Phase I dose-escalation trials with more than one dosing regimen

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1 Phase I dose-escalation trials with more than one dosing regimen Burak Kürşad Günhan 1 Sebastian Weber 2 Abdelkader Seroutou 2 Tim Friede 1 IBS-DR, Göttingen, 7 December, Department of Medical Statistics, University Medical Center Göttingen 2 Novartis Pharma, Basel

2 Introduction

3 Background In drug development, earliest trials on humans = phase I dose-escalation trials Relationship between dose and toxicity Aim: Maximum tolerable dose (MTD) Small cohorts of patients, and treated in cycles Observed toxicities: dose limiting toxicities (DLTs) and non-dlts Based on DLTs data in first cycle 1/27

4 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs 2/27

5 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs No 2/27

6 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs No No 2/27

7 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs No No No 2/27

8 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs No No No No 2/27

9 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs No No No No Yes! 2/27

10 Background (cont.) Cohort Dose Number Number MTD (mg) of pats of DLTs No No No No Yes! Standard Methods Main approaches: algorithm-based (3+3) and model-based Model-based approaches display better performance. 2/27

11 Bayesian Logistic Regression Model (BLRM) (Neuenschwander et al., 28) For dose d Number of DLTs: r d Bin(π d, n d ) DLT probabilities: logit(π d ) = log(α 1 ) + α 2 log(d/d ) where d is the reference dose. Interpretation of α 1 is odds of a DLT probability at d. 3/27

12 Bayesian Logistic Regression Model (cont...) Metric for dose recommendation = Posterior distribution of π d is used. Three categories for π d π d <.16 Underdosing (UD).16 π d <.33 Targeted toxicity (TT) π d.33 Overdosing (OD) 4/27

13 Bayesian Logistic Regression Model (cont...) Metric for dose recommendation = Posterior distribution of π d is used. Three categories for π d π d <.16 Underdosing (UD).16 π d <.33 Targeted toxicity (TT) π d.33 Overdosing (OD) Escalation with overdose control (EWOC) principle = P(π d.33) should not exceed.25. 4/27

14 Visualization of EWOC principle d = 8 mg Probability density DLT probability (π d ) 5/27

15 Visualization of EWOC principle d = 8 mg Probability density DLT probability (π d ) 6/27

16 Visualization of EWOC principle d = 8 mg Probability density UD TT OD DLT probability (π d ) 7/27

17 Visualization of EWOC principle d = 8 mg Probability density UD TT OD DLT probability (π d ) 8/27

18 Visualization of EWOC principle d = 8 mg Probability density UD TT OD.35 > DLT probability (π d ) 9/27

19 Visualization of EWOC principle d = 8 mg Probability density UD TT OD.35 >.25 Too toxic! DLT probability (π d ) 1/27

20 More than one dosing regimen Weekly and daily regimens BLRM does NOT allow! 11/27

21 More than one dosing regimen Weekly and daily regimens BLRM does NOT allow! Ad-hoc approach: BLRM MAP BLRM is used for the first regimen. Meta-analytic-predictive (MAP) prior is derived from analysis based on first regimen. Then, MAP prior is used to analyse the second regimen. 11/27

22 TITE-PK

23 Time-to-event pharmacokinetic model (TITE-PK) Time-to-first-DLTs model using an exposure measure Exposure measure based on drug pharmacokinetics Use of planned dosing regimen and known PK parameters 5 mg/daily 2 mg/weekly E(t) E(t) time (weeks) time (weeks) 12/27

24 Time-to-event pharmacokinetic model (TITE-PK) (cont.) A time-varying Poisson process Hazard is given by h(t) =β E(t) = H(t) =β AUC E (t). Follow-up time until the end of cycle 1 (t ) Dosing regimen (amount d and frequency f ) End-of-cycle 1 DLT probability P(T t d, f ) = 1 S(t d, f ) S(t d, f ) = exp( H(t d, f )) 13/27

25 Time-to-event pharmacokinetic model (TITE-PK) (cont.) E(t) is scaled using reference regimen (d and f ) at t : AUC E (t d, f ) = 1. Analogous to reference dose in the BLRM Crucial for prior specification 14/27

