EPP 246 Clinical Biostatistics Lecture 3, Jan 19, 2007

1. EPP 246 Clinical Biostatistics Lecture 3, Jan 19, 2007 Lihong Qi lhqi@ucdavis.edu Division of Biostatistics Department of Public Health Sciences Rowe Program in Human Genetics UCD School of Medicine

2. Formulating the problem Define the question, primary, secondary, ancillary, adverse effects the intervention the response variables, primary, secondary, ancillary, adverse effects study population the design What is the necessary sample size

3. Basic study designs Randomized control studies Nonrandomized concurrent control studies Historical controls/data bases Cross-over designs Withdrawal studies Factorial design Group allocation designs Studies of equivalency Large simple clinical trials

4. How big is enough? -- Size of a trial Fundamental point: Clinical trials should have sufficient statistical power to detect differences between groups considered to be of clinical interest. Therefore calculation of sample size with provision for adequate levels of significance and power is an essential part of planning.

5. Classification of sample size calculation Sample size estimation/determination Sample size justification Statistical justification for a selected sample size Sample size adjustment For factors like dropouts or covariates to yield enough evaluable subjects for statistical analysis Sample size re-estimation For planned or unplanned interim analyses

6. Considerations before calculation Clear state the study objective/hypotheses Valid study design with proper statistical tests Based on the test for the hypotheses Based on the primary end points Clinically meaningful difference of primary end points

7. Study objectives Safety equivalence non-inferiority superiority ------------------------------------------------------------------------------- Equivalence E/E E/N E/S Efficacy non-infer N/E N/N N/S Superiority S/E S/N S/S -------------------------------------------------------------------------------

8. Hypotheses A postulation/assumption/statement about the population regarding the effectiveness and safety of a treatment under investigation.

9. Types of Hypotheses Test for equality H0: u1 = u0 vs H1: u1 != u0, 1: Rx, 0: control Test for non-inferiority H0: u0 – u1 >= delta vs u0– u1 < delta u0: standard, u1: Rx delta = difference of clinical importance Test for superiority H0: u1 – u0 <= delta vs H1: u1 – u0 > delta Test for equivalence H0: |u1 – u0| >= delta vs H1: |u1 – u0| < delta

10. Clinically meaningful difference Important in equivalence/non-inferiority trials Equivalence limit in therapeutic equivalence trials Non-inferiority margin in non-inferiority trials Based on statistical reasoning and clinical judgment No prior knowledge of clinical performance of the test treatment standard effect size between 0.25 – 0.5

11. sample size calculation Focus on power analysis: The null hypothesis can be tested at pre-determined significance level with a desired power based on levels of both type I and II errors type I (confidence level) and type II errors (power) Type I error: reject H0 when H0 is true significance level = false positive rate = P{type I error) Type II error: fail to reject H0 when H0 is false power = sensitivity = 1 – P{type II error} = P{reject H0 when H0 is false} Two-arm randomized control trial

12. Power

13. Factors affecting power

15. Types of primary outcome Continuous Eg. Blood pressure Dichotomous Eg. Success vs failure Non-binary categorical variable Eg. blood pressure below, within, or above a normal range Time to event Eg. time to breast cancer

16. Continuous response Two-sided, test of equality, a=significance level, b=power, u1:treatment, u0:control

17. Different-sized arms: 1 to k test-control allocation

18. Continuous response, test for non-inferiority/superiority

19. Continuous response, test for equivalence

20. Example: vitamin D to pregnant women A trial giving vitamin D to pregnant women for the prevention of neonatal hypocalcaemia. Randomize women to D or placebo, Measure infant’s serum calcium level one week after birth as primary outcome Mean response in placebo arm: u0 = 9 mg/100ml Standard deviation v1 = v0 = 1.8 mg/100ml Mean difference in response u1 = 9.5 mg/100ml u1 – u0 = 0.5 mg/100ml H0: u1 = u0 vs H1: u1 != u0 a = 0.05 => critical value = 1.96 b = 0.95 => critical value = 1.64

21. vitamin D to pregnant women, test for equality Two-sided test For each arm

22. vitamin D to pregnant women (cont) One-side test H0: u1 = u0 vs H1: u1 > u0 a = 0.05 => 1.64 , b = 0.95 => 1.64

23. Online resource http://www.swogstat.org/statoolsout.html In the example u1 = 9.5 u0 = 9.0 a = 0.05 b = 0.95

24. Continuous response, compare means (cont) Key values Significance level, common range 0.01 – 0.05 Power, common values 0.80 and 0.90 “minimum detectable difference" between the treatment groups under consideration Larger difference => fewer patients standard deviation of the clinical parameter under consideration, or at least a possible range for it derive either from similar studies in literature or from an internal pilot study.

25. Binary outcome, 2 arm trial p1 = percentage of successes on one treatment (eg. treatment interested) p2 = percentage of successes on the other treatment (eg. control) a = significance level b = power

26. Binary outcome, test for equality two-sided, 1:1 test-control allocation

27. Binary outcome, test for equality (cont)

28. Binary outcome, test for Non-inferiority/superiority

29. Binary outcome, test for Non-inferiority/superiority (cont) When delta > 0, rejecting H0 indicates the superiority of the test treatment over control When delta < 0, rejecting H0 indicates the non-inferiority of the test treatment against control

30. Binary outcome, test for equivalence

31. An example 

32. Online resource http://www.swogstat.org/statoolsout.html In the example P1 = 2/10 P2 = 6/10 a = 0.05 b = 0.80

33. Another example A drug company is planning to conduct a trial to compare the efficacy, safety, and tolerability of two antimicrobial drugs in the treatment of patients with skin and skin structure infections Response: cure and failure (not cure) after 4 to 8 days Consider three situations: Equality of mean cure rates Non-inferiority or superiority of the test drug compared to the active control drug Therapeutic equivalence

34. Assumptions for the example Significance level: 0.05 Power: 0.80 Equal size arms P0 = 0.65 P1 = 0.85

35. Sample size for testing equality

36. Sample size for testing non-inferiority Define no clinical importance if difference < -10%

37. Sample size for testing superiority Define no clinical importance if difference < 5% (superiority margin)

38. Sample size for testing equivalence p1 = 0.75, p2 = 0.80 Equivalence limit is 0.20

39. Some cautions Only an estimate Guessing parameters, may guess wrong Attrition (loss to follow-up, death) may decrease your effective sample size. Many calculations use normal theory approximations that are valid only for large Reference: Chow, Shao and Wang “Sample size calculations in clinical research”, 2003, Taylor & Francis