BOIN: A Novel Platform for Designing Early Phase Clinical Tri

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1 BOIN: A Novel Platform for Designing Early Phase Clinical Trials Department of Biostatistics The University of Texas, MD Anderson Cancer Center

2 Outline Introduction Bayesian optimal interval (BOIN) designs Software and practical implementation

3 Phase I clinical trials The objective of phase I clinical trials is to find the maximum tolerated dose (MTD) that has a target toxicity rate φ. Target toxicity rate

4 Performance vs Simplicity Good CRM Performance Poor 3+3 Difficult Implementa)on Easy

5 Performance vs Simplicity Good CRM Performance Poor 3+3 Difficult Implementa)on Easy

6 Performance vs Simplicity Good CRM BOIN Performance Poor 3+3 Difficult Implementa)on Easy

7 Objective To introduce the BOIN design as a platform that is easy to implement in a transparent way as the 3+3 design, but yields better performance comparable to more complicated, model-based designs, such as the CRM. Can handle both single-agent trials and drug-combination trials (to find a single MTD or the MTD contour).

8 BOIN design DLT rate at the current dose = No. of patients experienced DLT at the current dose No. of patients treated at the current dose

9 Escalation/de-escalation boundaries Table: The escalation/de-escalation boundaries (λ e, λ d ) under the BOIN design for different target toxicity rates*. Target toxicity rate φ boundaries λ e λ d * using the default underdosing toxicity rate φ 1 = 0.6φ and overdosing toxicity rate φ 2 = 1.4φ.

10 Escalation/de-escalation boundaries Table: The escalation/de-escalation boundaries (λ e, λ d ) under the BOIN design for different target toxicity rates*. Target toxicity rate φ boundaries λ e λ d * using the default underdosing toxicity rate φ 1 = 0.6φ and overdosing toxicity rate φ 2 = 1.4φ.

11 BOIN design with target toxicity rate of 25% DLT rate at the current dose = No. of patients experienced DLT at the current dose No. of patients treated at the current dose

12 Statistical principle behind BOIN design How are dose escalation trials conducted in practice? Start the trial by treating the 1st cohort at the lowest or pre-specified dose.

13 Statistical principle behind BOIN design How are dose escalation trials conducted in practice? Start the trial by treating the 1st cohort at the lowest or pre-specified dose. Then

14 Statistical principle behind BOIN design How are dose escalation trials conducted in practice? Start the trial by treating the 1st cohort at the lowest or pre-specified dose. Then Three possible decisions: 1 Escalation 2 Retaining the current dose 3 Deescalation

15 The oracle design If we knew the true toxicity probability of the current dose level j, denote as p j.

16 The oracle design If we knew the true toxicity probability of the current dose level j, denote as p j. We should escalate the dose if p j < φ.

17 The oracle design If we knew the true toxicity probability of the current dose level j, denote as p j. We should escalate the dose if p j < φ. retain the dose if p j = φ.

18 The oracle design If we knew the true toxicity probability of the current dose level j, denote as p j. We should escalate the dose if p j < φ. retain the dose if p j = φ. deescalate the dose if p j > φ.

19 The oracle design Then,

20 The oracle design Then,... escalate the dose if p j < φ. retain the dose if p j = φ. deescalate the dose if p j > φ.

21 The oracle design If p j was known, we obtain the oracle design No decision error Optimize dosing for each patient In reality, the oracle design does not exist because p j is unknown We have to estimate p j based the observed data and make the decision For example, use the observed toxicity rate ˆp j = m j /n j as an estimate of p j, where m j is the number of patients experienced toxicity at dose j, and n j is the number of patients treated at those j

22 Decision errors The decision is often incorrect Escalate/retain when the current dose is above the MTD Deescalate/retain when the current dose is below the MTD Escalate/deescalate when the current dose is the MTD Such decision errors cannot be completely avoided because of small sample size and estimation uncertainty When the truth toxicity = 30%, there is 34% to observe 0/3 having toxicity. What is the best we can do in practice?

23 Decision errors The decision is often incorrect Escalate/retain when the current dose is above the MTD Deescalate/retain when the current dose is below the MTD Escalate/deescalate when the current dose is the MTD Such decision errors cannot be completely avoided because of small sample size and estimation uncertainty When the truth toxicity = 30%, there is 34% to observe 0/3 having toxicity. What is the best we can do in practice? Minimize incorrect decisions and get as close as possible to the oracle design!

24 Decision errors The decision is often incorrect Escalate/retain when the current dose is above the MTD Deescalate/retain when the current dose is below the MTD Escalate/deescalate when the current dose is the MTD Such decision errors cannot be completely avoided because of small sample size and estimation uncertainty When the truth toxicity = 30%, there is 34% to observe 0/3 having toxicity. What is the best we can do in practice? Minimize incorrect decisions and get as close as possible to the oracle design! This is the motivation of the BOIN (Bayesian Optimal INterval) design

25 A class of nonparametric designs 1 The first cohort are treated at the lowest dose level. 2 At the current dose level j: if ˆp j λ 1j, escalate if ˆp j λ 2j, deescalate otherwise, i.e., λ 1j < ˆp j < λ 2j, retain where λ 1j λ 1j (n j, φ) and λ 2j λ 2j (n j, φ) denote the prespecified dose escalation and deescalation boundaries. 3 Repeat step 2 until the maximum sample size is reached.

