Alternative Trial Designs

Transcription

1 Alternative Trial Designs STATS 773: DESIGN AND ANALYSIS OF CLINICAL TRIALS Dr Yannan Jiang Department of Statistics May 16 th 01, Wednesday, 08:30-10:00

2 Standard Design of RCT Individual subject is randomly allocated to receive either the intervention or the control Intervention (N) Participants (N) Control (N) Randomisation (1:1) Follow up

3 Other Types of Trial Design Cluster Randomised Trial A group of subjects ( cluster ) are randomly allocated to receive either the intervention or the control Example of clusters: School, GP clinic, Hospital, District Logistic constraints with reduced efficiency Factorial Design Evaluate two (or more) interventions vs. the control in a single experiment Examples: chemotherapy and radiation therapy in cancel patients Appeal of getting more experiments done at once, given the cost and effort in trial recruitment and conduct Cross-over Design Each subject receives consecutively two or more treatments during the course of the study, i.e. serve as his/her own control Smaller sample size with a prolonged trial period Fairly strict assumption on carrying-over effect 3

4 x Factorial Design Two interventions A and B Each intervention has two groups to compare: With intervention (with A or with B) Without intervention (without A or without B) Participants are randomised to one of the 4 treatment arms: A only B only Both A and B Control (Not A and Not B) Intervention B Intervention A Yes No Total Yes n AB n BO N B No n AO n CT N B Total N A N A N 4

5 Why Factorial Design? If we compare two groups with and without Intervention A as in a standard RCT, sample size required per group is: Same calculation can be used for Intervention B under the same assumptions Advantage One set of participants serve two trial objectives ( for 1 deal) Disadvantage N ( z z / ) Intervention was evaluated between two groups, regardless of the potential effect of another intervention on the same participants Question: Is this a valid assumption? A N A 5

6 The Interaction Effect The effect of one intervention differs depending on the effect of another intervention Trials employing a factorial design often have either of the two objectives to achieve: 1. Test >1 interventions in one trial to save time and budget, assuming there is no interaction effect. Test a combination of drugs, and examine the size of interaction effect between drugs Which assumption is true depends on the nature of interventions 6

7 Y No Interaction Effect AB () BO AO () () CT

8 What if no-interaction is violated? Sample size estimation based on the test for main effects of A and B (i.e. assuming no interaction) is no longer valid Reduced effective sample size or power depending on the size of the interaction effect The statistical test of interaction may lack power to detect an interaction if exists False negative of no interaction 8

9 Sample Size With Interaction Assume now we need m participants in each of the four treatment combinations (i.e. per cell in the x table) To detect interaction effect (Δ), we actually look at the difference of the differences, (M AB -M BO ) (M AO -M CT ) which has twice the variability when we compare only two treatment arms m ( z z / ) ( ) vs. n ( z z / ) (No Interaction) 9

10 Change to Sample Size Interaction effect ( ) Main effect (ε) Sample size per cell (m) 0 1 n 1 n 1 1 4n n ( z / z ) ( ) ( z / z ) m vs. n (No Interaction)

11 Statistical Analysis (Model 1) Define two binary indicators A and B, Y 0 1A B 3( A: B) A=1 if Intervention A is used, 0 otherwise B=1 if Intervention B is used, 0 otherwise A:B is the interaction term between A and B A:B=1 if both A and B are used The reference group is control (A=B=0) 11

12 Statistical Analysis (Model ) Define a categorical variable with four levels, each indicating one treatment arm This is equivalent to three dummy variables Y 0 1( AO) ( BO) 3( AB) AO=1 if only Intervention A is used, 0 otherwise BO=1 if only Intervention B is used, 0 otherwise AB=1 if both interventions are used, 0 otherwise The reference group is control (AO=BO=AB=0) 1

13 Arms Model 1 Model Factors Effect Factors Effect Control A=0 B=0 A:B=0 0 AO=0 BO=0 AB=0 0 A only A=1 B=0 A:B=0 1 AO=1 BO=0 AB=0 1 B only A=0 B=1 A:B=0 AO=0 BO=1 AB=0 A and B A=1 B=1 A:B=1 1 3 AO=0 BO=0 AB=1 3 13

