[PPT] - Phase I dose-escalation trials with more than one dosing regimen PowerPoint Presentation

SLIDE 1

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

Burak Kürşad Günhan1 Sebastian Weber2 Abdelkader Seroutou2 Tim Friede1 IBS-DR, Göttingen, 7 December, 2018

1Department of Medical Statistics, University Medical Center Göttingen 2Novartis Pharma, Basel

SLIDE 2

Introduction

SLIDE 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

SLIDE 4

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

2/27

SLIDE 5

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

1 1 3 No

2/27

SLIDE 6

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

1 1 3 No 2 2 5 No

2/27

SLIDE 7

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

1 1 3 No 2 2 5 No 3 4 4 No

2/27

SLIDE 8

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

1 1 3 No 2 2 5 No 3 4 4 No 4 8 5 1 No

2/27

SLIDE 9

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

1 1 3 No 2 2 5 No 3 4 4 No 4 8 5 1 No 5 8 6 1 Yes!

2/27

SLIDE 10

Background (cont.)

Cohort Dose Number Number MTD (mg)

f pats
f DLTs

1 1 3 No 2 2 5 No 3 4 4 No 4 8 5 1 No 5 8 6 1 Yes! Standard Methods

Main approaches: algorithm-based (3+3) and model-based
Model-based approaches display better performance.

2/27

SLIDE 11

Bayesian Logistic Regression Model (BLRM) (Neuenschwander et al., 2008)

For dose d
Number of DLTs:

rd ∼ Bin(πd, nd)

DLT probabilities:

logit(πd) = log(α1) + α2 log(d/d∗) where d∗ is the reference dose.

Interpretation of α1 is odds of a DLT probability at d∗.

3/27

SLIDE 12

Bayesian Logistic Regression Model (cont...)

Metric for dose recommendation

= ⇒ Posterior distribution of πd is used.

Three categories for πd
πd < 0.16 Underdosing (UD)
0.16 ≤ πd < 0.33 Targeted toxicity (TT)
πd ≥ 0.33 Overdosing (OD)

4/27

SLIDE 13

Bayesian Logistic Regression Model (cont...)

Metric for dose recommendation

= ⇒ Posterior distribution of πd is used.

Three categories for πd
πd < 0.16 Underdosing (UD)
0.16 ≤ πd < 0.33 Targeted toxicity (TT)
πd ≥ 0.33 Overdosing (OD)
Escalation with overdose control (EWOC) principle

= ⇒ P(πd ≥ 0.33) should not exceed 0.25.

4/27

SLIDE 14

Visualization of EWOC principle

0.00 0.25 0.50 0.75 1.00

DLT probability (πd) Probability density

d = 8 mg

5/27

SLIDE 15

Visualization of EWOC principle

0.00

0.16 0.25 0.33 0.50 0.75 1.00

DLT probability (πd) Probability density

d = 8 mg

6/27

SLIDE 16

Visualization of EWOC principle

OD TT UD

0.00

0.16 0.25 0.33 0.50 0.75 1.00

DLT probability (πd) Probability density

d = 8 mg

7/27

SLIDE 17

Visualization of EWOC principle

0.35 OD TT UD

0.00

0.16 0.25 0.33 0.50 0.75 1.00

DLT probability (πd) Probability density

d = 8 mg

8/27

SLIDE 18

Visualization of EWOC principle

0.35 > 0.25 OD TT UD

0.00

0.16 0.25 0.33 0.50 0.75 1.00

DLT probability (πd) Probability density

d = 8 mg

9/27

SLIDE 19

Visualization of EWOC principle

0.35 > 0.25 OD TT UD Too toxic!

0.00

0.16 0.25 0.33 0.50 0.75 1.00

DLT probability (πd) Probability density

d = 8 mg

10/27

SLIDE 20

More than one dosing regimen

Weekly and daily regimens
BLRM does NOT allow!

11/27

SLIDE 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

SLIDE 22

TITE-PK

SLIDE 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

0.000 0.002 0.004 0.006 1 2 3 4

time (weeks) E(t)

5 mg/daily

0.000 0.002 0.004 0.006 1 2 3 4

time (weeks) E(t)

20 mg/weekly

12/27

SLIDE 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 AUCE(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

SLIDE 25

Time-to-event pharmacokinetic model (TITE-PK) (cont.)

E(t) is scaled using reference regimen (d∗ and f ∗) at t∗:

AUCE(t∗|d∗, f ∗) = 1.

Analogous to reference dose in the BLRM
Crucial for prior specification

14/27

SLIDE 26

Time-to-event pharmacokinetic model (TITE-PK) (cont.)

E(t) is scaled using reference regimen (d∗ and f ∗) at t∗:

AUCE(t∗|d∗, f ∗) = 1.

Analogous to reference dose in the BLRM
Crucial for prior specification
TITE-PK is implemented in Stan.

14/27

SLIDE 27

Simulations

SLIDE 28

Settings

Comparison of the performance: TITE-PK vs BLRM
Data generation under each model separately
Using exactly same decision criteria

rd ≥ 6 where d is declared as the MTD, etc.

15/27

SLIDE 29

Settings

Comparison of the performance: TITE-PK vs BLRM
Data generation under each model separately
Using exactly same decision criteria

rd ≥ 6 where d is declared as the MTD, etc.

