Design for Targeted Therapies: Statistical Considerations

Transcription

1 Design for Targeted Therapies: Statistical Considerations J. Jack Lee, Ph.D. Department of Biostatistics University of Texas M. D. Anderson Cancer Center

2 Outline Premise General Review of Statistical Designs A Specific Example

3 Premise Many new targeted agents Many, many more potential combination therapies Don t know the best dose, schedule Targeted agents do not work for all patients or may not work at all May or may not know the predictive markers May or may not know how best to gauge the treatment effect tumor regression, stabilizing disease, improving survival Limited patient population enrolled in clinical trials Time is of the essence

4 Agent(s) Key Issues Single or combination Dose, schedule (sequential or concurrent?) Population All comers or enriched population Predictive Markers What markers to use? Sensitivity and Specificity Endpoints Response, Disease Control, PFS, OS Biomarkers in targeted tissue, marker modulation Conduct Equal randomization versus Adaptive randomization Stratification Analysis Pre-specified or post-doc subgroup analysis

5 Statistical Design Goals Be able to answer the question correctly Low prob of choosing undesirable tx Control Type I (false positive) error rate High prob of choosing desirable tx Control Type II (false negative) error rate / maintain high stat.. power Be able to answer the question quickly: less N Give better tx to pts - Enhance ethics Treat more (less) subj in the arms doing well (not working) Align pts with best available treatments based on pt characteristics tics Allow changes on treatment arm(s) Terminate the non-performing arm(s) early Add promising new treatment(s) Identify a subset of subjects who may respond better to a targeted treatment Who will respond? Does the treatment work?

6 Design Goals Summary We want a design that is : Accurate Efficient Ethical Flexible Smart Continuing to learn during the trial

7 An Application of Adaptive Randomization and Hierarchical Bayes Model in Biomarker-Based Based Cancer Clinical Trials

8 BATTLE (Biomarker-based Approaches of Targeted Therapy for Lung Cancer Elimination) Evaluate targeted therapy agent(s) ) in patients with different biomarker profiles Stage IV recurrent non-small cell lung cancer (NSCLC) with endpoint: 8-week 8 progression- free survival rate (i.e., disease control rate [DCR]).

9 BATTLE Goals Treat more patients in promising groups according to each patient s biomarker profile Shut down or suspend ineffective groups early Provide an accurate estimate for the true disease control rate in each of the biomarker/treatment combination groups Borrow strength from pts treated with the same agent but different biomarker profile

10 Four Molecular Pathways Targeted in NSCLC: BATTLE Program Enrollment into BATTLE Umbrella Protocol Biomarker Profile and Adaptive Randomization Biomarker MG EGFR K-ras and/or B-raf VEGF and/or VEGFR RXR and/or cyclin D1 Frequency 1 + x x x x x x Erlotinib Sorafenib Vandetanib Erlotinib + Bexarotene Endpoint: Progression-free survival at 8 weeks Disease Control Rate (DCR)

11 Bayesian Hierarchical Ordinal Probit Model Ordinal probit model with hyper prior (Albert et al, 1993) y γ ijk 1 if zijk > 0 = 0 otherwise = Pr( y = 1) = Pr( z > 0) jk ijk ijk z ~ N ( µ, 1), for i = 1,..., n ijk jk jk j jk 2 ~ N ( j, ), for k = 1,...,5 µ φ σ φ N τ 2 ~ (0, ), for 1,...,4 Notation -- i th : subject, i=1,..., n jk -- j th : treatment arm, j=1,, 4 -- k th : marker group, k=1,, 5 -- y ijk : 8-week progression-free survival status: 0(no) vs 1(yes) -- z ijk : latent variable -- µ jk : location parameter -- φ j : hyper-prior on µ jk -- γ jk : disease control rate (DCR) -- σ 2,τ 2 : hyper-parameters control borrowing across MGs within and between treatments j =

12 Computation of the Posterior Conditional Distribution Gibbs Sampling The random variables are generated from their complete posterior conditional distributions as follows. The latent variable z ijk is sampled from a truncated normal distribution centering at µ jk. The full conditional distribution of µ jk and Φ j are the linear combination of the prior distribution and the sampling distribution.