14 Effect of Intervention A (Model 1) )] ( ) [( ] ) [( Eff A ) ( _ A Y No _ A A No A Eff Y Y 14

15 Effect of Intervention A (Model ) ) ( ) ( AB AO A Y Y Y ) ( ) (

16 Y Size of Interaction Effect (Example 1) AB (4) BO AO () () CT

17 Y Size of Interaction Effect (Example ) BO AO (AB) () () CT

18 Y Size of Interaction Effect (Example 3) BO AO () () CT AB

19 SHOP A Case Study A X factorial randomized controlled trial was conducted in 8 NZ supermarkets in Over 1000 shoppers were randomly assigned to one of four treatment groups, with a combination of two interventions: Price discounts (1.5%) on healthier foods [A] Tailored nutrition education [B] Outcomes were measured repeatedly at 6 and 1 months post intervention: Primary: change in % energy from saturated fat Secondary: change in other nutrients and foods purchased Electronic data collection using supermarket records Ni Mhurchu et al. (010), Am J Clin Nutr 91:

20 Participant Flow Chart Ni Mhurchu et al. (010), Am J Clin Nutr 91:

21 Sample Size Evaluation With a x factorial design and the No-Interaction assumption, the total sample size required should be N=600 (i.e. 300 per intervention group, either A or B) The above sample size, however, has presented as a four-arm trial, with n=300 per arm Although not stated, the sample size has powered to detect an interaction effect of.85 (if true) 1

22 Data Analysis and Results

23 Other Types of Trial Design Cluster Randomised Trial A group of subjects ( cluster ) are randomly allocated to receive either the intervention or the control Example of clusters: School, GP clinic, Hospital, District Logistic constraints with reduced efficiency Factorial Design Evaluate two (or more) interventions vs. the control in a single experiment Examples: chemotherapy and radiation therapy in cancel patients Appeal of getting more experiments done at once, given the cost and effort in trial recruitment and conduct Cross-over Design Each subject receives consecutively two or more treatments during the course of the study, i.e. serve as his/her own control Smaller sample size with a prolonged trial period Fairly strict assumption on carrying-over effect 3

24 Crossover Design in RCT A cross-over trial is one in which subjects are given sequences of treatments with the objective of studying differences between individual treatments (or sub-sequences of treatments) Not all trials in which patients are assigned to sequences of treatments are cross-over trials It is the individual treatments which make up the sequences are of particular interest, rather than the sequences Advantages Fewer patients to recruit than the parallel trial (one treatment per patient) Achieve same precision in estimation using (smaller) within-patient variation Disadvantages Longer study period with multiple treatments p.p. and potentially drop-outs Not suitable to conditions where patients may have considerable deterioration or improvement during the course of treatment Potential carry-over effect which is the persistence of a treatment applied in one period in a subsequent period of treatment More complex statistical analysis Stephen Senn (00), Cross-over trials in clinical research, nd Ed 4

25 Application of Crossover Design Crossover trials are often employed to investigate treatments for ongoing or chronic diseases, where there is no condition of curing the illness but moderating its effects through the treatment E.g. asthma, rheumatism, epilepsy Can be long-term Carry-over effect (period-by-treatment interaction) is one of the major concerns in such trials Two-stage procedure to examine the CO effect first If no CO effect, conduct a within-patient test With CO effect, conduct a between-patient test using the first period only Can be potentially misleading and should not be used Include parameters for carry-over and estimate its effects together with the treatment Use a wash-out period during which the effect of a treatment given previously is believed to disappear Stephen Senn (00), Cross-over trials in clinical research, nd Ed 5

26 A Simple AB/BA Design Randomization Treatment A Treatment B Group 1 Treatment B Treatment A Group First treatment period Washout period Second treatment period 6

27 Sample Size Calculation In AB/BA design, we compare the results of two treatments on the same group of patients The variance of the outcome variable can be expressed in two forms: Variance of repeated observations in the same individual ( ) Variance of the difference between two measurements in the same individual ( ) D W The number of participants required per sequence can be calculated as: ( z z ) n s / D W 7

28 In practice, Sample Size Calculation D is usually unknown! Suppose the variance of the outcome measure on the population of interest is Y Information is often obtainable from the literature or previous studies The correlation between a pair of measurements on the same subject is ρ The variance of the difference, estimated as: [(1 D Y )] D, can be 8

