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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. Epidemiology of Randomized Trials • Among 519 trials published in December 2000 • 74% were parallel group with a median enrollment of 80 participants total • 22% were crossover with a median of 15 participants Lancet 2005; 365:1159-1162.

  3. Parallel Group Studies Eligible Patients Informed Consent Yes, randomize No A B + Variability of response =  =   between subject within subject   = + s e

  4. B B B A A A  i Parallel Group StudiesStratified Randomization Eligible Patients Informed Consent Yes No Stratum 1 Stratum 2 . . . Stratum i Variability of response = wi    = + is i ie

  5. Immediate Versus Deferred Treatment: Concorde Study Randomization AZT Placebo If AIDS/ARC or CD4+ declines to<500 cells/mm3 Open-labelAZT Open-labelAZT Lancet 1994; 343:871-881.

  6. Invasive versus Conservative Management Strategy for Acute non-Q-wave Myocardial Infarction (VANQUISH Trial)Immediate vs Deferred Parallel Group Design • Invasive: coronary angiography as the initial diagnostic test • Conservative: radionuclide ventriculography followed by a symptom-limited treadmill test with thallium scintigraphy • Coronary angiography performed if: • Recurrent post-infarction angina with ischemic ECG changes • ST segment depression during peak exercise • Redistribution defects on scintigraphy N Engl J Med 1998; 338:1785-1792

  7. Parallel Group “Switchover” Trial: A Simple Example of A Dynamic Treatment Regimen (Treatment Individualized to Patient) Eligible Patients Informed Consent Randomize A B Use B if A fails Use A if B fails

  8. Didanosine (ddI) versus Zalcitabine (ddC) for Patients with Advanced HIV Patient Who Failed on AZT OR Intolerant to AZT RANDOMIZATION ddI ddC If fail/ intolerant If fail/ intolerant ddC ddI N Engl J Med 1994; 330:657-662

  9. Sequential Randomization (Dynamic Treatment Regimens) No. OIArmsTreatment Groups PCP 2 Daily vs. 3x weekly TMP/SMX (1:1) PCP 2 2nd line treatment: dapsone vs. atovaquone

  10. Randomization (R) Daily 3x week R R A D A D Sequential Randomization For A vs. D, daily/3x weekly is a baseline characteristic for defining subgroups Stat Med 1996; 15:2445-2453.

  11. Parallel Group Studies: 2 x 2 Factorial Design – both A and B Controlled Experimentally Eligible Patients Informed Consent Yes, randomize No A, B A, no B No A, B No A, no B Variability of response =  wi i    = + is ie i Two factors each at 2 levels = 2x2.

  12. Fisher on Factorial Designs “If the investigator…confines his attention to a single factor, we may infer either that he is the unfortunate victim of a doctrinaire theory as to how experimentation should proceed, or the time, material, or equipment at his disposal is too limited to allow him to give attention to more than one narrow aspect of his problem.” The Design of Experiments (7th edition, 1st published 1935)

  13. W.G. Cochran supposedly said something like… Factorial designs are useful when you are interested in an interaction and when there is unlikely to be an interaction.

  14. Parallel Group StudyFactorial DesignAnother Representation A No A No B B No B B Note: This is different than recording factor A (Y/N) and/or possibly using it as a stratifying variable. The analysis of the effect of B versus no B is similar but inferences are different.

  15. Example: 2x2 factorial study of pain from peripheral neuropathy for individuals with HIV Randomization Placebo + Alt Points Placebo + Acupuncture Amitriptyline + Alt Points Amitriptyline + Acupuncture JAMA 1998;280:1590-1595

  16. Example: Physician’s Health Study2 x 2 Factorial Design Factor 1: 2 levels, Factor 2: 2 levels Factor 1 Factor 2 Placebo Aspirin Carotene Placebo Aspirin Main Effect: No. Participants 11,037 11,034 No. CVD deaths 44 44 No. Fatal/non-fatal myocardial infarctions 104 189

  17. Factorial Design Considerations 1. Interest in multiple Rx – can be efficient • Interaction • Generalizability – treatments studied experimentally under different conditions. • Safety, logistics – may not be feasible • Mechanism of action – if different, efficiency increases

  18. 2 x 2 Factorial Design Treatment B No Yes 2n Yes n, XA n, XAB Treatment A 2n No n, X n, XB 2n 4n 2n ( XA - X ) + ( XAB - XB) Main Effect of A : 2 ( XB - X ) + ( XAB - XA) Main Effect of B : 2 Interactions A with B : ( XA - X ) - ( XAB - XB) B with A : ( XB - X ) - ( XAB - XA)

