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Common Designs for Controlled Clinical Trials

Common Designs for Controlled Clinical Trials. A. Parallel Group Trials 1. Simplest example - 2 groups, no stratification 2. Stratified design 3. Matched pairs 4. Factorial design B. Crossover Trials. Parallel Group Design. y. T. e. =. m. +. +. ij. i. ij. overall mean. m. =.

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Common Designs for Controlled Clinical Trials

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  1. Common Designs for Controlled Clinical Trials A. Parallel Group Trials 1. Simplest example - 2 groups, no stratification 2. Stratified design 3. Matched pairs 4. Factorial design B.Crossover Trials

  2. Parallel Group Design y T e = m + + ij i ij overall mean m = th T effect of i treatment = i (i = A, B) th th e error term for j patient in i group = ij 2 e ~ N(0, ) s ij 2 y ~ N ( T , ) m + s ij i 2 2 2 s = s + s s e

  3. 2 s  2 s 2 e 2 s 2 e 2 s 2 e       2 s 2 e Estimates of  and  for Selected Response Variables Diastolic BP (mmHg) 58 36 94 0.62 Serum cholesterol 1200 400 1600 0.75 (mg/dl) Viral load 0.16 0.09 0.25 0.64(log10 copies/mL) Overnight urine 325 625 950 0.34 excretion of Na+ (meq/L) Carbohydrate intake 110 208 318 0.35 (% of calories) Total    

  4. A Poorly Designed “Crossover” Trial: Why? 2n patients Drug A Drug B . . . or or Low Dose Low Dose Also referred to as “changeover” or “switchover”

  5. Two-Period Crossover Trial Period 1 2 W A S H O U T Drug A Drug B n 2n - Randomize Patients n Drug B Drug A

  6. SNaP 100 mEq NaCI Placebo Group I (n=25) Schematic design of study to determine effects of dietary sodium on blood pressure in normotensive adults WASH-OUT Group II (n=23) Placebo 100 mEq NaCI Weeks -8 0 4 6 10 Low Sodium Diet Hypertension 1991; 17:I21-I26.

  7. Crossover Trial Advantages: • Fewer patients required in most situations due to elimination of between subject component of variability, therefore: • recruitment may be easier • can be more easily done in single center • fewer patients exposed to experimental treatment • Less data collection Disadvantages: • Interaction due to: • differential carry-over effects of treatments • treatment x period interaction • differences between the two randomized groups (AB and BA) at baseline • Patients must be observed longer • Losses to follow-up/missing data • Naturally occurring changes in underlying disease state

  8. Situations where crossover design is most applicable: 1. Rapid response and response is transitory 2. Variability between patients is large compared to variability within patients 3. Steady state physiological condition; disease or condition cannot be cured 4. No residual or carry-over effects of treatment expected

  9. Survey of Randomized Trials in 2000 • 116 of 526 published trials were crossover • Median sample size for crossover trials = 15 • 78% of crossover studies involved 2 treatments • 70% of crossover studies reported a washout period • 17% reported a test for carry-over effect and 13% tested for period effects Mills EJ et al. Trials 2009

  10. General Model for 2-Period Crossover Trial y = + + T + + + m p l g e ijk u v ij ijk k = overall mean m = effect of kth period (k = 1, 2) p k T = effect of uth treatment (u = A, B) u (direct effect) = residual effect of treatment given in first period l v on second period response (v = A, B) ( = 0 for first period measurements, l v i.e., when k = 1) Hills and Armitage Br J Clin Pharmac 1979; 8:7-20. Senn Stat Methods Med Res 1994;3:303-324.

  11.  2 s 2 e   = random effect between subject of jth g ij patient in group i (I or II); same in each period 2 N(0, ) » s s = random within patient effect for kth period e ijk 2 N(0, ) » s e Motivation for crossover

  12. 2-Period Crossover TrialFixed Effects 1 2 I (AB) II (BA) Period  +  + T +  +  + T  A A B 1 2 Group  +  + T +  +  + T  B B A 1 2

  13. Group I (AB) Patient (i = 1)Response - Patient j Period 1 : y = + + T + + m p g e 1j1 1 A 1j 1j1 Period 2 : y = + + T + + + m p l g e ij2 2 B A 1j 1j2 Paired difference dI = y - y 1 1j1 1j2 = (T - T ) - + ( ) ( ) l p - p + e - e A B A 1 2 1j1 1j2 E(d ) = (T - T ) - + ( ) l p - p I A B A 1 2