29 An Example A two-treatment twoperiod cross-over trial comparing the effects of a single inhaled dose of 00μg salbutamol (the comparator), and 1μg formoterol (the new drug) on 13 children with moderate or severe asthma Primary outcome was peak expiratory flow (PEF), a continuous measure of lung function Stephen Senn (00), Cross-over trials in clinical research, nd Ed 9

30 A Simple Analysis Perform a matchedpairs t-test, ignoring the cross-over design The results are significant (p-value ) What assumptions have been made here? The crossover differences to be distributed at random about the true treatment effect Any concerns? 30

31 Problems With Simple Analysis 1. Period (trend) effect can be simply dealt with Crossover differences differed between two sequences. Period by treatment interaction major concern in CO design The effect of treatment varied according to the period it was given 3. Carry-over effect major concern in CO design The persistence of first treatment in the period of second treatment 4. Patient by treatment interaction The treatment effect varied from patient to patient 5. Patient by period interaction Patients were subject to different period effects The last two points do not affect the validity of the analysis but add to the general variability of the results 31

32 A Model for AB/BA Design Sequence 1: AB Sequence : BA Basic estimator: The given treatment contrast calculated for an individual patient 3

33 Hills-Armitage Analysis An approach for adjusting for the period effect Generalizable to more complex designs To form an unbiased estimator, assuming there is no carryover effect: Calculate the mean of crossover differences for each sequence Average the resulting means Often referred as the CROS estimator (Freeman 1989) d j = τ π λ A d k = τ + π + λ B (d k +d j )/ estimates (i.e. the treatment effect) (d k d j )/ estimates p (i.e. the period effect) The variance of both estimates (same) is: σ = ss 1 + ss n j + n k ; var τ = (σ n j + σ n k )/4 Divide by its SE to obtain test statistic etc. 33

34 Back to Example The results are similar to the simple analysis ignoring the period effect For a balanced cross-over design with same number of patients per sequence, adjusting for the period effect will NOT change the treatment estimate However, reduce the standard error of treatment estimate (by eliminating the period difference) 34

35 Testing for Carry-over Effect In AB/BA design, the effects of carry-over and treatment-by-period interaction are not separately identifiable The latter may affect any trial with the treatment effect changing over time For simplicity, we assume that a test of the former would be adequate for both We may do this using the patient totals (S i = y 1 +y ) and perform a two-sample t-test on the difference of the totals between two sequences z = (s A -s B )/( var(s) + var(s B )) where Z has a standard Normal distribution under H o 35

36 Back to Example (Not significant) 36

37 What If There Is Carryover Effect? A very simple unbiased estimate of the treatment effect is available: - Compare the results between groups for the first period only - Often referred as the PAR estimator (Freeman 1989) - Discard the data from the second period as if it was a parallel trial - A between-patient estimator with large standard error Estimated value of : Estimated standard error: % confidence interval: -46 l/min 153 l/min T statistic: 1.19 P value: 0.13 (not significant) 37

38 Use of Baselines Baselines are measurements made on the patient with the objective of giving general or background information rather than direct information on the treatment Adjustment of baselines may increase the precision of measurements made directly on the treatment There are three kind of baselines in AB/BA design: 1. Before the start of the first treatment (true baseline!). After the completion of the first treatment and before the start of the second treatment (subject to carryover effect if it exists) 3. After completion of the second treatment Analysis of covariance should be used with caution 38

39 Fixed vs Random Effects Using the PEF example, the following variables can be defined for modeling: OUTCOME: the response of interest, i.e. PEF TREAT: treatment groups, A or B PATIENT: patient unique identification PERIOD: crossover periods, 1 or SEQ: crossover sequences, AB or BA Two SAS procedures are generally considered for the analysis of crossover trials: PROC GLM for fixed effects analysis; PROC MIXED for random effects analysis; 39

40 SAS Example Code proc glm; class PATIENT PERIOD TREAT; model OUTCOME = PATIENT PERIOD TREAT; estimate for-sal TREAT 1-1; run; proc mixed; class SEQ PATIENT PERIOD TREAT; model PEF = SEQ PERIOD TREAT; random PATIENT(SEQ); estimate treatment TREAT 1-1; estimate carry-over SEQ 1-1; run; Random effects models should be considered: - to test for carryover effect - to account for missing data if some patients have dropped out at random (and therefore completed the first period only) 40

