Satoshi Morita Dept. of Biostatistics and Epidemiology, Yokohama City University Medical Center

1. Practical Application of the Continual Reassessment Method to a Phase I Dose-Finding Trial in Japan: East meets West Satoshi Morita Dept. of Biostatistics and Epidemiology, Yokohama City University Medical Center

2. Why a phase I dose-finding study of CEX in Japan?Cyclophosphamide, Epirubicin, Xeloda Capecitabine (Xeloda) was/is a novel oral fluoropyrimidine derivative with high single-agent anti-tumor activity in metastatic breast cancer (BC). A research team from the EORTC conducted a phase I dose-finding study to determine the recommended dose of CEX. (Bonnefoi, et al., 2003) Japanese patients/doctors would need CEX as a treatment option.

3. Recommended dose(s) > Caucasians Japanese Why CEX trial in Japanese patients? A concern was raised over possible differences in the tolerability of CEX between Caucasians and Japanese. In many cases, Ex. FEC (5-FU, Epi, CPA) EORTC Bonnefoi et al., 2001 Japan Iwata et al. 2005

4. The Japanese CEX phase I trialMorita et al.(2007) & Iwata et al.(2007) To answer this question, we conducted a phase I dose-finding study of CEX in Japanese patients (J-CEX) from Dec., 2003 to Feb., 2006. Based on the prior information: - The EORTC CEX study (3+3 cohort design) - The previous studies for other combinations such as FEC, CAF, etc, we applied CRM!!

5. EORTC (4 levels) Japanese (5 levels) EPI (mg/m2) 100 2500 2100 1800 1500 EPI (mg/m2) 100 90 90 75 75 Cape (mg/m2/day) 1800 1800 1657 1657 1255 Dose Level 4 3 2 1 0 CPA (mg/m2) 600 Cape (mg/m2/day) CPA (mg/m2) 600 DLT 2/2 9/15 1/3 1/3 : starting dose level Dose levels in the CEX studies : Recommended dose level

6. CRM in J-CEX One-parameter logistic model Pr(DLT|dose j) = exp(m +bxj) p(xj, b) = 1 + exp(m +bxj) for j=0,…,4, with fixed m=3, b> 0, A target Pr(DLT) = 0.33 DLT = Grade 3,4 hematologic / non-hematologic toxicity or grade 3 hand-foot syndrome

7. Implementation of CRM in J-CEX A dose-escalation/de-escalation rule: Each cohort is treated at the dose level with an estimated Pr(DLT | x, Data) closest to 0.33 and NOT exceeding 0.40. Pick x to minimize |E[p(x,b)|Data] – 0.33| Untried dose is not skipped when escalating. A trial stopping rule: The trial is to be stopped if level 0 is considered too toxic: Pr(DLT | dose 0, Data) > 0.40. Nmax = 22 treated in cohorts of 3 Start with the 1st cohort of 1 patient at dose level 1.

8. Setting up a CRM in J-CEX Step 1. Obtain pre-study point estimation of Pr(DLT) at each dose level from clinical oncologists, 2. Pre-determine the intercept m, 3. Specify a prior distribution function of the slope b, 4. Specify a numerical value of xj, j= 0,…,4, 5. Specify the hyperparameters of the prior of b, p(b) in terms of how informative p(b) is.

9. Step 3: Prior of the slope, b For computational convenience and to constrain the slope b to be positive, b>0, One more restrictiona=b Þ E(b)=1, Var(b)=1/a b ～ Ga(a,b) with E(b)=a/b and Var(b)=a/b2 Fixing the prior mean dose-toxicity curve regardless of magnitude of prior confidence.

10. We set a = 5. Step 5: Specify the hyperparameter, a The hyperparameter a determines the credible interval of the dose-toxicity curve. Making several patterns of graphical presentations, and asking the oncologists, “which depicts most appropriately your pre-study perceptions on dose-toxicity relationship?”, a=8 a=5 a=5 a=2

11. In the first cohort (patient),… C: 600 E: 75 X: 1657 Level 1 (1pt) DLT1例 HFS(G3)

12. The dose-toxicity curve after updating the prior curve with toxicity data from the 1st pt Dose level for the 2nd cohort 0 1 2 3 4

13. C: 600 E: 75 X: 1255 C: 600 E: 75 X: 1657 C: 600 E: 75 X: 1657 C: 600 E: 90 X: 1657 C: 600 E: 90 X: 1800 Level 3 (6pts) 2 DLTs Anorexia(G3) Mucositis(G3) Level 2 (3 pts) No DLT Level 1 (1pt) 1 DLT HFS (G3) Level 1 (3pts) No DLT Level 0 (3 pts) No DLT Results: Dose escalation history and toxicity response

14. 0 1 2 3 4 Posterior mean dose-toxicity curve and its 90% CI after treating 16 patients

15. Posterior density functions of Pr(DLT | x, Data)estimated at each of the five dose levels Selected as RD db dp f [p(xj, b)|data] = p(b|data)

16. Concern & Question I had We made many “arbitrary choices” when designing the study, especially eliciting the prior from the oncologists. Based on the EORTC study, using graphical presentations,……, BUT, still arbitrary!! My concern was…‘didn’t Ga(5,5) dominate the posterior inferences after enrolling the first two / three cohorts?’ My question was…‘how could we determine the strength of the prior relative to the likelihood?’.