  14. Group II (BA) Patient (i = 2)Response - Patient jI Period 1 : y = + + T + + m p g e 2j' 1 1 B 2j' 2j' 1 Period 2 : y = + + T + + + m p l g e 2j' 2 2 A B 2j' 2j' 2 Paired difference y - y 2j' 1 2j2 = (T - T ) - + ( ) + ( ) l p - p e - e B A B 1 2 2j' 1 2j' 2 Consider difference in opposite direction and call it dll d = (T - T ) + + ( ) + ( ) l p - p e - e II A B B 2 1 2j' 2 2j' 1 E(d ) = (T - T ) + + ( ) l p - p II A B B 2 1

  15. = d + d 2 (T - T ) - ( - ) l l I II A B A B - d d = 2 ( ) - ( + ) p - p l l I II 1 2 A B d + d I II estimates T - T if = l l A B A B 2 d - d I II estimates if = 0 p - p l l = 1 2 A B 2

  16. How Do We Convince Ourselves That AB Consider the sum of the period 1 and period 2 responses. Group I (AB) : E(Sum ) = 2 + ( ) m p + p I 1 2 + (T + T ) + l A B A Group II (BA) : E(Sum ) = 2 + ( + ) m p p II 1 2 + (T + T ) + l A B B Note that Sum Sum estimates - I II - l l A B

  17. Test for Carryover Has Low Power • It is a between, instead of within, patient test (even when considering change from baseline, variance is 4 times larger) • Although totals are used, direct information on carry over only comes from 2nd period – effect is diluted with sum’s. • If there is evidence of a carryover effect (p<0.10 or 0.15), Grizzle proposed that the 1st period effects be used. This has been shown to be a sequential testing procedure that is not optimal. Some believe it is better not to carry out the test at all. • Better be sure in the design that there is no carryover effect!

  18. Possible Reasons for Rejecting Hypothesisof Equal Carry-over Effects 1. True carry-over effect for A or B, or both 2. Psychological carry-over effect 3. Difference between treatments depends on pre-treatment level of response variable 4. Group I and Group II differ significantly by chance

  19. A A Group II Response x x B Group I B 1 2 Period 1. Treatment effect 2. No period effect 3. No interaction

  20. A x Group II Response B A x B Group I 1 2 Period 1. Treatment effect 2. Period effect 3. No interaction

  21. Quantitative Interaction A Group II A Group I B Response B 1 2 Period

  22. Qualitative Interaction A B Response B Group I A Group II 1 2 Period

  23. Example from SennStatistical Issues in Drug DevelopmentJohn Wiley & Sons, 1997 BA 2000 2300 300 AB 2300 2000 300 300 Beta-Agonist (A) vs. Placebo (B)for Patients with Asthma FEV1.0 (mL) A-B Difference Sequence Period 1 Period 2

  24. Senn Example (cont.) • Add 350 mL to BA BA 2350 2650 300 AB 2300 2000 300 300 A-B Difference Sequence Period 1 Period 2 Differences are recovered in spite of difference between sequences

  25. Senn Example (cont.) • Add 350 mL to BA; and • Add a secular trend causing FEV1.0 to be 100 mL HIGHER in 2nd period BA 2350 2750 400 AB 2300 2100 200 300 A-B Difference Sequence Period 1 Period 2 Difference in each sequence not recovered, but average is okay – crossover still works!

  26. Senn Example (cont.) • Add 350 mL to BA; and • Add a secular trend causing FEV1.0 to be 100 higher in 2nd period; and • Add a carry-over effect of A (still completely effective when B is given) BA 2350 2750 400 AB 2300 2400 -100 150 A-B Difference Sequence Period 1 Period 2 Crossover does not work!

  27. Variance Estimates (1) d + d I II Treatment Effect = 2 (2) d - d I II Period Effect = 2 (3) Carryover Effect = Sum - Sum I II Variance of (1) and (2) 2 2 1 é ù s s d d = I + II ê ú 4 n n ë û I II 2 pooled variance s = d 2 2 (n - 1) + (n - 1) s s d d I II I II = n + n - 2 I II Variance of (3) 2 2 s s Sum Sum I II = + n n I II 2 2 (n - 1) + (n - 1) s s Sum Sum 2 I II = pooled variance = I II s n + n - 2 Sum I II

  28. Hypothesis Testing 1) H : no interaction o SUM - SUM I II t(n + n - 2) = I II 1 æ ö 1 1 2 ˆ ç + ÷ s ç ÷ SUM n n è ø I II 2) H : no treatment effect o d + d I II 2 t(n + n - 2) = I II 1 æ ö ˆ 1 1 2 s d ç + ÷ ç ÷ 2 n n è ø I II 3) H : no period effect o d - d I II 2 t(n + n - 2) = I II 1 æ ö ˆ 1 1 2 s d ç + ÷ ç ÷ 2 n n è ø I II