41 Adaptive Designs It is not uncommon to adjust trial design and/or statistical methods at the planning stage and during the conduct of clinical trials To learn from accumulating data and apply what is learned ASAP To mitigates the risk in uncertain of study design features (e.g. dose, population, effect size, variability) To increase the probability of success for identifying the clinical benefit of the treatment under investigation Design features for adaptation: Stopping early Increase sample size Add/drop treatment arms Treatment allocation ratio Patient population Primary endpoints Phases of trial development 41

42 Definition of AD A clinical study design that uses accumulating data to decide on how to modify aspects of the study as it continuous, without undermining the validity and integrity of the trial Validity means Providing correct statistical inference Assuring consistency between different stages of the study Minimizing operational bias Integrity means Providing convincing results to a broader scientific community Preplanning based on intended adaptations as much as possible Maintaining confidentiality of data Gallo et al. (006), The PhRMA Working Group 4

43 Operational Bias The KEY issue introduced by leakage of interim data results Changes in trial design can release information Issue with delegating business decisions to an IDMC Confidentiality of data should be maintained with Limited, controlled sponsor involvement Minimal access to information Strong firewalls and documentation Examples of OB: Selection bias: knowing or suspecting the next treatment assignment can influence patient selection Accrual bias: knowledge of patients enrolled later more likely to receive effective treatment can influence the treatment allocation and stopping rules 43

44 Adaptive by Design Prospectively planned potential to change design features of a study while it is ongoing based on analysis of data from subjects in the study Adaption should be part of the design feature upfront, not a remedy for poor planning Some pitfalls: A study with protocol amendments is not necessarily an adaptive design Protocol with an adaptive design should not be vague to allow for flexibility Adaptive designs are not always better 44

45 Seamless Design An important class of AD that combines objectives traditionally addressed in separate trials Eliminates time between trials if done separately Provide additional efficiencies with combined inferences Operationally seamless Separate inference for each stage of the study Inferentially seamless Combines inference across data at different stages Preferable if more unknowns at time of trial design 45

46 Examples of Trial Adaption Exploratory Dose Finding/Dose Response Trials APBG Workshop: Adaptive designs for clinical trials 46

47 Examples of Trial Adaption Confirmatory Trials APBG Workshop: Adaptive designs for clinical trials 47

48 A Case Study Two dose regimens evaluated vs. placebo Two stages in design: Stage 1: three treatment arms Blinded sample size re-estimation (variance) Interim analysis on efficacy and safety Stage : drop one dose and continue with the other two treatment arms APBG Workshop: Adaptive designs for clinical trials 48

49 Dose Selection APBG Workshop: Adaptive designs for clinical trials 49

50 Group Sequential Design In clinical trials, sequential methods are often used when there are formal interim analyses that are intended to assess treatment effect with respect to efficacy or safety at any time prior to the completion of the trial Different from adaptive design with fixed hypotheses May lead to saving in sample size, time and cost compared with the standard fixed trial design Should be carefully planned in advance in the study protocol and statistical analysis plan to avoid bias to subsequent clinical evaluations A sequential test is referred to as a test conducted based on accrued data after every new patient is observed Group sequential test is referred to as a test performed on a group of patients accrued at pre-specified intervals Chow and Chang (007), Adaptive design methods in clinical trials 50

51 Group Sequential Design Data accumulate gradually in a trial Interim analysis 1 cont. Interim analysis cont... Interim analysis K stop stop stop Analyse data Perform GS tests after every group of new patients observed Stopping boundaries: a set of critical values that the test statistics calculated from actual data will be compared with, to either stop or continue the trial 51

52 GS Analysis using SAS Procedures 5

53 References Gallo et al. (006) Adaptive designs in clinical drug development: an executive summary of the PhRMA working group. Journal of Biopharmaceutical Statistics, 16:75-83 Gaydos et al. (009) Good practices for adaptive clinical trials in pharmaceutical product development. Drug Information Journal, 43(05): Chow and Chang (007) Adaptive design methods in clinical trials. Chapman & Hall/CRC O Brien, P.C. and Fleming, T.R.(1979). A multiple testing procedure for clinical trials. Biometrics, 35: Pocock, S.J. (1977). Group sequential methods in the design and analysis of clinical trials. Biometrika, 64: Pocock, S.J.(1997). The role of external evidence in data monitoring of a clinical trial (with discussion). Statistics in Medicine, 15: