1 of 20

Generalized Toxicity Dose Finding: Moving Beyond Binary Toxicity

September 2023

Orange County Biostatistics Symposium: Bayesian and Regression Methods

Frank Shen

Sr. Biostatistician

Bristol Myers Squibb Company

Biostatistics/GBDS

2 of 20

Oncology Dose Finding Study: an Essential Step in the Development of Anticancer Drugs

  • Objective is to establish the recommended dose and/or schedule of new drugs or drug combinations for later phase studies.
  • Patient’s safety is the primary concern
  • Use patients rather than healthy volunteers
  • Relevant throughout the rest of drug development (choice regimen, choice of population, choice of indication)

2

  • 3+3
  • CRM
  • TPI
  • BLRM
  • mTPI
  • bCRM, Eff-Tox
  • BOIN
  • mTPI2
  • TITE-BOIN, Rolling 6
  • i3+3, BOIN12, BOIN-ET

​

1980s

1990s

2000s

2010s

2020s

Biostatistics/GBDS

3 of 20

Toxicity Endpoints in Dose Finding ��

  • Early Dose Finding Assumptions:
    • Primary focus on binary toxicity endpoint (# of patients with Dose Limiting Toxicity [DLT])
    • Higher toxicity = more efficacy
    • Start at a low dose and escalate to find the Maximum Tolerated Dose (MTD)
  • Some newer methods seek to find the Optimal Biologic Dose (OBD) instead
    • Utilizes two endpoints to guide dose escalation, one toxicity endpoint and one efficacy endpoint
    • But the toxicity endpoint is still a binary endpoint (usually DLTs)
  • But adverse events that are not severe enough to be dose limiting can provide important information
  • Generalized Dose Finding methods allow for ordinal or continuous toxicity endpoints, moving beyond DLTs

3

Biostatistics/GBDS

4 of 20

Ordinal or Continuous Toxicity Endpoints

  • Total Toxicity Burden (TTB) = weighted sum of different adverse events, where the severity weights come entirely from clinicians
    • Example: Gr3 Radiation pneumonitis (2) + Atrial fibrillation (3) + Pulmonary embolism (6) = 11 TTB
  • Toxicity Burden Score (TBS) = weighted sum of different adverse events, where the severity weights come from a regression based on historical data
  • Total Toxicity Profile = weighted Euclidian norm of different adverse events, where the severity weights come entirely from clinicians
  • normalized Equivalent Toxicity Score (ETS) = all important adverse events are scored as fractions of a DLT based on clinician expertise
    • Example: Most severe AE is a Gr2 Nausea => Clinical considers this 50% as severe as a DLT => 0.5 ETS

​

​

4

Biostatistics/GBDS

5 of 20

Bayesian Framework for Non-Binary Toxicity Endpoints

  •  

5

Biostatistics/GBDS

6 of 20

Generalized BOIN (Continuous)

  •  

6

Biostatistics/GBDS

7 of 20

Generalized BOIN (Quasi-Binomial)

  •  

7

Rongji, et al, 2019

Biostatistics/GBDS

8 of 20

Generalized mTPI-2 (Quasi Binomial)

  •  

8

Escalate

Stay

Deescalate

Deescalate

Deescalate

Deescalate

decision

Biostatistics/GBDS

9 of 20

Generalized mTPI2 (Continuous)

  •  

9

Biostatistics/GBDS

10 of 20

Simulation Scenario (Quasi-Binomial)

  • Cohort size = 3
  • Max # of subjects = 30
  • Max # of subjects at a single dose level = 12
  • Target DLT equivalent rate/ETS = 0.30
  • gmTPI2 target interval = 0.25 – 0.35

10

Biostatistics/GBDS

11 of 20

Simulation Scenario (Continuous)

  • Cohort size = 3
  • Max # of subjects = 30
  • Max # of subjects at a single dose level = 12
  • Max TTB = 4
  • Target TTB = 1.47
  • gmTPI2 target interval = 1.07 – 1.87

​

​

11

Biostatistics/GBDS

12 of 20

Simulation Results (Quasi Binomial)

12

Scenario

% Dose Selected

Too Low

% Dose Selected

Correctly

% Dose Selected

Too High

% Dose Selected

Too Low

% Dose Selected

Correctly

% Dose Selected

Too High

​

gmTPI2

gBOIN

A

NA

71.07

26.23

NA

72.37

24.33

B

2.17

75.23

22.60

2.10

77.40

20.50

C

12.20

56.03

31.77

15.37

55.50

29.13

D

14.47

68.23

17.30

15.13

68.83

16.03

E

22.77

77.23

NA

26.90

73.10

NA

Scenario

A

B

C

D

E

Ideal Dose

10 (lowest dose)

20

40

60

80 (highest dose)

Biostatistics/GBDS

13 of 20

Simulation Results (Quasi Binomial)

13

Scenario

% Patients Allocated at Ideal Dose

% Patients Allocated above Ideal Dose

Average Toxicity

% Patients Allocated at Ideal Dose

% Patients Allocated above Ideal Dose

Average Toxicity

​

gmTPI2

gBOIN

A

0.67

0.33

6.92

0.73

0.27

6.59

B

0.50

0.26

6.94

0.48

0.21

6.68

C

0.37

0.25

6.88

0.34

0.20

6.55

D

0.36

0.15

6.40

0.34

0.13

6.10

E

0.38

NA

4.92

0.31

NA

4.80

Scenario

A

B

C

D

E

Ideal Dose

10 (lowest dose)

