1. Extensions of the TEQR and mTPI designs including non-monotone efficacy in addition to toxicity in dose selection
Revathi Ananthakrishnan
The 3rd Stat4Onc Annual Symposium

2. Introduction
Traditional Phase 1 dose-finding oncology trials aim to identify the maximum tolerated dose (MTD); however, they may not always accurately select the MTD due to their small sample size
3+3 Design
Braun TM. The current design of oncology phase I clinical trials: progressing from algorithms to statistical models. Chin Clin Oncol. 2014;3(1):2.

3. Introduction
Furthermore, efficacy of an anti-cancer agent may not always monotonically increase with dose, and can peak at any dose level.
Thus, Phase 1 trials may not target the optimal dose taking into consideration both toxicity and response.
Assessment of both DLTs and efficacy/responses in a reasonably sized, larger trial has the potential for a more accurate determination of a suitable dose, compared to a Phase 1 followed by a Phase 2 trial.
Basically, there are 3 issues to highlight: 1) traditional trials only target MTD using DLT; 2) small size; 3) efficacy should be in consideration

4. Objectives
We extend the mTPI (Ji 2010) and TEQR (Toxicity Equivalence Range design; Blanchard 2011) designs with a moderately large sample size to choose an optimal dose for safety and efficacy. We also create a frequentist version of the TEPI design, the 2D TEQR design.
A key part of our evaluation is to determine the performance when the efficacy response rate does not necessarily increase with dose.
Finally, we compare our extended TEQR and mTPI designs and the 2D TEQR design with the TEPI, Eff-Tox and OBD Isotonic designs.
Ji Y, Liu P, Li Y, Bekele BN. A modified toxicity probability interval method for dose-finding trials. Clin Trials Dec;7(6):
Blanchard MS, Longmate JA. Toxicity equivalence range design (TEQR): a practical Phase I design. Contemp Clin Trials. 2011 Jan;32(1):

5. mTPI Design
The Bayesian mTPI dose-finding design uses a statistic for the dosing decision rules, the unit probability mass (UPM), defined as the ratio of the probability mass of an interval and the interval length.
pT – target toxicity e1, e2 – interval around pT
Dosing decisions depend on which of these intervals has the highest UPM based on a beta-binomial distribution with a beta(1,1) prior.
The mTPI trial stops if dose level 1 is too toxic or if the pre-specified maximum sample size is reached.
pT-e1 pT
pT+e2 1
Stay at same dose
escalate
de-escalate

6. TEQR Design
The TEQR design is a frequentist version of the mTPI design based on the empirical DLT rate and not on a posterior probability.
The TEQR trial stops if dose level 1 is too toxic or when a dose level achieves the pre-specified sample size at the MTD.
pT-e1 pT
pT+e2 1
Stay at same dose
escalate
de-escalate

7. mTPI, TEQR Designs
In both the mTPI and TEQR designs, we stay at the current dose if it is safe but the DLT data indicate that the next higher dose may be too toxic.
Using a standard mTPI or TEQR design, the dose chosen for safety is the highest dose with DLT rate ≤ the pre-specified DLT rate (say 0.33) after applying isotonic regression at the end of the trial.

8. Eff-Tox, OBD, TEPI Designs
The Eff-Tox design (Thall et al., 2006) is a Bayesian design that trades-off the probabilities of drug toxicity and efficacy to determine the optimal dose for each new cohort of patients.
In the OBD Isotonic design (Zang, 2014), an admissible set of doses satisfying a safety criterion, is first defined. The OBD is then the lowest dose with the highest response rate within the admissible set.
The TEPI design is an extension of the mTPI design that includes efficacy and safety in dose selection (Li et al., 2017).
The stopping point is usually at a pre-specified sample size.
Thall PF, Cook JD, Estey EH. Adaptive dose selection using efficacy-toxicity trade-offs: illustrations and practical considerations. J Biopharm Stat. 2006;16(5):
Zang Y, Lee JJ, Yuan Y. Adaptive designs for identifying optimal biological dose for molecularly targeted agents. Clin Trials. 2014 Jun;11(3):
Li DH, Whitmore JB, Guo W, Ji Y. Toxicity and Efficacy Probability Interval Design for Phase I Adoptive Cell Therapy Dose-Finding Clinical Trials. Clin Cancer Res. 2017 Jan 1;23(1):13-20.