26 Time-to-event pharmacokinetic model (TITE-PK) (cont.) E(t) is scaled using reference regimen (d and f ) at t : AUC E (t d, f ) = 1. Analogous to reference dose in the BLRM Crucial for prior specification TITE-PK is implemented in Stan. 14/27

27 Simulations

28 Settings Comparison of the performance: TITE-PK vs BLRM Data generation under each model separately Using exactly same decision criteria r d 6 where d is declared as the MTD, etc. 15/27

29 Settings Comparison of the performance: TITE-PK vs BLRM Data generation under each model separately Using exactly same decision criteria r d 6 where d is declared as the MTD, etc. Consider two different set of scenarios Only daily regimen 1, 2, 4, 8, 15, 3 mg/daily Firstly weekly regimen, then daily regimen 8, 16, 32, 64, 115, 23 mg/weekly Choice of prior: Matching a priori DLT probabilities 15/27

30 Dose-toxicity scenarios 1. Daily regimen DLT probabilities Dose (mg/daily) 16/27

31 Dose-toxicity scenarios DLT probabilities Scenario 1) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic Daily regimen Dose (mg/daily) 17/27

32 Performance measures I. Average proportion of patients in UD (< 16%) 18/27

33 Performance measures I. Average proportion of patients in UD (< 16%) II. Average proportion of patients in TT (16% 33%) III. Average proportion of patients in OD ( 33%) 18/27

34 Performance measures I. Average proportion of patients in UD (< 16%) II. Average proportion of patients in TT (16% 33%) III. Average proportion of patients in OD ( 33%) IV. Proportion of trials with MTD in UD (< 16%) V. Proportion of trials with MTD in TT (16% 33%) VI. Proportion of trials with MTD in OD ( 33%) 18/27

35 Performance measures I. Average proportion of patients in UD (< 16%) II. Average proportion of patients in TT (16% 33%) III. Average proportion of patients in OD ( 33%) IV. Proportion of trials with MTD in UD (< 16%) V. Proportion of trials with MTD in TT (16% 33%) VI. Proportion of trials with MTD in OD ( 33%) Stopped (eg. too toxic) Average N Average DLT 18/27

36 Results Measure III: Average proportion of patients in OD ( 33%) 3 III value 2 1 1) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic scenario 5) 75% more toxic 6) Very toxic 19/27

37 Results: TITE-PK vs BLRM Measure III: Average proportion of patients in OD ( 33%) III 3 Method BLRM TITE PK value 2 1 1) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic scenario 5) 75% more toxic 6) Very toxic 2/27

38 I II III IV V VI ) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic Stopped AveDLT AveN 4 3 BLRM TITE PK 1 1 1) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic I. Prop of patients in UD II. Prop of patients in TT III. Prop of patients in OD IV. Trials with MTD in UD V. Trials with MTD in TT VI. Trials with MTD in OD ) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic 21/27

39 BLRM 4 2 I II III IV V VI ) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic Stopped AveDLT AveN TITE PK 2 TITE PK 1 1 (a=.2) 1) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic I. Prop of patients in UD II. Prop of patients in TT III. Prop of patients in OD IV. Trials with MTD in UD V. Trials with MTD in TT VI. Trials with MTD in OD ) 75% less toxic 2) 25% less toxic 3) Prior medians 4) 25% more toxic 5) 75% more toxic 6) Very toxic 22/27

40 Weekly + Daily regimen: TITE-PK Sc.1 and Sc.1 Sc.2 and Sc.2 I II III IV V VI 15 Sc.3 and Sc.3 Sc.4 and Sc.4 Sc.5 and Sc.5 Sc.6 and Sc Sc.1 and Sc.1 Sc.2 and Sc.2 Sc.3 and Sc.3 Sc.4 and Sc.4 Sc.5 and Sc.5 Sc.6 and Sc Daily Sc.1 and Sc.1 Sc.2 and Sc.2 Weekly + Daily I. Prop of patients in UD II. Prop of patients in TT III. Prop of patients in OD IV. Trials with MTD in UD V. Trials with MTD in TT VI. Trials with MTD in OD Sc.3 and Sc.3 Sc.4 and Sc.4 Sc.5 and Sc.5 Sc.6 and Sc.6 23/27

