Title: Practical Application of the Continual Reassessment Method to a Phase I Dose-Finding Trial in Japan: East meets West
1Practical 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
2Why 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.
3Why CEX trial in Japanese patients?
- A concern was raised over possible differences in
the tolerability of CEX between Caucasians and
Japanese. - In many cases,
4The 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 (33 cohort design)
- - The previous studies for other combinations
such as FEC, CAF, etc, - we applied CRM!!
5Dose levels in the CEX studies
Recommended dose level
6CRM in J-CEX
- One-parameter logistic model
A target Pr(DLT) 0.33
DLT Grade 3,4 hematologic / non-hematologic
toxicity or grade 3 hand-foot syndrome
7Implementation 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 Ep(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) gt
0.40. - Nmax 22 treated in cohorts of 3
- Start with the 1st cohort of 1 patient at dose
level 1.
8Setting 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.
9Step 3 Prior of the slope, b
- For computational convenience and to constrain
the slope b to be positive, bgt0, - One more restriction ab 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.
10Step 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?,
a8
a5
a5
a2
11In the first cohort (patient),
C 600 E 75 X 1657
Level 1 (1 pt) DLT1? HFS(G3)
12The 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
13Results Dose escalation history and toxicity
response
14Posterior mean dose-toxicity curve and its 90 CI
after treating 16 patients
15Posterior density functions of Pr(DLT x, Data)
estimated at each of the five dose levels
Selected as RD
16Concern 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 wasdidnt Ga(5,5) dominate the
posterior inferences after enrolling the first
two / three cohorts? - My question washow could we determine the
strength of the prior relative to the
likelihood?.
17Fundamental question in Bayesian analysis
- The amount of information contained in the prior?
18Trans-Pacific Research Project!!December 2005
Time difference 15 hours
Japan
MDACC, Houston
19Prior 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.
20Work together as a team
Paper?
You all right?
Peter (Müller)
You all right?
Peter (Thall)
21The answer seems straightforward
- For many commonly used models,
- e.g., beta distribution
Be (3,8)
Be (16,19)
22For many parametric Bayesian models, however
- How to determine the ESS of the prior is NOT
obvious. - E.g., usual normal linear regression model
23General approach to determine the ESS of prior
p(q ) Morita, Thall, Müller (2008) Biometrics
- 1) Construct an e-information prior q0(?)
- 2) For each possible ESS m 1, 2, ..., consider
a sample Ym of size m - 3) Compute posterior qm(?Ym) starting with
prior q0(?) - 4) Compute distance between qm(?Ym) and p(?)
- 5) The value of m minimizing the distance is the
ESS
24Definition of e-information prior
- has the same mean and correlations as
, while inflating the variances
25The basic idea is
- To find the sample size m, that would be implied
by normal approximation of the prior p(?) and the
posterior qm(?Ym). - This led us to use the second derivative of the
log densities to define the distance.
M m m1
26Distance between p and qm
- Difference of the traces of the two information
matrices, evaluated at the prior mean
27DEFINITION 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
28Algorithm
Step 2. Compute for each
analytically or using simulation-based numerical
approximation
Step 3. ESS is the interpolated value of m
minimizing
29J-CEX
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.
31In 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
criteriain order to obtain a sensible prior. - ? One of the on-going projects!!
32Thank you for your kind attention!!
33 34Step 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
35Step 2 Intercept m 3
m 3
m -3
refrecting oncologists greater confidencein
higher than lower dose levels.
36Step 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)
37Prior dose-toxicity curve and its 90 credible
interval
38In 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
Prp(x,q)gt0.99 Prp(x,q)lt0.01, - 3) the sensitivity to dose selection decision,
- in order to obtain a sensible prior.
39ESS of a beta distribution
- Saying Be(a, b) has ESS a b
- implicitly refers to the fact that
- ? Be(a, b) and Y ? bin(n, ?) implies
- ? Y ? Be(aY, bn-Y)
- which has ESS abn
40ESS of a beta distribution (contd)
- Saying Be(a,b) has ESS a b
- implictly refers to an earlier
- Be(c,d) prior with very small cd e
- and solving for
- m ab (cd) ab e
- for a very small value e gt 0
41Prior ESS of a beta distribution- Beta-binomial
case -