  19. 2 x 2 Factorial Variance of main effects, e.g., A é ù ( X - X ) + ( X - X ) Var ê ú A AB B = 2 ê ú ë û 2 2 é ù 1 4 s s ê ú = 4 n n ê ú ë û Variance of AB interaction 2 4 s [ ] Var ( X - X ) - ( X - X ) = A AB B n

  20. Quantitative Interaction O Factor 2, Level 2 Level 1-2 of Factor 2 is negative for Level 1 of Factor 1 Level 1-2 of Factor 2 is more negative for Level 2 of Factor 1 X Factor 2, Level 1 Response O X 1 2 Factor 1

  21. Qualitative Interaction Level 1-2 of Factor 2 is negative for Level 1 of Factor 1 Level 1-2 of Factor 2 is positive for Level 2 of Factor 1 O X X - Level 1 of Factor 2 Response X O - Level 2 of Factor 2 O 1 2 Factor 1

  22. X X C X B X BC X A X AC X AB 2 x 2 x 2 Factorial Design No. Patients Results A B C – – – n – – + n – + – n – + + n + – – n + – + n + + – n + + + n 8n X ABC Main effect of A : 1 [ ] ( X - X ) + ( X - X ) + ( X - X ) + ( X - X ) A AC C AB B ABC BC 4

  23. AB Interaction: ABC Interaction: 1 { } [ ] [ ] ( X - X ) - ( X - X ) + ( X - X ) - ( X - X ) A AB B AC C ABC BC 2 Two estimates of AB interaction, one in the presence of C and one in the absence of C. { } [ ] [ ] ( X - X ) - ( X - X ) - ( X - X ) - ( X - X ) A AB B AC C ABC BC There are 3 equivalent interpretations of 3-way interaction, like there are 2 equivalent interpretations for AB in 2x2 factorial. One is that AB interaction depends on presence of C.

  24. 2 x 2 x 2 FactorialVariance Estimates 2 s Main effect : 2n 2 2 2 4 s s 2 - way interaction : = n 2n 2 2 8 1 6 s s 3 - way interaction : = n 2n

  25. Women’s Antioxidant Cardiovascular Study (WACS) • 2x2x2 factorial double-blind study • Vitamin C versus placebo • Vitamin E versus placebo • Beta-carotene versus placebo • High risk women willing to forgo individual supplements • Primary endpoint: combined endpoint of CVD morbidity and mortality Arch Int Med 2007; 167:1610-1618.

  26. How Do Interactions Arise? • Both factors affect the endpoint through the same biologic process • Non-compliance resulting from more complicated regimen and/or knowledge of the intervention (unblinded trial) • Scaling (e.g., additive on logarithmic or arithmetic scale)

  27. 2 x 2 Factorial Design Factor 1: 2 levels, Factor 2: 2 levels Example: Physician’s Health Study Factor 1 Factor 2 Placebo Aspirin Carotene Placebo Interaction unlikely.

  28. Simvastatin (F1) No Yes Yes Vitamin Supp. (F2)+ No 2 x 2 Factorial DesignMRC/BHF Heart Protection Study + Vitamin E, Vitamin C, and beta carotene Interaction unlikely.

  29. Acupuncture (F1) No Yes Yes Amitriptyline(F2) No 2 x 2 Factorial Design Pain from Peripheral Neuropathy Pain reduction (F1 + F2) < pain reduction (F1) + pain reduction (F2) Pain reduction (F1 + F2) > pain reduction (F1) > pain reduction (F2) Quantitative interaction likely.

  30. Microbicide (F1) No Yes Yes Behavioral Intervention(F2) No 2 x 2 Factorial Design HIV Infection Knowledge of microbicide could effect response to different behavioral interventions, e.g., disinhibition on standard counseling arm if taking microbicide but not on enhanced counseling arm Quantitative interaction likely.