  29. Patient Accession No. Period 1 (A) Period 2 (B) A-B Difference Group I Sum 1 8 5 3 13 3 14 10 4 24 4 8 0 8 8 6 9 7 2 16 7 11 6 5 17 9 3 5 -2 8 11 6 0 6 6 13 0 0 0 0 16 13 12 1 25 18 10 2 8 12 19 7 5 2 12 21 13 13 0 26 22 8 10 -2 18 24 7 7 0 14 25 9 0 9 9 27 10 6 4 16 28 2 2 0 4

  30. Group II Patient Accession No. Period 1 (B) Period 2 (A) A-B Difference Sum 2 12 11 -1 23 5 6 8 2 14 8 13 9 -4 22 10 8 8 0 16 12 8 9 1 17 14 4 8 4 12 15 8 14 6 22 17 2 4 2 6 20 8 `13 5 21 23 9 7 -2 16 26 7 10 3 17 29 7 6 -1 13

  31. Group I (N = 17) Period 1 (A) Period 2 (B) A-B Difference Sum Mean 8.12 5.29 2.82 13.41 SD 3.84 4.25 3.47 7.32 SE 0.84 1.78 Group II (N = 12) Period 1 (B) Period 2 (A) A-B Difference Sum Mean 7.67 8.92 1.25 16.58 SD 2.99 2.81 2.99 4.98 SE 0.86 1.44

  32. Ho : No interaction 1) Determine pooled variance of sum 2 2 (n - 1)s + (n - 1)s 2 I I II II s = SUM n + n - 2 I II 2 2 16(7.32) + 11(4.98) = 27 = 41.9

  33. 2) Calculate test statistic SUM - SUM t(n + n - 2) = I II I II æ ö 1 1 2 s ç + ÷ ç ÷ SUM n n è ø I II 16 - 13.49 = 1 1 41.86 + 17 12 = 1.30 3) Compare with t-tables with 27df, p = 0.20

  34. Ho : No treatment difference same procedure 2 2 (n - 1)s + (n - 1)s I I II II 2 s = d d d n + n - 2 I II 2 2 16(3.47) + 11(2.99) = 27 = 10.78

  35. æ ö d + d I II ç ÷ ç ÷ 2 è ø t(n + n - 2) = I II æ ö s 1 1 d ç + ÷ ç ÷ 2 n n è ø I II æ 2.82 + 1.24 ö ç ÷ 2 è ø = 3 . 28 = 10 . 78 1 1 + 2 17 12 p = 0.0028

  36. Similarly for Ho : No Period Effect æ ö d - d I II ç ÷ ç ÷ 2 è ø t(n + n - 2) = I II æ ö s 1 1 d ç + ÷ ç ÷ 2 n n è ø I II æ 2.82 - 1.24 ö ç ÷ 2 è ø = 1 . 27 = 10 . 78 1 1 + 2 17 12 p = 0.21

  37. Two-Period Crossover Trial Period 1 2 W A S H O U T Drug A Drug B n 2n - Randomize Patients n Drug B Drug A

  38. Consider Period 1 Dataand Estimated SE of Treatment Difference(Parallel Group Design) 2 2 (3.84) (16) + (2.99) (11) 2 s = p 2 7 = 12.38 1 1 1 SE = (12.38) 2 + 17 12 = 1.33 compared to 0.62 for crossover

  39. Advantages of Baseline Measurements 1. Description of study participants at entry 2. Comparability of treatment groups: AB vs. BA 3. More powerful test for treatment x period interaction 4. Improved precision for estimating treatment differences (e.g., analysis of covariance or change from baseline when correlation >0.5.) 5. Subgroup analysis

  40. Advantage of a 2nd “Baseline” during Washout Between Periods • Differences between “baseline” measurements for Group I and Group II may provide support for unequal residual effects. NOTE! This comparison does not replace comparison of sums of observation at the end of periods for Group I and Group II that was previously discussed.

  41. Design for Estimating Direct and Residual Treatment Effects Square 1 Period Group1 2 3 I A B C II B C A III C A B Square 2 Period Group1 2 3 I A C B II B A C III C B A

  42. Recommendations 1. Always measure initial baseline. 2. If washout is employed, measure B2. 3. Take multiple measures during each treatment period, e.g., comparison of treatment A with placebo (P). Week of Study Period 1 Period 2 Group 1 2 3 4 5 6 7 8 I P A A A P P P P II P P P P P A A A B1 B2

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