13 Adaptive Randomization The adaptive randomization & stopping rule will be applied after enrolling at least one patient in each (Treatment x MG) subgroup. Adaptively assign the next patient into the treatment arms proportional to the marginal posterior disease control rates. Randomization Rate (RR): proportional to the marginal posterior DCR. a ( ˆ γ ) / ( ˆ γ ) jk w set a minimum RR to 10% to ensuring a reasonable probability of randomizing pts in each arm wk a

14 Probability Response Adaptive Randomization Next pt pt received TX=1 e.g., a pt w/ EGFR mutation (+), K-rasK and and (-), had VEGF had a response (+), RXR ( )( ) & Cyclin D1 ( )( TX P(Resp) P(Rand) P(Resp) P(Rand) After Tx

15 Decision Rules Suspend the treatment arm j for k th biomarker group if Pr(Pr(Z ijk >0 Data) > θ * ) δ L θ * =0.5 : target DCR δ L =0.1 : critical probability for the early stopping. Declare the success of the treatment if Pr(Pr(Z ijk >0 Data) θ) ) > δ U θ = : null DCR δ U =0.8 : critical probability for declaring an effective treatment.

16 Simulation The trial s operating characteristics (OC) are studied by simulation in R Choose parameters to yield good OC s Sample size: N = 200 Target: 20% type I error rate and 80% power 1,000 runs for each of the 6 scenarios varying the DCR s to cover various alternative and null cases adaptive randomization vs. equal randomization vague prior vs. more informative prior with early stopping vs. without early stopping

17 Simulation Scenario 1 One effective treatment for MG 1-4, 1 no effective treatment for MG 5, adaptive randomization (AR), without early stopping, and with vague prior MG 1 MG 2 MG 3 MG 4 MG 5 TX TX 2 TX 3 TX 4

18 Simulation Results (scenario 1)

19 Simulation Scenario 2 No effective treatments for MG 1-5, 1 AR,, without early stopping, and with vague prior MG 1 MG 2 MG 3 MG 4 MG 5 TX 1 TX 2 TX 3 TX 4

20 Simulation Results (scenario 2)

21 Simulation Scenario 3 One effective treatment for MG 1-4, 1 no effective treatment for MG 5, equal randomization,, without early stopping, and with vague prior MG 1 MG 2 MG 3 MG 4 MG 5 TX TX 2 TX 3 TX 4

22 Simulation Results (scenario 3)

23 Simulation Scenario 4 Varying effective treatment for MG 1-4, 1 one effective treatment for MG 5, AR, without early stopping, and with varying informative prior (τ 2 = 10 6, σ 2 = 100/10/1) MG 1 MG 2 MG 3 MG 4 MG 5 TX TX 2 TX 3 TX 4

24 Simulation Results (scenario 4)

25 Simulation Scenario 5 One effective treatment for MG 1-4, 1 no effective treatment for MG 5, AR, with early stopping,, and with vague prior MG 1 MG 2 MG 3 MG 4 MG 5 TX TX 2 TX 3 TX 4

26 Simulation Results (scenario 5)

27 Simulation Scenario 6 One effective treatment for MG 1-4, 1 no effective treatment for MG 5, equal randomization, with early stopping, and with vague prior MG 1 MG 2 MG 3 MG 4 MG 5 TX TX 2 TX 3 TX 4

28 Simulation Scenario 6

29 Number (% in randomized) of Patients with Disease Control Equal Rand., no early stopping: 76.3 (38.2%) Adaptive Rand., no early stopping: 80.9 (40.5%) Equal Rand., w/ early stopping: 81.4 (41.9%) Adaptive Rand., w/ early stopping: 83.0 (43.0%)

30 Summary of Simulation Results Provides good estimations of marginal posterior disease control rates and with high probability of making the correct inference. Assigns more patients into the treatment arm most likely to result in a response given the patients biomarker profile. Allows early stopping for the ineffective treatment arm, hence, it is more efficient than the non-adaptive methods.

31 Challenges Inform Consent Missing or incomplete biomarker profile Not every pt has adequate amount of tissue Adaptive Randomization vs. Equal Randomization For AR When to start AR? How to determine randomization ratio? Choice of the prior distribution Independent outcome assessment Reveal interim results? Inform pt about biomarker profile? How much interim result should be reported to PI? DMC: Monitoring trial conduct and interim results

32 Conclusions This trial design allows us to identify the effective agents for patients with different biomarker profiles and treat patients on the trial with the best corresponding treatment with high probability in real time a step towards personalized medicine.

33 Conclusions (continued) The success of such trials requires an integrated multi-functional research team Clinicians who see patients and perform biopsies Basic scientists who run the biomarker analysis Computer programmers who build web-based database applications for trial conduct Statisticians who provide the design and implement of the algorithm for adaptive randomization.