statistical methods for phase i/ii trials of molecularly ... · introduction methods conclusions...

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

Maria-Athina Altzerinakou Think Tank 2 / 18

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


IntroductionMethods


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.


IntroductionMethods


Current challenges I

Association of activity and dose in molecularly targeted agents


IntroductionMethods


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.


IntroductionMethods


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


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.


IntroductionMethods

Conclusions


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


IntroductionMethods

Conclusions


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


IntroductionMethods

Conclusions


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)


IntroductionMethods

Conclusions


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


IntroductionMethods

Conclusions


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


IntroductionMethods

Conclusions


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


IntroductionMethods

Conclusions

Conclusions

v Small bias

v Satisfying coverage

v Suggested after 30 subjects


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.


IntroductionMethods

Conclusions

Further...

ä Define an optimal dose

ä Propose an adaptive design for early phase I trials based on joint modelling


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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