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Statistical methods for phase I/II trials of molecularlytargeted agents in oncology
Maria-Athina Altzerinakou1
Xavier Paoletti2
1. CESP OncoStat, INSERM, Université Paris-Saclay, Université Paris-Sud, UVSQ, Institut Gustave Roussy,Villejuif, France
2. Institut Gustave Roussy, CESP OncoStat, Université Paris-Sud, UVSQ, INSERM, Université Paris-Saclay,Villejuif, France
23 June, 2016
IntroductionMethods
Conclusions
Contents
1 IntroductionMolecularly Targeted AgentsChallenges
2 MethodsJoint ModellingSimulationsResults
3 Conclusions
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Brief reminder
Phase I trials in oncology
Assessment of safety of the new treatment, i.e. toxicity
Determination of a range of sufficiently safe doses and the maximumtolerated dose
Pharmocokinetics and pharmacodynamics in patients
Phase II trials in oncology
More information gathered around the activity of the treatment
Additional information on pharmocokinetics and pharmacodynamics
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Molecularly targeted therapies
Targeted cancer therapies are drugs or other substances that block the growthand spread of cancer by interfering with specific molecules, that are involved inthe growth, progression, and spread of cancer1
Targeted therapies act onspecific molecular targets
Targeted therapies aredeliberately designed tointeract with their target
Targeted therapies are oftencytostatic
1. National Cancer Institute. Targeted Cancer Therapies.
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Current challenges I
Association of activity and dose in molecularly targeted agents
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Current challenges I
Association of activity and dose in molecularly targeted agents
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Current challenges I
Association of activity and dose in molecularly targeted agents
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Current challenges II
Evaluation of the MTD, using data collected during the first treatment cycle.
1 Ignore late onset toxicities
2 Ignore cumulative toxicities after extensive exposure to a specific dose level
3 Ignore information on activity measurements2
2. Postel-Vinay, S. et al. (2011). Phase I Trials of Molecularly Targeted Agents: Should We Pay MoreAttention to Late Toxicities? J Clin Oncol, 29(13): 1728-1735.
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IntroductionMethods
ConclusionsMolecularly Targeted AgentsChallenges
Objective
ä Propose an adaptive design for phase I/II trials
ä Define an optimal dose
v A dose that maximizes the activity while providing acceptable level oftoxicity
ä Combine data of time to first severe toxicity and biomarker activity
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Solution
ä Joint modelling3 of
interval censored time to first severe toxicity data4
repeated activity measurements on a continuous scale
v Shared random effects
3. Rizopoulos, D. (2012). Joint models for longitudinal and time-to-event data, with applications in R.CRC Press.4. Sinclair, K. et al. (2014). A Bayesian approach to dose-finding studies for cancer therapies:incorporating later cycles of therapy. Stat Med, 33(15): 2665-2680.
