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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

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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:

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Parallel Group Studies Informed Consent Yes, randomize No Eligible Patients AB Variability of response = = between subject within subject = + e s +

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Parallel Group Studies Stratified Randomization Informed Consent YesNo Eligible Patients Stratum 1Stratum iStratum 2... A B A B A B Variability of response = = + ie is i wiwi i

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Immediate Versus Deferred Treatment: Concorde Study AZTPlacebo Open-label AZT Randomization If AIDS/ARC or CD4+ declines to <500 cells/mm 3 Lancet 1994; 343:

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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:

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

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

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Sequential Randomization (Dynamic Treatment Regimens) No. OIArmsTreatment Groups PCP2Daily vs. 3x weekly TMP/SMX (1:1) PCP22 nd line treatment: dapsone vs. atovaquone

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Sequential Randomization For A vs. D,daily/3x weekly is a baseline characteristic for defining subgroups Daily3x week Randomization (R) AD R AD R Stat Med 1996; 15:

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Parallel Group Studies: 2 x 2 Factorial Design – both A and B Controlled Experimentally Informed Consent Yes, randomizeNo Eligible Patients A, no BNo A, no BA, B Variability of response = = + ieis i wiwi i No A, B Two factors each at 2 levels = 2x2.

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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 (7 th edition, 1 st published 1935)

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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.

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Parallel Group Study Factorial Design Another Representation A B No B No A BNo 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.

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

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Example: Physician’s Health Study 2 x 2 Factorial Design Factor 1: 2 levels, Factor 2: 2 levels Aspirin Main Effect: No. Participants11,03711,034 No. CVD deaths4444 No. Fatal/non-fatal myocardial infarctions Aspirin Carotene Placebo Factor 2 Factor 1

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Factorial Design Considerations 1.Interest in multiple Rx – can be efficient 2.Interaction 3.Generalizability – treatments studied experimentally under different conditions. 4.Safety, logistics – may not be feasible 5.Mechanism of action – if different, efficiency increases

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

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2 x 2 Factorial Variance of main effects, e.g., A Var (X A - X)+ (X AB - X B ) 2 2 n 2 n Variance of AB interaction Var(X A - X)- (X AB - X B ) 4 2 n

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Quantitative Interaction 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 Response Factor 2, Level 2 X X O O 1 2 Factor 1 Factor 2, Level 1

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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 Response X - Level 1 of Factor 2 O - Level 2 of Factor 2 X X O O 1 2 Factor 1

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

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AB Interaction: ABC Interaction: 1 2 (X A - X)- (X AB - X B ) + (X AC - X C )- (X ABC - X BC ) (X A - X)- (X AB - X B ) - (X AC - X C )- (X ABC - X BC ) Two estimates of AB interaction, one in the presence of C and one in the absence of C. 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.

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2 x 2 x 2 Factorial Variance Estimates Main effect: 2 2n 2-way interaction: 2 2 n 4 2 2n 3-way interaction: 8 2 n 16 2 2n

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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:

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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)

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

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

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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) Yes No Amitriptyline (F2) Acupuncture (F1) Quantitative interaction likely.

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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 Yes No Behavioral Intervention (F2) Microbicide (F1) Quantitative interaction likely.

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

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

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Women’s Health Initiative Partial Factorial Design (cont.) Factor 3:Calcium and vitamin D supplementation Ca + + Vitamin D vs. Placebo N = 36,282 (1:1) N = 48, , , ,282 = 112,465 68,133 women = 60.6% of total enrollments

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Multiple Opportunistic Infection Prophylaxis Study (MOPPS) Protocol: Sequential versus Simultaneous (Factorial) Randomization SequentialSimultaneous CD4+ Count 300Candidiasis 200PCP 100CMV 50MAC2x2x2x3 Factorial

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Treatments of Interest No. OIArmsTreatment Groups PCP2Daily vs. 3x weekly TMP/SMX (1:1) Candidiasis2Fluconazole vs. Placebo (1:1) MAC3Clarithromycin (C) vs. Rifabutin (R) vs. C + R (1:1:1) CMV2Ganciclovir vs. Placebo (2:1) One randomization with 24 arms (factorial) vs. 4 separate sequential randomizations

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Sequential Randomization or Factorial For G vs. P,daily/3x weekly is a baseline characteristic for defining subgroups Daily G P 3x or Daily3x week Randomization GP R GP R Stat Med 1996; 15:

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Concept of Interaction is Model Dependent yes no no no interaction - additive model A B yes no no no interaction - multiplicative model A B

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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

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Comparison of Power for Testing Main Effects for 4 Designs (Byar, Cancer Treatment Reports, 1985.) = 0.1 (no interaction) yes no no A B yes no no A B Assumptions: =.05 (1-sided) = 0.2 (interaction) p AB pApA = 0.3 pBpB p AB(placebo) = 0.5

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Design 1 Two Separate Trials Each with Two Treatments A120 Trial 1:Placebo120 Trial 2:B120 Placebo120 Total no. of patients = 480 Independent assessments of A and B No information on interactions 0.93 No. Patients Power

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Design 2 One Trial with Three Treatment Groups A120 B120 Placebo120 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 0.93 (0.90) † No. Patients Power

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Design 3 2 x 2 Factorial Design A60 B60 AB60 Placebo60 Total no. of patients = 240 Independent comparisons Information on interactions Problem: considerable loss of power with interaction 0.96 No. Patients Power

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Alternative Design 3 2 x 2 Factorial Design A90 B90i)0.99 AB90ii)0.92 Placebo90 Total no. of patients = 360 No. Patients Power Power for interaction test = 0.18

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Design 4 One Trial Comparing the Combination of A and B with Placebo AB120 Placebo120 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 0.99* No. Patients Power

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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 = For that need 65 per group; 260 total.

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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:

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Summary Factorial 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. 4.If interest is in treatment interaction, sample size will have to be substantially increased 5.It is important to report “cell” summary statistics, e.g., summary statistics for each combination of factors.

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