Consider two different set of scenarios
Only daily regimen

1, 2, 4, 8, 15, 30 mg/daily

Firstly weekly regimen, then daily regimen

8, 16, 32, 64, 115, 230 mg/weekly

Choice of prior: Matching a priori DLT probabilities

15/27

SLIDE 30

Dose-toxicity scenarios

0.00

0.16

0.25

0.33

0.50 0.75 1.00

1 2 4 8 15 30

Dose (mg/daily) DLT probabilities

Daily regimen

16/27

SLIDE 31

Dose-toxicity scenarios

0.00

0.16

0.25

0.33

0.50 0.75 1.00

1 2 4 8 15 30

Dose (mg/daily) 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

17/27

SLIDE 32

Performance measures

I. Average proportion of patients in UD (< 16%)

18/27

SLIDE 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

SLIDE 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

SLIDE 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

SLIDE 36

Results

Measure III: Average proportion of patients in OD (≥ 33%)

III 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 10 20 30

scenario value

19/27

SLIDE 37

Results: TITE-PK vs BLRM

Measure III: Average proportion of patients in OD (≥ 33%)

III 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 10 20 30

scenario value

Method

BLRM TITE−PK 20/27

SLIDE 38

Stopped AveDLT AveN IV V VI I II III 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 10 20 30 5 10 15 10 20 30 20 40 60 20 40 60 80 1 2 3 4 20 40 60 80 20 40 60 20 40 60 BLRM 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

21/27

SLIDE 39

Stopped AveDLT AveN IV V VI I II III 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 1 ) 7 5 % l e s s t

x

i c 2 ) 2 5 % l e s s t

x

i c 3 ) P r i

r

m e d i a n s 4 ) 2 5 % m

r

e t

x

i c 5 ) 7 5 % m

r

e t

x

i c 6 ) V e r y t

x

i c 10 20 30 5 10 15 10 20 30 20 40 60 20 40 60 80 1 2 3 4 20 40 60 80 20 40 60 20 40 60

BLRM TITE−PK TITE−PK (a=0.20)

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

22/27

SLIDE 40

Weekly + Daily regimen: TITE-PK

IV V VI I II III S c . 1 a n d S c . 1 S c . 2 a n d S c . 2 S c . 3 a n d S c . 3 S c . 4 a n d S c . 4 S c . 5 a n d S c . 5 S c . 6 a n d S c . 6 S c . 1 a n d S c . 1 S c . 2 a n d S c . 2 S c . 3 a n d S c . 3 S c . 4 a n d S c . 4 S c . 5 a n d S c . 5 S c . 6 a n d S c . 6 S c . 1 a n d S c . 1 S c . 2 a n d S c . 2 S c . 3 a n d S c . 3 S c . 4 a n d S c . 4 S c . 5 a n d S c . 5 S c . 6 a n d S c . 6 10 20 30 5 10 15 25 50 75 25 50 75 20 40 60 80 20 40 60 Daily 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

23/27

SLIDE 41

Weekly + Daily regimen: TITE-PK vs BLRM MAP

IV V VI I II III S c . 1 a n d S c . 1 S c . 2 a n d S c . 2 S c . 3 a n d S c . 3 S c . 4 a n d S c . 4 S c . 5 a n d S c . 5 S c . 6 a n d S c . 6 S c . 1 a n d S c . 1 S c . 2 a n d S c . 2 S c . 3 a n d S c . 3 S c . 4 a n d S c . 4 S c . 5 a n d S c . 5 S c . 6 a n d S c . 6 S c . 1 a n d S c . 1 S c . 2 a n d S c . 2 S c . 3 a n d S c . 3 S c . 4 a n d S c . 4 S c . 5 a n d S c . 5 S c . 6 a n d S c . 6 5 10 15 20 4 8 12 25 50 75 25 50 75 20 40 60 80 20 40 60 80 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

24/27

SLIDE 42

Discussions

SLIDE 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

SLIDE 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

SLIDE 45

Possible extensions

Multiple compounds
Usage of MAP prior
Long-term safety events

26/27

SLIDE 46

Possible extensions

Multiple compounds
Usage of MAP prior
Long-term safety events
A motivating example is discussed in our preprint (arXiv:1811.09433)
Code: https://github.com/gunhanb/TITEPK_code

26/27

SLIDE 47

References

Carpenter, B., Gelman, A., Hoffman, M., Lee, D., Goodrich, B., Betancourt, M., Brubaker, M., Guo, J., Li, P., and Riddell, A. (2017). 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):625–644. Günhan, B., Weber, S., Seroutou, A., and Friede, T. (2018). Phase I dose-escalation trials with more than one dosing regimen. ArXiv e-prints: 1811.09433. Neuenschwander, B., Branson, M., and Gsponer, T. (2008). Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27(13):2420–2439. Schmidli, H., Gsteiger, S., Roychoudhury, S., O’Hagan, A., Spiegelhalter, D., and Neuenschwander, B. (2014). Robust meta-analytic-predictive priors in clinical trials with historical control information. Biometrics, 70(4):1023–1032.

27/27

SLIDE 48

Application: Everolimus

SLIDE 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: 60
Minimum number of patients: 21
MTD declaration: P(OD) ≤ 0.25 and P(TT) ≥ 0.50

SLIDE 50

Weekly + Daily regimen: Scenario

0.00

0.16

0.25

0.33

0.50 0.75 8 16 32 64 115 230

Dose (mg/weekly) DLT probabilities

Weekly regimen

0.00

0.16

0.25

0.33

0.50 0.75 1.00 1 2 4 8 15 30

Dose (mg/daily) 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

SLIDE 51

AUC

0.00 0.25 0.50 0.75 1.00 1 2 3 4

time (weeks) AUC(t)

5 mg/daily

0.00 0.25 0.50 0.75 1.00 1 2 3 4

time (weeks) AUC(t)

20 mg/weekly

SLIDE 52

Priors

BLRM: BVN prior with following parameters:

(m1 = logit(πd∗ = 0.175), m2 = 0, s1 = 2, s2 = 1, ρ = 0)

TITE-PK: log(β) ∼ N(cloglog(P(T ≤ t∗|d∗, f ∗) = 0.175), 1.752).