Key parameters to calculate sample size must be estimated, i.e. r and p for these outcomes has not been published • Grant reviewers demand 2-sided until the direction of effect is well established • Room for more work in applying these in medical research

  33. Acknowledgements • Marko Simunovic MPH, FRCS(C)1,2,3 • Charlie Goldsmith, PhD2 1. Departments of Surgery, McMaster University 2. Clinical Epidemiology and Biostatistics, McMaster University 3. Juravinski Cancer Centre, Hamilton Health Sciences

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