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Joint Model
Repeated measurements
Yj = xTj β + aT
j U + Zj, j = 1, 2, ..., l
where Y measured on continuous scale, U ∼ N(0,Σ) random effects andZ ∼ MVN(0, v2I) mutually independent measurement errors
Event times
P(S = s|S > s − 1,U) = 1 − Φ
{x̃T
s β̃ +
p∑k=1
γskWk(s)
}, s = 1, 2, ...,m
where Φ standard normal distribution and W (s) vector of linear combinationsof random effects U
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Model evaluation
ä Assessment of joint modelling parameter estimations on small sample sizes
ä Time to event: Time to first severe toxicity
v Evaluation after each treatment cycle
v Discrete time scale
v Allowing for censoring
ä Repeated measurements: Activity of biomarker Ý e.g. tumor size per visit
v Measurements provided on a continuous scale
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Scenario
9 dose levels Ý target dose 5th Ý 31.6% after 3 cycles
3 treatment cycles
max 10 visits per patient
5 different sample sizes (n1 = 15, n2 = 20, n3 = 30, n4 = 60, n5 = 100)
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Models
t é timed é dose
j é patients’ visitss é treatment cycles
Linear mixed effects model
Yj = β0 + β1t + β2d + a1t + Zj, j = 1, 2, ..., l
Probit model
P(S = s|S > s − 1,U) = 1 − Φ {δ0 + δ1t + δ2d + γ1W (s)} , s = 1, 2, ...,m
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Bias
Table 1: Bias of parameter estimations of time to event and longitudinal joint model, within5000 simulations per sample size
Sample Size
Parameters n=15 n=20 n=30 n=60 n=100
Longitudinal Intercept 1.76 × 10−4 −1.37 × 10−4 2.31 × 10−4 4.00 × 10−5 −1.05 × 10−4
Longitudinal Time 3.31 × 10−3 2.36 × 10−2 8.21 × 10−4 −2.14 × 10−3 −1.84 × 10−3
Longitudinal Dose 2.23 × 10−6 1.12 × 10−4 2.25 × 10−4 1.19 × 10−5 −1.03 × 10−4
Survival Intercept 4.56 × 10−1 4.03 × 10−1 2.42 × 10−1 9.31 × 10−2 5.42 × 10−2
Survival Time −7.77 × 10−1 −4.50 × 10−1 −1.67 × 10−1 4.51 × 10−3 5.74 × 10−3
Survival Dose 4.51 × 10−1 4.12 × 10−1 2.53 × 10−1 1.02 × 10−1 5.60 × 10−2
Longitudinal Residual Variance −3.58 × 10−2 −2.95 × 10−2 −1.52 × 10−2 −7.64 × 10−3 −5.20 × 10−3
Longitudinal Slope Variance −6.61 × 10−2 −7.23 × 10−2 −5.86 × 10−2 −4.08 × 10−2 −2.06 × 10−2
Survival Gamma 4.86 × 10−1 −8.60 × 10−2 2.45 × 10−1 1.34 × 10−1 8.99 × 10−2
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IntroductionMethods
Conclusions
Joint ModellingSimulationsResults
Coverage
Table 2: Coverage of parameter estimations of time to event and longitudinal joint model,within 5000 simulations per sample size
Sample Size
Parameters n=15 n=20 n=30 n=60 n=100
Longitudinal Intercept 0.93 0.93 0.94 0.95 0.94
Longitudinal Time 0.92 0.93 0.94 0.94 0.95
Longitudinal Dose 0.92 0.93 0.94 0.95 0.94
Survival Intercept 0.99 0.98 0.98 0.96 0.96
Survival Time 0.97 0.97 0.97 0.96 0.95
Survival Dose 0.98 0.99 0.97 0.96 0.96
Longitudinal Residual Variance 0.97 0.96 0.96 0.96 0.96
Longitudinal Slope Variance 0.98 0.99 0.99 0.99 0.98
Survival Gamma 0.99 0.99 0.99 0.98 0.96
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IntroductionMethods
Conclusions
Conclusions
v Small bias
v Satisfying coverage
v Suggested after 30 subjects
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IntroductionMethods
Conclusions
Why joint modelling ?
ä Incorporate information on activity Ý utilize all available information
ä Take into account missing at random
ä Exact likelihood inference5
v Avoid numerical integration of approximate likelihood Ý biasedestimations due to small sample size
v Better parameter estimations
v More rapid estimations
5. Barrett, J. et al. (2015). Joint modelling of repeated measurements and time-to-event outcomes:flexible model specification and exact likelihood inference. J R Stat Soc Series B Stat Methodol.,77(1): 131-148.
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IntroductionMethods
Conclusions
Further...
ä Define an optimal dose
ä Propose an adaptive design for early phase I trials based on joint modelling
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IntroductionMethods
Conclusions
Thank you !
This project has received funding from the European Union’s Horizon 2020 research and
innovation programme under the Marie Sklodowska-Curie grant agreement No 633567.
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