Designs for Clinical Trials

Transcription

1 Designs for Clinical Trials

2 Design issues Research question Statistical optimality not enough! Use simulation models! Confounding Objective Control Statistics Design, Variables Ethics Variability Cost Feasibility

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4 Parallel Group Designs R Test Control Control Easy to implement ccepted Easy to analyse Good for acute conditions Yij i i,,n j ij j,,k ~ N, ij

5 Where does the varation go? Placebo Drug X 8 week blood pressure Y Xβ ε nything we can explain Unexplained

6 etween and within subject variation DP mmhg Placebo Drug X Female Male aseline 8 weeks

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12 Variance formulas for equations on prev slide Only end of study: Var[ ] Y end Change from baseline Var[ Y end Y baseline Corr[ Y ] Var[ Y end, Y end baseline ] Var[ Y ] baseline aseline as covariate: Some other time ] Cov[ Y Corr[ Y end, Y end, Y baseline baseline ] ]

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15 Model for a cross over study Obs=Period+sequence+subject+treament+carryover+error Yijk i effect of sequence i, i( k) effect of subject k,, ni within sequence i iid N, j effect of period j, t effect of treatment t, random error iid N, ijk i i( k) j t j r ijk s

16 by Crossover design E Y ijk Effect of treatment and carry over can not be separated!

17 Model: Sum to zero: Matrix formulation Yijk Matrix formulation,, i i( k) X, T T X j t ijk (Restrictions madeso these parameters become uniquely defined and not only up to some additive constants)

18 Matrix formulation Parameter estimate: X T X X T Y ˆ ˆ T Y Y T X ˆ Y Cov ˆ X T X ˆ X T X Estimates independent and Var ˆ.5 ˆ

19 lternatives to * Compare to Same model but with 3 periods and a carry over effect Yijk i i( k) i j i( k) effect of subject k,, ni within sequence i iid N, effect effect of of sequence period i, j,,3 t effect of treatment t, random error iid N, ijk j t j r ijk s

20 Parameters of the, design Yijk i i k j t ( ) ijk E Y ijk ijk

21 Matrix again X X T X Effect of treatment and carry over can be estimated independently!

22 Other sequence 3 period designs 3 4 Var ˆ Var ˆ Corr ˆ, ˆ N/.5.. N/ N/

23 Comparing the, and the, designs Var ˆ.5 ˆ ˆ Var.9 ˆ Can t include carry over Carry over estimable treatments per subject 3 treatments per subject Shorter duration Longer duration

24 More than treatments Tool of the trade: Define the model X T X C C C C C C D C D C C D C D Investigate C C C C C Watch out for drop outs!

25 Titration Designs Increasing dose panels (Phase I): SD (Single scending Dose) MD (Multiple scending Dose) Primary Objective: Establish Safety and Tolerability Estimate Pharmaco Kinetic (PK) profile Increasing dose panelse (Phase II): Dose - response

26 VERY careful with first group! Titration Designs (SD, MD) Dose: Z mg X on drug Y on Placebo Dose: Z mg X on drug Y on Placebo Dose: Z k mg X on drug Y on Placebo Stop if any signs of safety issues

27 Titration Designs Which dose levels? Start dose based on exposure in animal models. Stop dose based on toxdata from animal models. Doses often equidistant on log scale. Which subject? Healty volunteers Young Male How many subjects? Rarely any formal power calculation. Often on placebo and 6-8 on drug.

28 Titration Designs Not mandatory to have new subject for each group. X mg X mg X 3 mg X 4 mg X 5 mg X Y mg Gr. Gr. Gr. Gr. Gr. 3 Gr Slighty larger groups to have sufficiently many exposed. Dose in fourth group depends on results so far. Possible to estimate within subject variation.

29 Factorial design clinical trials Factorial randomised trials allows to evaluate more than one intervention in a single experiment, whether () testing the treatment effects independently or () when the aim is to investigate the treatment interactions. In the simplest case, a design is a study when two treatment factors are involved each with two levels. nalysis of factorial trials requires more attention than simple parallel studies. Specifically, choice of statistical methods and how to handle treatment interactions.

30 Factorial design clinical trials For example, in a cardiovascular disease prevention trial, patients are being randomized to receive aspirin vs. matching placebo and then betacarotene vs. matching placebo. eta-carotene Yes spirin No Yes Group spirin + eta-carotene Group spirin placebo + eta-carotene No Group 3 spirin + eta-carotene placebo Group 4 spirin placebo + eta-carotene placebo

31 Factorial design Evaluation of a fixed combination of drug and drug placebo placebo active placebo P placebo active active active The U.S. FD s policy ( CFR 3.5) regarding the use of a fixed-dose combination The agency requires: Each component must make a contribution to the claimed effect of the combination. Implication: t specific component doses, the combination must be superior to its components at the same respective doses

32 daptive Designs Dragalin V. daptive Designs: Terminology and Classification. Drug Information Journal. 6; 4(4):

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35 Definition daptive Design uses accumulating data to decide on how to modify aspects of the study without undermining the validity and integrity of the trial Validity means providing correct statistical inference (such as adjusted p- values, unbiased estimates and adjusted confidence intervals, etc) assuring consistency between different stages of the study minimizing operational bias Integrity means providing convincing results to a broader scientific community preplanning, as much as possible, based on intended adaptations maintaining confidentiality of data

36 daptive Plan not daptive Plane n adaptive design should be adaptive by "design" not an ad hoc change of the trial conduct and analysis daptation is a prospective design feature, not a remedy for poor planning

37 General Structure n adaptive design requires the trial to be conducted in several stages with access to the accumulated data n adaptive design may have one or more rules: llocation Rule: how subjects will be allocated to available arms Sampling Rule: how many subjects will be sampled at next stage Stopping Rule: when to stop the trial (for efficacy, harm, futility) Decision Rule: the terminal decision rule and interim decisions pertaining to design change not covered by the previous three rules t any stage, the data may be analyzed and next stages redesigned taking into account all available data

38 Examples Group Sequential Designs: only Stopping Rule Response daptive llocation: only llocation Rule Sample Size Re-assessment: only Sampling Rule Flexible Designs: Changing the randomization ratio Changing the timing of the next interim analysis Changing the stopping Rule Changing the target treatment difference; changing the primary endpoint; varying the form of the primary analysis; modifying the patient population; etc nything goes?