17. Prior p(θ) ((( ((( ((( ((( Fundamental question in Bayesian analysis The amount of information contained in the prior?

18. Trans-Pacific Research Project!!December 2005 ~ Time difference 15 hours Japan MDACC, Houston

19. Prior effective sample size These concerns may be addressed by quantifying the prior information in terms of an equivalent number of hypothetical patients, i.e., a prior effective sample size (ESS). A useful property of prior ESS is that it is readily interpretable by any scientifically literate reviewer without requiring expert mathematical training. This is important, for example, for consumers of clinical trial results.

20. Work together as a team Paper? You all right? Peter (Müller) You all right? Peter (Thall)

21. Effective sample size 1.5 + 2.5 = 4 3 + 8 = 11 16 + 19 = 35 Be (1.5,2.5) The answer seems straightforward For many commonly used models, e.g., beta distribution Be (3,8) Be (16,19)

22. For many parametric Bayesian models, however… How to determine the ESS of the prior is NOT obvious. E.g., usual normal linear regression model

23. General approach to determine the ESS of prior p(q ) Morita, Thall, Müller (2008) Biometrics 1) Construct an “ε-information” prior q0(θ) 2) For each possible ESS m = 1, 2, ...,consider a sample Ymof sizem 3) Compute posterior qm(θ|Ym) starting withprior q0(θ) 4) Compute distance between qm(θ|Ym) and p(θ) 5) The value of m minimizing the distance is the ESS

24. Definition of ε-information prior has the same mean and correlations as , while inflating the variances

25. The basic idea is To find the sample size m, that would be implied by normal approximation of the prior p(θ) and the posterior qm(θ|Ym). This led us to use the second derivative of the log densities to define the distance. M m m=1 … ……

26. Distance between p and qm Difference of the traces ofthe two information matrices, evaluated at theprior mean:

27. DEFINITION of ESS The effective sample size (ESS) of with respect to the likelihood is the (interpolated) integer m that minimizes the distance between p and qm

28. Step 1. Specify Algorithm Step 2. Compute for each analytically or using simulation-based numerical approximation Step 3. ESS is the interpolated value of m minimizing

29. J-CEX Step 1: Step 2: Use simulation to obtain Assume a uniform distribution for Xi ESS = 2.1

30. A computer program, ESS_RegressionCalculator.R, to calculate the ESS for a normal linear or logistic regression model is available from the website http://biostatistics.mdanderson.org /SoftwareDownload.

31. In the context of dose-finding studies, Prior assumptions (arbitrary choices) include - one- / two-parameter model, - priors of the intercept and slope parameters, - numerical values for dose levels, etc. It may be interesting to discuss the impact of prior assumptions in terms of prior ESS and other criteria…in order to obtain a “sensible prior”. → One of the on-going projects!!

32. Thank you for your kind attention!!

33. Back-up

34. Step 1: Pre-study point estimation of Pr(DLT | dose j) Dose level 0 1 2 3 4 Elicited Pr(DLT) .05 .10 .25 .40 .60

35. Step 2: Intercept m = 3 m = -3 m = 3 refrecting oncologists’ greater confidencein higher than lower dose levels.

36. exp(3 +xj) p(xj, b=1) = 1 + exp(3 +xj) Step 4: Dose levels, x Based on the elicited Pr(DLT | dose j), specify the numerical values xj, j= 0,…,4. “Backward fitting” (Garrett-Mayer,2006,Clinical Trials)

37. Prior dose-toxicity curve and its 90% credible interval 0 1 2 3 4

38. In the context of dose-finding studies, Prior assumptions (arbitrary choices) include - one- / two-parameter model, - priors of the intercept and slope parameters, - numerical values for dose levels, etc. It may be interesting to discuss the impact of prior assumptions in terms of 1) prior ESS, 2) prior predictive probabilities: Pr[p(x,q)>0.99] & Pr[p(x,q)<0.01], 3) the sensitivity to dose selection decision, in order to obtain a “sensible prior”.

39. ESS of a beta distribution Saying Be(a, b) has ESS = a+ b implicitly refers to the fact that θ ~Be(a, b) and Y | θ ~ bin(n, θ) implies θ | Y〜Be(a+Y, b+n-Y) which has ESS = a+b+n

40. ESS of a beta distribution (cont’d) SayingBe(a,b) has ESS = a +b implictly refers to an earlier Be(c,d) prior with very small c+d=ε and solving for m = a+b –(c+d) =a+b – ε for a very small value ε> 0

41. p(θ) q0(θ) qm(θ|Ym) Be(a,b) Be(c,d) Be(c+Y,d+m-Y) where c+d= e is very small Solving for m = a+b – (c+d) = a+b – e Be(a,b)has a prior ESS = a + b Prior ESS of a beta distribution- Beta-binomial case -