9. Extending TEQR and mTPI Designs to Include Efficacy
In our extended TEQR or mTPI designs that also consider efficacy, isotonic regression is applied to the observed DLT rates at the end of the trial.
Monotonically Increasing or Plateauing Dose-Response Curve
Umbrella-Shaped Dose-Response Curve
If the true response rates are thought to peak at a central dose level, isotonic regression on the difference in observed response rates between adjacent dose levels, along with the sign of these differences, can reveal this peak; the optimal dose for efficacy and safety can then be determined.
If the true response rates are thought to increase monotonically with an increase in dose or plateau after a certain dose, isotonic regression on the observed response rates can determine the optimal dose for efficacy and safety.
Ananthakrishnan R, Green S, Li D, LaValley M. Extensions of the mTPI and TEQR designs to include non-monotone efficacy in addition to toxicity for optimal dose determination for early phase immunotherapy oncology trials. Contemp Clin Trials Commun Jan 31;10:62-76.

10. Monotonically Increasing or Plateauing Dose-Response Curve – Hypothetical Example
Dose Level
Underlying DLT Rate
Underlying Response Rate
Observed DLT Rate
Observed Response Rate
Isotonic Regression on the observed DLT rate
Isotonic Regression on the observed response rate 1
0.01
0.1
0.04
0.14
0.03
0.13 2
0.02
0.2
0.12 3
0.06
0.4
0.08
0.43
0.41 4
0.55
0.22
0.39 5
0.71
0.6
0.66
0.63 6
0.97
0.62
Optimal Dose is dose level 4
Threshold for safety<=0.33; threshold for efficacy>=0.4

11. Umbrella-Shaped Dose-Response Curve – Hypothetical Example
Dose Level
Underlying DLT Rate
Underlying Response Rate
Observed DLT Rate
Observed Response Rate
Isotonic Regression on the observed DLT rate
Difference in response rates between adjacent dose levels
Isotonic Regression on Difference in observed response rate 1
0.01
0.1
0.04
0.05
0.03 2
0.02
0.35
0.3
-0.25 3
0.06
0.5
0.08
-0.2 4
0.2
0.22
0.15 5
0.71
0.66
0.63 6
0.97
0.6
Optimal Dose is dose level 3
Threshold for safety<=0.33; threshold for efficacy>=0.4

12. Examples of Umbrella-Shaped Dose Response Curves

13. Finding the Optimal Dose – Extended mTPI and TEQR Designs
Monotonically Increasing Dose-Response Curve or Plateauing Dose-Response Curve
The optimal dose for safety and efficacy is the highest dose that is safe, and above the efficacy threshold.
Umbrella-shaped Dose-Response Curve
If the peak dose for efficacy is lower than or equal to the highest dose that is safe, then the peak dose for efficacy is the optimal dose if it is above the efficacy threshold.
If the peak dose for efficacy is higher than the highest dose that is safe, then the highest dose that is safe is the optimal dose, but only if the response rate is above the efficacy threshold at this dose.

14. Simulations for Extended mTPI, TEQR Designs
We generate binary random variables X1~Bernoulli(p) and X2~Bernoulli(q) for toxicity and efficacy, which can be correlated.
We use a logistic dose-toxicity curve for the true DLT rates; the true response rate curves are specified as monotonically increasing, plateau shaped or umbrella-shaped.

15. Simulations for Extended mTPI, TEQR Designs
We have created SAS code to obtain the statistical operating characteristics for extended mTPI and TEQR designs - we perform 1000 simulated trials under varying scenarios.
The rules for escalation, de-escalation or remaining at the same dose depend on the number of observed DLTs.
A trial stops when the planned sample size is reached or if dose level 1 is too toxic.
We also track the efficacy response of patients. At the end of a trial, we choose a dose that is optimal for both safety and efficacy from the observed DLT and response rates at each dose level.