20

40

60

80 (highest dose)

Biostatistics/GBDS

14 of 20

Simulation Results (Continuous)

14

Scenario

% Dose Selected

Too Low

% Dose Selected

Correctly

% Dose Selected

Too High

% Dose Selected

Too Low

% Dose Selected

Correctly

% Dose Selected

Too High

​

gmTPI2

gBOIN

A

NA

97.08

2.93

NA

99.58

0.43

B

2.93

83.50

13.58

0.23

97.78

2.00

C

21.10

51.05

27.85

18.78

74.80

6.43

D

26.45

44.43

29.13

26.68

54.80

18.53

E

46.10

53.90

NA

46.40

53.60

NA

Scenario

A

B

C

D

E

Ideal Dose

5 (lowest dose)

10

40

60

80 (highest dose)

Biostatistics/GBDS

15 of 20

Simulation Results (Continuous)

15

Scenario

% Patients Allocated at Ideal Dose

% Patients Allocated above Ideal Dose

Average Toxicity

% Patients Allocated at Ideal Dose

% Patients Allocated above Ideal Dose

Average Toxicity

​

gmTPI2

gBOIN

A

0.94

0.06

23.34

0.97

0.03

22.14

B

0.58

0.19

37.02

0.72

0.05

29.15

C

0.28

0.25

37.90

0.39

0.10

31.79

D

0.22

0.22

32.13

0.26

0.11

28.95

E

0.30

NA

27.32

0.22

NA

25.37

Scenario

A

B

C

D

E

Ideal Dose

5 (lowest dose)

10

40

60

80 (highest dose)

Biostatistics/GBDS

16 of 20

Discussion

  • Both methods are not too complex, can run a simulation scenario in under 3 minutes
  • Both methods provide a good chance of selecting the correct ideal dose
  • gBOIN and gmTPI2 operating characteristics can be very similar when target interval is set up to be similar to the gBOIN recommended target interval
  • gmTPI2 favors earlier doses with tighter intervals and later doses with looser intervals
  • Perhaps a non-negative distribution (gamma?) would be a better model for pseudo-continuous toxicity scores

16

Biostatistics/GBDS

17 of 20

Discussion

  • Creating the toxicity score/burden/profile is challenging
    • Needs major clinician input
    • Weights for different types of sub-DLT adverse events is unavoidably subjective
    • May want to focus on a few key sub-DLT adverse events to keep it manageable
    • gBOIN implemented in R package “UnifiedDoseFinding”, gmTPI2 is personal development
  • Other expansions on gBOIN exist with software to support the continuous toxicity (gBOIN-ET, TITE-gBOIN, TITE-gBOIN-ET)
    • Ease of use is still a very important for clinical statistical models

17

Biostatistics/GBDS

18 of 20

Frank.Shen@bms.com

Thank you

Biostatistics/GBDS

19 of 20

References

Guo, Wentian, et al. "A Bayesian interval dose-finding design addressing Ockham's razor: mTPI-2." Contemporary clinical trials 58 (2017): 23-33.

Mu, Rongji, et al. "gBOIN: a unified model-assisted phase I trial design accounting for toxicity grades, and binary or continuous end points." Journal of the Royal Statistical Society Series C: Applied Statistics 68.2 (2019): 289-308.

Takeda, Kentaro, Satoshi Morita, and Masataka Taguri. "gBOIN‐ET: The generalized Bayesian optimal interval design for optimal dose‐finding accounting for ordinal graded efficacy and toxicity in early clinical trials." Biometrical Journal 64.7 (2022): 1178-1191.

Takeda, Kentaro, et al. "TITE‐gBOIN‐ET: Time‐to‐event generalized Bayesian optimal interval design to accelerate dose‐finding accounting for ordinal graded efficacy and toxicity outcomes." Biometrical Journal (2023): 2200265.

Bekele, B. N. and Thall, P. F. (2004) Dose-finding based on multiple toxicities in a soft tissue sarcoma trial. J. Am. Statist. Ass., 99, 26–35.

Lee, S., Hershman, D., Martin, P., Leonard, J. and Cheung, Y. (2012) Toxicity burden score: a novel approach to summarize multiple toxic effects. Ann. Oncol., 23, 537–541

19

Biostatistics/GBDS

20 of 20

References

Chen, Z., Krailo, M., Azen, S. and Tighiouart, M. (2010)Anovel toxicity scoring system treating toxicity response as a quasi-continuous variable in phase I clinical trials. Contemp. Clin. Trials, 31, 473–482.

Ezzalfani, M., Zohar, S., Qin, R., Mandrekar, S. J. and Deley, M.-C. L. (2013) Dose-finding designs using a novel quasi-continuous endpoint for multiple toxicities. Statist. Med., 32, 2728–2746.

Papke, L. E. and Wooldridge, J. M. (1996) Econometric methods for fractional response variables with an application to 401(k) plan participation rates. J. Appl. Econmetr., 11, 619–632.

20

Biostatistics/GBDS