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

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

3. 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 Motivation for Total Mesorectal Excision (TME) Research

4. Rectal Cancer Patient Back View

5. TME – Total Mesorectal Excision x-ray Visceral Fascia Parietal Fascia Seminal Vesicles   

6. 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. TMESurgery + Chemo + Radiation England Netherlands Sweden 5% 4.1% 11% 13.5% 11.5% 27% TME Recurrence Rates in Europe: TME versus Conventional Surgery

7. Basingstoke Medical Centre Radiation (N=35) No Radiation (N=115) Number of local recurrences17.1%2.6% Permanent colostomy17.1%6.1% 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 Outcome Measures for Radiation Groups in English Hospital

8. TME Pilot Study at Three Hospitals in Ontario CasesPre- Intervention Post- Intervention FullIntervention Cases874839 Colostomies15114 Rate22.9%10.3% PartialIntervention Cases331221 Colostomies1147 Rate33.3%

9. 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 The QIRC Trial

10. 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 QIRC Trial Randomization

11. 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. Approximating Binomial with Normal Distribution Mendenhall W, Wackerly D, Scheaffer RL. Mathematical Statistics with Applications, 4 th ed. p. 326, PWS-KENT Publishing Company, 1990.

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

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

14.  = P(D>k under H 0 :  =0) = P(Z>z  ), Z~N(0,1)  =1-  = P(D d) = P(Z<=-z  ) Test Level and Power

15. X ~N(n ,n  (1-  )) P=X/n ~N( ,  (1-  )/n) Assume pooled variance Var[D] = {  e (1-  e )+  c (1-  c )}/n k=z  {  e (1-  e )+  c (1-  c )} ½ n -½ k=z  {  e (1-  e )+  c (1-  c )} ½ n -½ Test Statistic

16. The sample size of each arm n = (z  +z  ) 2  p 2 /  2 where  is the level of the test  =1- , and  is the power of the test  p 2 = (  e (1-  e ) +  c (1-  c ))*k the variance of a single case  =  e –  c the difference between arm proportions Sample Size in Clustered Randomized Control Trial 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. ICC proportion of total variance that is attributed to between clusters variation  =  n i  i (1-  i ) (m-1)  (1-  ) where n i and  i are the cluster size and proportion, and m and  are the average cluster size and proportion when cluster sizes are not too variable Then inflation factor k = [1-(1-m)r] Intra-Class Correlation

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

19. Power of Clinically Relevant Difference Test

20.  =  e –  c.01.20.60 Power.063.6341.000 Effect of Difference in Proportions

21. .02.04.10 Power.792.634.381 Effect of Intra-Class Correlation on Power

22. Test2-sided1-sided Power.634.745 Effect of One or Two Sided Tests

23. n 42168336 Power.209.634.903 Sample Size Effect on Power

24. The Power(d) function of selected sample size, n d= p e – p c 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 Power function of Difference

25. Some Power (d) curves

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

27. Colostomy Rates in Ontario

28. 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 Local Recurrence Rates Theriault M, Simonovic M. Hierarchical Modeling in Cancer Outcomes. CIHR Annual Research Conference, 2003.

29. 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 Long-term Survival Rate Theriault M, Simonovic M. Hierarchical Modeling in Cancer Outcomes. CIHR Annual Research Conference, 2003.

30. icc  =.04 cluster size m=42 Test level  =05 is standard Reviewers demand 2-sided test Power  =.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 Samples Size Inputs

31. Sample Size Requirements Outcome cc ee dnk Colostomy.30.15-.153117.4 Recurrence.20.08-.123368.0 5-yr Survival.35.50.1544010.5

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.  and  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, PhD 2 1. Departments of Surgery, McMaster University 2. Clinical Epidemiology and Biostatistics, McMaster University 3. Juravinski Cancer Centre, Hamilton Health Sciences