41 Weekly + Daily regimen: TITE-PK vs BLRM MAP Sc.1 and Sc.1 Sc.2 and Sc.2 I II III IV V VI Sc.3 and Sc.3 Sc.4 and Sc.4 Sc.5 and Sc.5 Sc.6 and Sc Sc.1 and Sc.1 Sc.2 and Sc.2 Sc.3 and Sc.3 Sc.4 and Sc.4 Sc.5 and Sc.5 Sc.6 and Sc Sc.1 and Sc.1 Sc.2 and Sc.2 BLRM MAP TITE PK I. Prop of patients in UD II. Prop of patients in TT III. Prop of patients in OD IV. Trials with MTD in UD V. Trials with MTD in TT VI. Trials with MTD in OD Sc.3 and Sc.3 Sc.4 and Sc.4 Sc.5 and Sc.5 Sc.6 and Sc.6 24/27

42 Discussions

43 Discussions TITE-PK displays desirable performance in simulations Preserves advantages of BLRM (e.g. interpretable parameters, EWOC principle) Allows trials with dose regimen changes using PK principles Takes into account timing of DLTs 25/27

44 Discussions TITE-PK displays desirable performance in simulations Preserves advantages of BLRM (e.g. interpretable parameters, EWOC principle) Allows trials with dose regimen changes using PK principles Takes into account timing of DLTs A Bayesian adaptive model to support the design and analysis of phase I dose-escalation trials 25/27

45 Possible extensions Multiple compounds Usage of MAP prior Long-term safety events 26/27

46 Possible extensions Multiple compounds Usage of MAP prior Long-term safety events A motivating example is discussed in our preprint (arxiv: ) Code: 26/27

47 References Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., and Riddell, A. (217). Stan: A probabilistic programming language. Journal of Statistical Software, Articles, 76(1):1 32. Cox, E., Veyrat-Follet, C., Beal, S., Fuseau, E., Kenkare, S., and Sheiner, L. (1999). A population pharmacokinetic pharmacodynamic analysis of repeated measures time-to-event pharmacodynamic responses: The antiemetic effect of ondansetron. Journal of Pharmacokinetics and Biopharmaceutics, 27(6): Günhan, B., Weber, S., Seroutou, A., and Friede, T. (218). Phase I dose-escalation trials with more than one dosing regimen. ArXiv e-prints: Neuenschwander, B., Branson, M., and Gsponer, T. (28). Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27(13): Schmidli, H., Gsteiger, S., Roychoudhury, S., O Hagan, A., Spiegelhalter, D., and Neuenschwander, B. (214). Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics, 7(4): /27

48 Application: Everolimus

49 Dose-escalation decision criteria Cohort sizes randomly from (3, 4, 5, 6) Next dose / Current dose 2 Minimum number of patients at MTD: 6 Maximum number of patients: 6 Minimum number of patients: 21 MTD declaration: P(OD).25 and P(TT ).5

50 Weekly + Daily regimen: Scenario Weekly regimen Daily regimen 1. Scenario 1) 75% less toxic.75 2) 25% less toxic 3) Prior medians.75 4) 25% more toxic 5) 75% more toxic 6) Very toxic DLT probabilities DLT probabilities Dose (mg/weekly) Dose (mg/daily)

51 AUC 5 mg/daily 2 mg/weekly AUC(t).5 AUC(t) time (weeks) time (weeks)

52 Priors BLRM: BVN prior with following parameters: (m 1 = logit(π d =.175), m 2 =, s 1 = 2, s 2 = 1, ρ = ) TITE-PK: log(β) N (cloglog(p(t t d, f ) =.175), ).

Using mixture priors for robust inference: application in Bayesian dose escalation trials

Using mixture priors for robust inference: application in Bayesian dose escalation trials Astrid Jullion, Beat Neuenschwander, Daniel Lorand BAYES2014, London, 11 June 2014 Agenda Dose escalation in oncology