Practical Application of the Continual Reassessment Method to a Phase I DoseFinding Trial in Japan:

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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
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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.

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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,

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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 (33 cohort design)
• - The previous studies for other combinations
  such as FEC, CAF, etc,
• we applied CRM!!

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Dose levels in the CEX studies
Recommended dose level
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CRM 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
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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 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.

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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.

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Step 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.
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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?,

a8
a5
a5
a2
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In the first cohort (patient),
C 600 E 75 X 1657
Level 1 (1 pt) DLT1? HFS(G3)
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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
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Results Dose escalation history and toxicity
response
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Posterior mean dose-toxicity curve and its 90 CI
after treating 16 patients
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Posterior density functions of Pr(DLT x, Data)
estimated at each of the five dose levels
Selected as RD
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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 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?.

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Fundamental question in Bayesian analysis

• The amount of information contained in the prior?

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

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Work together as a team
Paper?
You all right?
Peter (Müller)
You all right?
Peter (Thall)
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The answer seems straightforward

• For many commonly used models,
• e.g., beta distribution

Be (3,8)
Be (16,19)
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For many parametric Bayesian models, however

• How to determine the ESS of the prior is NOT
  obvious.
• E.g., usual normal linear regression model

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General 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

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Definition of e-information prior

• has the same mean and correlations as
  , while inflating the variances

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The 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


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Distance between p and qm

• Difference of the traces of the two information
  matrices, evaluated at the prior mean

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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

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

• Step 1
• Step 2

Use simulation to obtain
Assume a uniform distribution for Xi
ESS 2.1
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• 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.

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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
  criteriain order to obtain a sensible prior.
• ? One of the on-going projects!!

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Thank you for your kind attention!!
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• Back-up

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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

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Step 2 Intercept m 3
m 3
m -3
refrecting oncologists greater confidencein
higher than lower dose levels.
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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)

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Prior dose-toxicity curve and its 90 credible
interval
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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
  Prp(x,q)gt0.99 Prp(x,q)lt0.01,
• 3) the sensitivity to dose selection decision,
• in order to obtain a sensible prior.

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ESS 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

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ESS 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

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Prior ESS of a beta distribution- Beta-binomial
case -