by Eddy Rempel

May 13, 2005

SOSGSSD 2005

Power Considerations in the “Quality Initiative in Rectal

Cancer” Trial Design

• Research on TME

• QIRC Trial

• Factors impacting power

• Sample Size Calculations

Presentation Outline

• 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

Rectal Cancer Patient Back View

TME – Total Mesorectal Excision x-ray

Visceral Fascia

Parietal Fascia

Seminal Vesicles

• 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.

TME Surgery + Chemo + Radiation

England

Netherlands

Sweden

5%

4.1%

11%

13.5%

11.5%

27%

TME Recurrence Rates in Europe: TME versus Conventional Surgery

Basingstoke Medical Centre Radiation

(N=35)No Radiation

(N=115)

Number of local recurrences 17.1% 2.6%

Permanent colostomy 17.1% 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

TME Pilot Study at Three Hospitals in Ontario

Cases Pre-Intervention

Post-Intervention

Full Intervention

Cases 87 48 39

Colostomies 15 11 4

Rate 22.9% 10.3%

Partial Intervention

Cases 33 12 21

Colostomies 11 4 7

Rate 33.3% 33.3%

• 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

• 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

• 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.

+/- ((1-) / n)½ in (0,1)

Approximating Binomial with Normal Distribution

Normal Approximation of the Binomial Distribution

X

pdf/p

mf

0 1 2 3 4

0.00.1

0.20.3

0.4

BinomialNormal

n 4p 0.5

Normal Approximation of the Binomial Distribution

X

pdf/p

mf

0 10 20 30 40

0.0

0.05

0.10

0.15

0.20

BinomialNormal

n 46p 0.08

Normal Approximation of the Binomial Distribution

p

pdf/p

mf

0.0 0.2 0.4 0.6 0.8 1.0

05

1015

BinomialNormal

n 168p 0.08

Test that there is a clinical relevant difference between the outcome proportions in the two arms.

H0: e – c = 0 vs. Ha: |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

= P(D>k under H0: =0) = P(Z>z), Z~N(0,1)

=1-= P(D<k under Ha: >d) =

P(Z<=-z)

Test Level and Power

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

The sample size of each arm

n = (z+z)2 p2 / 2 where

is the level of the test

=1-, and is the power of the test

p2 = (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.

•ICC proportion of total variance that is attributed to between clusters variation

= nii(1-i)

(m-1)(1-)where ni 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

•Differences in Proportions

•Intra-class correlation

•One or Two-sided Tests

•Sample Size

Power sensitivity to variables

Power of Clinically Relevant Difference Test

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

de

nsity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

4

ControlExperimentalk

d 0.2n 168

icc 0.04Power0.634

= e – c .01 .20 .60

Power .063 .634 1.000

Effect of Difference in Proportions

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

4

ControlExperimentalk

d 0.01n 168

icc 0.04Power0.063

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

45

ControlExperimentalk

d 0.6n 168

icc 0.04Power 1

.02 .04 .10

Power .792 .634 .381

Effect of Intra-Class Correlation on Power

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

45

ControlExperimentalk

d 0.2n 168

icc 0.02Power0.792

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

de

nsi

ty

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

ControlExperimentalk

d 0.2n 168

icc 0.1Power0.381

Test 2-sided 1-sided

Power .634 .745

Effect of One or Two Sided Tests

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

4

ControlExperimentalk

d 0.2n 168

icc 0.04Power0.634

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

4

ControlExperimentalk

d 0.2n 168

icc 0.04Power0.745

n 42 168 336

Power .209 .634 .903

Sample Size Effect on Power

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.0

0.5

1.0

1.5

2.0

ControlExperimentalk

d 0.2n 42

icc 0.04Power0.209

Normal Approximation of Control and Experimental Proportions

Distribution of Estimated Arm Proportions

dens

ity

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

01

23

45

6

ControlExperimentalk

d 0.2n 336

icc 0.04Power0.903

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

Power function of Difference

Some Power (d) curvesPower Function of difference between two Proportions

Difference in Proportions

Po

we

r(d

iffe

ren

ce

)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Power n=336Power n=168Power n=84Power n=42Power n=21

•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

Colostomy Rates in OntarioColostomy Rate by Rectal Cancer Hospital Case Volume in Ontario

Hospital Case Volume (April 1995- March 1998 )

Co

losto

my R

ate

(%

)

0 50 100 150

02

04

06

08

01

00

• 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.

• 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.

• 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

Sample Size Requirements

Outcome c e d n k

Colostomy .30 .15 -.15 311 7.4

Recurrence .20 .08 -.12 336 8.0

5-yr Survival .35 .50 .15 440 10.5

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

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