Maria-Athina Altzerinakou1, Xavier Paoletti2. 9 May, 2017

Transcription

1 An adaptive design for the identification of the optimal dose using joint modelling of efficacy and toxicity in phase I/II clinical trials of molecularly targeted agents 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 9 May, 2017

2 Contents 1 General framework Maria-Athina Altzerinakou Inserm 2 / 18

3 Current challenges I Maria-Athina Altzerinakou Inserm 3 / 18

4 Current challenges I Probability of efficacy Dose Association of efficacy and dose in cytotoxic and cytostatic agents, respectively. Maria-Athina Altzerinakou Inserm 3 / 18

5 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 efficacy measurements 1,2 1. Postel-Vinay, S. et al. (2011). Phase I Trials of Molecularly Targeted Agents: Should We Pay More Attention to Late Toxicities? J Clin Oncol, 29(13): Soria, J-C. (2011). Phase 1 trials of molecular targeted therapies: Are we evaluating toxicities properly? European Journal of Cancer, 47(10): Maria-Athina Altzerinakou Inserm 4 / 18

6 Objective Propose an adaptive design for phase I/II trials Define a maximum tolerated dose (MTD) and an optimal dose (OD) MTD: The maximal dose acceptably tolerated cumulatively over all treatment cycles OD: A dose that maximizes the efficacy, while satisfying certain toxicity requirements Combine data of time to first severe toxicity and biomarker efficacy over several treatment cycles Maria-Athina Altzerinakou Inserm 5 / 18

7 Population Evaluation of toxicity End of treatment cycle Evaluation of efficacy Fixed time within cycles Drop out: 1) Dose limiting toxicity 2) Lack of efficacy 3) Non-informative censoring Maria-Athina Altzerinakou Inserm 6 / 18

8 Joint modelling Joint modelling of interval censored time to first severe toxicity data repeated efficacy measurements on a continuous scale shared random effects Why joint modelling??? Incorporate information on efficacy utilize all available information Take into account missing Maria-Athina Altzerinakou Inserm 7 / 18

9 Model selection t time of visit d dose c treatment cycle Linear mixed effects model - Efficacy Y j = β 0 + β 1 t 2 j + β 2 t j d + β 3 t j log d + ut j + Z j, j (0, 3m) and t j < m where Y measured on continuous scale, u N(0, σ 2 ) random effects and Z MVN(0, v 2 I) mutually independent measurement errors. Maria-Athina Altzerinakou Inserm 8 / 18

10 Model selection t time of visit d dose c treatment cycle Linear mixed effects model - Efficacy Y j = β 0 + β 1 t 2 j + β 2 t j d + β 3 t j log d + ut j + Z j, j (0, 3m) and t j < m where Y measured on continuous scale, u N(0, σ 2 ) random effects and Z MVN(0, v 2 I) mutually independent measurement errors. Probit model - Toxicity P(S = s S > s 1, U) = 1 Φ {δ 0 + δ 1 c + δ c d + γu}, s = 1, 2,..., m + 1 where Φ standard N, δ c is a constant and u is the shared random time slope. Key assumption: Given the random effect the two processes are independent Maria-Athina Altzerinakou Inserm 8 / 18

11 Why this joint modelling method? Exact likelihood inference (skew normal distribution properties) 3,4 avoid numerical integration of approximate likelihood Better parameter estimations Small bias, even with small sample sizes Satisfying coverage More rapid estimations Suggested after 25 subjects 3. 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): Arnold, B.C. (2009). Flexible univariate and multivariate models based on hidden truncation. J. Statist. Planng Inf., 139(11): Maria-Athina Altzerinakou Inserm 9 / 18

12 Design Steps Probit survival model Time to first severe toxicity Intervals - treatment cycles 2+2 Probit-CRM Joint Modelling Dose allocation Cohorts of 1 patient Estimation of model parameters Estimation of toxicity over several treatment cycles Dose allocation Maria-Athina Altzerinakou Inserm 10 / 18

13 Scenario Objective: Evaluate the correct selection of the MTD and OD, through different sets of scenarios and extensive simulations. 60 patients 6 dose levels 6 treatment cycles max 18 visits per patient (balanced data, 3 per cycle) drop outs based on DLTs, lack of efficacy or non-informative censoring target toxicity level 40% after 6 cycles max mean clinical difference between 2 doses 20 units Maria-Athina Altzerinakou Inserm 11 / 18

14 Simulation results Table 1: Selection percentage of each dose at the end of the trial, on 1080 simulations Scenario Dose 1 Dose 2 Dose 3 Dose 4 Dose 5 Dose 6 1 (Eff, Tox) (43, 0.03%) (52, 0.35%) (62, 2.40%) (71, 11.2%) (80, 34.3%) (89, 68.2%) n/ % (Eff, Tox) (24, 34.9%) (39, 67%) (55, 90.7%) (70, 98.7%) (85, 99.9%) (100, 99.9%) n/ % (Eff, Tox) (24, 0.03%) (39, 0.03%) (55, 2.40%) (70, 11.2%) (85, 34.3%) (100, 68.2%) n/ % (Eff, Tox) (39, 1.9%) (42, 7.30%) (45, 20.4%) (48, 42.5%) (52, 68.1%) (55, 87.8%) n/ % (Eff, Tox) (24, 0.01%) (56, 0.11%) (88, 0.71%) (120, 3.49%) (152, 12.6%) (183, 33.1%) n/ % (Eff, Tox) (24, 0.01%) (39, 0.11%) (55, 0.71%) (70, 3.49%) (85, 12.6%) (100, 33.1%) n/ % Maria-Athina Altzerinakou Inserm 12 / 18

15 Conclusions Identification of the OD > 98% correct dose selection when OD is on the tail of the dose range > 71% correct dose selection when OD is in the middle of the dose range 0% OD selection above the MTD Maria-Athina Altzerinakou Inserm 13 / 18

16 Discussion High percentage of correct OD selection Dose selection within a safe yet efficient range of doses Exclusion of patients due to lack of efficacy Model cannot identify accurately beginning of the plateau Maria-Athina Altzerinakou Inserm 14 / 18

17 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 Maria-Athina Altzerinakou Inserm 15 / 18

18 Efficacy in time Time Efficacy over time per dose Efficacy dose 1 dose 2 dose 3 dose 4 dose 5 dose Time Maria-Athina Altzerinakou Inserm 16 / 18

19 Bias Table 1: Bias 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 Longitudinal Time Longitudinal Dose Survival Intercept Survival Time Survival Dose Longitudinal Residual Variance Longitudinal Slope Variance Survival Gamma Maria-Athina Altzerinakou Inserm 17 / 18

20 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 Longitudinal Time Longitudinal Dose Survival Intercept Survival Time Survival Dose Longitudinal Residual Variance Longitudinal Slope Variance Survival Gamma Maria-Athina Altzerinakou Inserm 18 / 18