26 A family of nonparametric designs 1 The first cohort are treated at the lowest dose level. 2 At the current dose level j: if ˆp j λ 1j, escalate if ˆp j λ 2j, deescalate otherwise, i.e., λ 1j < ˆp j < λ 2j, retain where λ 1j λ 1j (n j, φ) and λ 2j λ 2j (n j, φ) denote the prespecified dose escalation and deescalation boundaries. 3 Repeat step 2 until the maximum sample size is reached.

27 A class of nonparametric designs 1 The first cohort are treated at the lowest dose level. 2 At the current dose level j: if ˆp j λ 1j, escalate if ˆp j λ 2j, deescalate otherwise, i.e., λ 1j < ˆp j < λ 2j, retain where λ 1j λ 1j (n j, φ) and λ 2j λ 2j (n j, φ) denote the prespecified dose escalation and deescalation boundaries. 3 Repeat step 2 until the maximum sample size is reached. Because λ 1j and λ 2j freely vary across the dose and n j, this class of designs include all possible nonparametric designs that do not impose a dose-toxicity curve.

28 Notations and setup Specify three point hypotheses H 0 : p j = φ H 1 : p j = φ 1 H 2 : p j = φ 2, φ 1 is the highest toxicity probability that is deemed subtherapeutic (i.e., below the MTD) such that dose escalation should be made φ 2 is the lowest toxicity probability that is deemed overly toxic such that dose deescalation is required Example: φ = 0.25, φ 1 = 0.15 and φ 2 = 0.35.

29 Remarks on the hypotheses The purpose of specifying three hypotheses, H 0, H 1 and H 2, is not to represent the truth and conduct hypothesis testing. H 1 and H 2, or more precisely δ 1 = φ 1 φ and δ 2 = φ 2 φ, represent the minimal differences (or effect sizes) of practical interest to be distinguished from the target toxicity rate φ (or H 0 ), under which we want to minimize the average decision error rate for the trial conduct. This is analogous to power calculation.

30 Remarks on the hypotheses In practice, we should avoid setting φ 1 and φ 2 at values very close to φ because of the limited power due to small sample sizes of phase I trials. At the significance level of 0.05, we have only 3% power to distinguish 0.35 from 0.25 with 30 patients. As default values, we recommend φ 1 = 0.6φ and φ 2 = 1.4φ. e.g., when φ = 0.25, φ 1 = 0.15 and φ 2 = 0.35.

31 Correct and incorrect decisions The correct decisions under H 0, H 1 and H 2 are R, E and D, respectively, where R, E and D denote dose retainment (of the current dose level), escalation and deescalation. The incorrect decisions under H 0, H 1 and H 2 are R, Ē and D, where R denotes the decisions complementary to R (i.e., R includes E and D), and D and R are defined similarly.

32 Decision error rate The probability of making an incorrect decision (or decision error rate) at each of the dose assignments is given by α pr(incorrect decision on dosing) = pr(h 0 )pr( R H 0 ) + pr(h 1 )pr(ē H 1 ) + pr(h 2 )pr( D H 2 )

33 Decision error rate The probability of making an incorrect decision (or decision error rate) at each of the dose assignments is given by α pr(incorrect decision on dosing) = pr(h 0 )pr( R H 0 ) + pr(h 1 )pr(ē H 1 ) + pr(h 2 )pr( D H 2 ) = pr(h 0 ){Bin(n j λ 1j ; n j, φ) + 1 Bin(n j λ 2j 1; n j, φ)} + pr(h 1 ){1 Bin(n j λ 1j ; n j, φ 1 )} + pr(h 2 )Bin(n j λ 2j 1; n j, φ 2 )

34 Optimal interval boundaries Assuming the non-informative prior that the current dose is equally likely to be below, above or equal to the MTD, the optimal dose escalation/deescalation boundaries that minimize decision error are given by ( ) / ( ) 1 φ1 φ(1 φ1 ) λ e λ 1j = log log 1 φ ( 1 φ λ d λ 2j = log 1 φ 2 ) / log φ 1 (1 φ) ( ) φ2 (1 φ). φ(1 φ 2 ) The optimal escalation/deescalation boundaries are independent of n j and j!! This makes BOIN extremely simple because the same pair of escalation/de-escalation boundaries can be used throughout of the trial.

35 Flowchart of the BOIN design DLT rate at the current dose = No. YingofYuan patients BOIN: experienced A Novel Platform DLT atfor the Designing currentearly dose Phase Clinical Tri

36 Statistical properties of the BOIN Coherence The BOIN design is (long-memory) coherent in the sense that the design will never escalate the dose when the observed toxicity rate ˆp j at the current dose is higher than the target toxicity rate φ; and will never deescalate the dose when the observed toxicity rate ˆp j at the current dose is lower than the target toxicity rate φ Example: suppose target toxicity rate = 30%, if 1/3 has toxicity, the BOIN design will never escalate dose; if 0/3 has toxicity, the design will never deescalate dose. Consistence Under the BOIN design, dose allocation and selection converge to the target dose.