  31. Women’s Health InitiativePartial Factorial Design Factor 1: Dietary modification (low fat) vs. Self-selected dietary behavior N = 48,836 (2:3)

  32. Women’s Health InitiativePartial Factorial Design (cont.) Factor 2: Postmenopausal hormone therapy I. (Post-hysterectomy) Estrogen vs. Placebo N = 10,739 (1:1) II. Intact uterus Estrogen + Progestinvs.Placebo N = 16,608 (1:1)

  33. Women’s Health InitiativePartial Factorial Design (cont.) Factor 3: Calcium and vitamin D supplementation Ca+ + Vitamin Dvs. Placebo N = 36,282 (1:1) N = 48,836 + 10,739 + 16,608 + 36,282 = 112,465 68,133 women = 60.6% oftotal enrollments

  34. Multiple Opportunistic Infection Prophylaxis Study (MOPPS) Protocol: Sequential versus Simultaneous (Factorial) Randomization SequentialSimultaneous CD4+ Count 300 Candidiasis 200 PCP 100 CMV 50 MAC 2x2x2x3 Factorial

  35. Treatments of Interest No. OIArmsTreatment Groups PCP 2 Daily vs. 3x weekly TMP/SMX (1:1) Candidiasis 2 Fluconazole vs. Placebo (1:1) MAC 3 Clarithromycin (C) vs. Rifabutin (R) vs. C + R (1:1:1) CMV 2 Ganciclovir vs. Placebo (2:1) One randomization with 24 arms (factorial) vs. 4 separate sequential randomizations

  36. Randomization Daily 3x week R R G P G P Sequential Randomization or Factorial 3x Daily G or P For G vs. P, daily/3x weekly is a baseline characteristic for defining subgroups Stat Med 1996; 15:2445-2453.

  37. A no yes 20 10 yes B 40 30 no no interaction - additive model Concept of Interaction is Model Dependent A no yes 20 10 yes B 60 30 no no interaction - multiplicative model

  38. Possible Designs (Approaches) for Comparing Two Experimental Treatments (A and B) with a Control (C) Using a Parallel Design 1. A vs. C then B vs. C 2. A vs. B vs. C 3, A vs. B vs. C vs. AB 4. AB vs. C

  39. A no yes 0.3 0.1 yes pA = 0.3 B pB = 0.3 0.5 0.3 no pAB(placebo) = 0.5 Comparison of Power for Testing Main Effects for 4 Designs(Byar, Cancer Treatment Reports, 1985.) Assumptions:  = .05 (1-sided) pAB = 0.1 (no interaction) pAB = 0.2 (interaction) A no yes 0.2 0.3 yes B 0.3 0.5 no

  40. Design 1Two Separate TrialsEach with Two Treatments A 120 Trial 1: Placebo 120 Trial 2: B 120 Placebo 120 Total no. of patients = 480 • Independent assessments of A and B • No information on interactions No. Patients Power 0.93 0.93

  41. Design 2One Trial with Three Treatment Groups No. Patients A 120 B 120 Placebo 120 Total no. of patients = 360 • Comparisons of A and B with placebo are not independent since they share the same control group • No information on interactions † Dunnett’s procedure Power 0.93 (0.90)†

  42. Design 32 x 2 Factorial Design No. Patients A 60 B 60 AB 60 Placebo 60 Total no. of patients = 240 • Independent comparisons • Information on interactions Problem: considerable loss of power with interaction Power 0.96

  43. Alternative Design 32 x 2 Factorial Design No. Patients A 90 B 90 i) 0.99 AB 90 ii) 0.92 Placebo 90 Total no. of patients = 360 Power Power for interaction test = 0.18

  44. Design 4One Trial Comparing the Combinationof A and B with Placebo No. Patients AB 120 Placebo 120 Total no. of patients = 240 • Not clear which treatment works • Information on combined use only * Power 0 = 0.93 if the failure rate for the combination of AB is 0.3, i.e., only one of the 2 treatments is effective Power 0.99*

  45. Another Approach – Same General Idea • Sample size for 40% versus 20% with α = 0.05 (2-sided) and power = 0.90 is 110 per group in each main effect comparison (55 per group for the 4 arms – 220 total). • Determine sample size so that each subgroup (e.g., A vs no A with and without B) can be analyzed separately with power = 0.70. • For that need 65 per group; 260 total.

  46. Reporting of Factorial Studies • State rationale for using factorial design • Report number assigned to individual treatments • Examine interaction for major efficacy and safety outcomes • Show data on outcomes for individual cells (as well as margins) so others can assess possible interaction (simply stating “no interaction” is not sufficient) JAMA 2003;289:2545-2553.

  47. SummaryFactorial Designs 1. Generally underutilized; should especially be considered by groups conducting multiple studies 2. Should be considered when multiple treatments (questions) are of interest – can be efficient way to study two questions. 3. If interest is in main effects and dilution due to interaction is a possibility, sample size should be increased. Power should be considered for each treatment vs no treatment (e.g., A vs no A or B) and for each simple effect. • If interest is in treatment interaction, sample size will have to be substantially increased • It is important to report “cell” summary statistics, e.g., summary statistics for each combination of factors.