39 chieving the goals There are plenty of available designs on statistician s shelf The greatest challenge is their implementation daptive designs have much more to offer than the rigid conventional parallel group designs in clinical trials

40 Group Sequential Design Determine N Conduct of Clinical Trial Final nalysis Interim analysis Interim analysis Interim analysis 3 Scope of Early termination of trial Overwhelming efficacy futility of the drug 4

41 Group sequential designs large study is a a huge investment, $, ethics What if the drug doesn t work or is much better than expected? Could we take an early look at data and stop the study is it look good (or too bad)? Group Sequential Methods with pplications to Clinical Trials by Christopher Jennison and ruce W. Turnbull.

42 Group Sequential Designs Group sequential designs are used to facilitate the conduct of interim analysis (see section 4.5 and Glossary). While group sequential designs are not the only acceptable types of designs permitting interim analysis, they are the most commonly applied because it is more practicable to assess grouped subject outcomes at periodic intervals during the trial than on a continuous basis as data from each subject become available. The statistical methods should be fully specified in advance of the availability of information on treatment outcomes and subject treatment assignments (i.e. blind breaking, see Section 4.5).

43 n Independent Data Monitoring Committee (see Glossary) may be used to review or to conduct the interim analysis of data arising from a group sequential design (see Section 4.6). While the design has been most widely and successfully used in large, long-term trials of mortality or major nonfatal endpoints, its use is growing in other circumstances. In particular, it is recognised that safety must be monitored in all trials and therefore the need for formal procedures to cover early stopping for safety reasons should always be considered.

44 Theoretical set-up Population I N (µ, σ =) Population II N (µ, σ =) x, x,., x N y, y,., y N Effect size, = µ - µ Our interest is to test (using two sample Z-test) H o : = vs H a : > ssuming = δ, total sample size (N) per population 44

45 Group-sequential structure Trial (K-) Interim Final Initiatio nalyses naly L- L K- n sis K dditional Subjects Cumulative Subjects Information Time n N n N n L- N L- n L N L n K- N K- n K N K =N Observed Effect size L- L K- K -sample Z Test Statistic T T T L- T L T K- T K Critical values Reject H o & Stop trial if: C C C L- C L C K- C K 45 T >C T >C T L- >C L- T L >C L T K- >C K- T K >C K

46 Conditional Power The conditional power evaluated at the L th interim analysis Sample size may be modified based on conditional power. { } is the Rejection Region. 46

47 Repeated significance test can we use same rejection limit for all interims? Let: ~ N, Y Test: ij Test statistic: j ˆ ˆ Z mk mk H : ˆ mk j Y ij mk i For k, K If Z k C Stop, reject For k K If H otherwise Continue to group k Z k C Stop, reject H otherwise stop accept H

48 True type I error rate Repeat testing until H rejected Tests Critical value P(type I error) Too high! Want to control error rate so that overall error rate = 5%

49 Pocock s test Suppose we want to test the null hypothesis 5 times using the same critical value each time and keep the overall significance level at 5% k If Z C K For, K fter group K Choose C p, K k p, Stop, reject otherwise Continue to group k Stop, reject H If Z C K Such that k p, otherwise stop accept H P( Reject H at any analysis k K) H

50 Pocock s test Z k Reject H.43 ccept H stage k -.43 Reject H.43 Nominal sign level.6%

51 Group sequential tests K c c

52 O rian & Flemmings test Increasing nominal significance levels decreasing rejection limits For, K k : If Z C, K K k fter group K : Choose C p, K k p / Stop, reject otherwise Continue to group k If Z C K k p, Stop, reject H otherwise stop accept H Such that P( Reject H at any analysis k K) H

53 O rian & Flemmings test Critical values and nominal significance levels for a O rian Flemming test with 5 interrim tests. Test (k) C (K,) C (K,)*Sqrt(K/k) Rather close to 5%

54 Group sequential tests Rather close to 5% K c c

55 O rian & Flemmings test Z k Stage K

56 Comparing Pocock and O rian Flemming O rian Flemming Pocock Test (k) C (K,a)*Sqrt(K/k) C P (K,a)

57 Comparing Pocock and O rian Flemming 6 4 Zk Stage k

58 Group Sequential Designs Pros: Efficiency Gain (Decreasing marginal benefit) Establish efficacy earlier Detect safety problems earlier Cons: Smaller safety data base Complex to run Need to live up to stopping rules!

59 Chapter 5 Reading Instructions 5.: Introduction 5.: Parallel Group Designs (read) 5.3: Cluster Randomized Designs (less important) 5.4: Crossover Designs (read+copies) 5.5: Titration Designs (read) 5.6: Enrichment Designs (less important) 5.7: Group Sequential Designs (read include.6) 5.8: Placebo-Challenging Designs (less important) 5.9: linded Reader Designs (less important) 5.: Discussion