37 Selection of the MTD At the end of the trial, based on all observed data, we select as the MTD dose j, whose isotonic estimate of toxicity rate p j is closest to φ; For patient safety, we impose the following dose elimination rule when implementing the BOIN design If pr(p j > φ m j, n j ) > 0.95 and n j 3, dose levels j and higher are eliminated from the trial, and the trial is terminated if the first dose level is eliminated, where pr(p j > φ m j, n j ) can be evaluated based on a beta-binomial model.

38 BOIN drug-combination design The BOIN design has been extended to handle drug-combination trials to find a single MTD (Lin and Yin, 2016) or the MTD contour (Zhang and Yuan, 2016). The BOIN drug-combination designs make the decision of dose escalation/de-escalation based on the same rule as the single-agent BOIN design described previously, thus are easy to implement and possess desirable statistical properties (Yuan and Zhang, 2017).

39 Simulation 6 doses, sample size = 36, target φ = 0.2 or 0.3. Considered 1000 does-toxicity scenarios randomly generated using the pseudo-uniform algorithm (Clertant and O Quigley, 2017) Simulated 2000 trials under each of the 1000 scenarios Compared the BOIN to CRM. It is known that the CRM has good performance close to the theoretical optimal bound

40 Dose-toxicity scenarios (a) (b) Toxicity probability Toxicity probability Dose Level Dose Level Figure: Panel (a) shows 50 randomly selected dose-toxicity curves, and panel (b) shows the distribution of the toxicity probabilities by dose level from the 1000 scenarios with 6 dose levels.

41 Percentage of correct selection (PCS) Difference between BOIN and CRM BOIN CRM in Percentage of correct selection BOIN CRM in PCS within 5% Percentage of correct selection (%) PCS within 5% (%) φ=0.20 φ=0.30 φ=0.20 φ=0.30 (a) Percentage of correct selection of the target (b) Percentage of correct selection within 5% of the target

42 Patient allocation Difference between BOIN and CRM BOIN CRM in Percentage of patients treated at MTD BOIN CRM in Percentage of patients treated at doses within 5% of target Percentage of patients treated at MTD (%) Percentage of patients treated at doses within 5% of target φ=0.20 φ=0.30 φ=0.20 φ=0.30 (c) Number of patients allocated to the target dose (d) Number of patients allocated to to the doses within 5% of the target

43 Overdose control Difference between BOIN and CRM (e) Number of patients allocated to the doses above the MTD φ=0.20 φ= BOIN CRM in Risk of overdosing 80% Risk of overdosing 80% (%) (f) The probability of allocating >80% patients to the doses above the MTD

44 Software Windows desktop program freely available at MD Anderson Biostatistics software download website softwaredownload/singlesoftware.aspx? Software_Id=99 Web applications at R package "BOIN" available at CRAN

45 Software for novel trial designs

46 Introduction Method Simulation Summary Software for novel trial designs

47 BOIN Desktop Program

48 BOIN Desktop Program

49 BOIN Desktop Program

50 BOIN Desktop Program

51 BOIN Desktop Program

52 BOIN Desktop Program

53 BOIN Desktop Program

54 BOIN Desktop Program

55 BOIN Desktop Program: Combination Trials

56 BOIN Desktop Program

57 BOIN Desktop Program

58 BOIN Desktop Program

59 BOIN Desktop Program

60 BOIN Desktop Program

61 BOIN Desktop Program

62 BOIN Desktop Program

63 BOIN Desktop Program

64 BOIN Desktop Program

65 Introduction Method Simulation Summary Web App An integrated platform for designing clinical trials

66 Web App An integrated platform for designing clinical trials

67 Summary BOIN provides a novel platform to design phase I single-agent and drug combination clinical trials. BOIN is extremely simple to implement and yields good performance comparable to more complicated model-based designs. Windows desktop program, Web App and R package are freely available to implement the design.

68 Reference Liu S. and Yuan Y. (2015) Bayesian Optimal Interval Designs for Phase I Clinical Trials, Journal of the Royal Statistical Society: Series C, 64, Yuan Y., Hess, K., Hilsenbeck S.G. and Gilbert M.R. (2016) Bayesian Optimal Interval Design: A Simple and Well-performing Design for Phase I Oncology Trials, Clinical Cancer Research, 22, Lin R. and Yin G. (2016) Bayesian Optimal Interval Designs for Dose Finding in Drug-combination Trials, Statistical Methods in Medical Research, in press Zhang, L. and Yuan, Y. (2016) A Practical Bayesian Design to Identify the Maximum Tolerated Dose Contour for Drug Combination Trials. Statistics in Medicine, 35, Yuan, Y. and Zhang, L. (2017) Designing Early-Phase Drug Combination Trials. Handbook of Methods for Designing, Monitoring, and Analyzing Dose Finding Trials, edited by O Quigley J., Iasonos, A and Bornkamp, B., Chapter 6, p109-p126.

69 Thank you!