16. Comparison of the Extended mTPI and TEQR Designs with TEPI, Eff-Tox and OBD Isotonic Design
Scenario
Dose Level 1 2 3 4 5 6
None
1 Monotonically Increasing DLT Rates and Monotonically Increasing Response Rates
True toxicity, true efficacy rate
.01, .1
.02, .30
.06, .4
.2, .45
.55, 0.55
.89, .6 -
Trade-off Value Eff-Tox Design
-0.82
-0.43
-0.30
-0.77
-1.2
% selected by Eff-Tox Design 44 49
% selected by OBD Design
20.5
27.8
45.5
6.2
% selected by TEPI Design
32.5
39.2 28
0.3
% selected by extended mTPI Design
0.08
7.01
69.22
0.72 23
% selected by extended TEQR Design
0.66
18.06
52.7
0.91
27.68
Stopping rule of the mTPI design used. Starting dose is dose level 2. Sample size of 50 and cohort size of 5 are used
Ananthakrishnan R, Green S, Li D, LaValley M. Extensions of the mTPI and TEQR designs to include non-monotone efficacy in addition to toxicity for optimal dose determination for early phase immunotherapy oncology trials. Contemp Clin Trials Commun Jan 31;10:62-76.

17. Comparison of the Extended mTPI and TEQR Designs with TEPI, Eff-Tox and OBD Isotonic Design
Scenario
Dose Level 1 2 3 4 5 6
None
2 Monotonically Increasing DLT Rates and Umbrella-Shaped Response Rates
True toxicity, true efficacy rate
.01, .1
.02, .35
.06, .5
.2, .3
.55, 0.2
.89, .05 -
Trade-off Value Eff-Tox Design
-0.82
-0.33
-0.1
-0.73
-1.48
-2.32
% selected by Eff-Tox Design 58 13 20
% selected by OBD Design
17.9
70.2
11.6
0.4
% selected by TEPI Design
37.2
59.1
3.6
0.1
% selected by extended mTPI Design
18.7
65.6
3.1
12.6
% selected by extended TEQR Design
17.7
64.1
3.9
14.3
Stopping rule of the mTPI design used. Starting dose is dose level 2. Sample size of 50 and cohort size of 5 are used.
Ananthakrishnan R, Green S, Li D, LaValley M. Extensions of the mTPI and TEQR designs to include non-monotone efficacy in addition to toxicity for optimal dose determination for early phase immunotherapy oncology trials. Contemp Clin Trials Commun Jan 31;10:62-76.

18. TEPI Design – Dosing Decisions based on the Joint UPM
mTPI Design – Dosing Decisions based on the UPM
TEPI Design – Dosing Decisions based on the Joint UPM
mTPI Design Dosing Decisions based on where the UPM is the highest
Toxicity Rate
Dosing Decision
Low (Underdosing)
E (Escalate)
Target Region (Right Dosing)
S (Stay)
High (Overdosing)
D or DU (De-escalate or De-escalate and do not go back to that dose)
Li DH, Whitmore JB, Guo W, Ji Y. Toxicity and Efficacy Probability Interval Design for Phase I Adoptive Cell Therapy Dose-Finding Clinical Trials. Clin Cancer Res. 2017 Jan 1;23(1):13-20.

19. Relation between mTPI, TEQR, TEPI and 2D TEQR Designs
Bayesian to Frequentist
mTPI Design
Bayesian design
Considers only drug toxicity (DLTs) in dose (MTD) selection
TEQR Design
Frequentist version of mTPI
Considers only drug toxicity (DLTs) in dose (MTD) selection
Considering Toxicity to Considering Both Toxicity and Efficacy in Dose Selection
Considering Toxicity to Considering Both Toxicity and Efficacy in Dose Selection
TEPI Design
Bayesian design
Considers both drug toxicity and efficacy in dose selection (extension of the mTPI design incorporating efficacy in addition to toxicity)
Proposed 2D (2 dimensional) TEQR Design
Frequentist version of TEPI
Considers both drug toxicity and efficacy in dose selection (extension of the TEQR design incorporating efficacy in addition to toxicity)
Bayesian to Frequentist

20. Proposed 2D TEQR Design
Scenario
Dose Level
Toxicity
Efficacy
Percentage Each Dose is Selected as Optimal in Proposed 2D TEQR Design
Percentage Each Dose is Selected as Optimal in TEPI Design
Percentage Each Dose is Selected as Optimal in Eff-Tox Design
Percentage Each Dose is Selected as Optimal in OBD Design
Number of Subjects Treated at Each Dose in our TEQR 2D Design
Number of Subjects Treated at Each Dose in TEPI Design
Number of Subjects Treated at Each Dose in Eff-Tox Design
Number of Subjects Treated at Each Dose in OBD Isotonic Design 1
0.15
0.8
66.5
83.9 66
37.9
9.0
9.1
17.8
9.9 2
0.2
19.7
13.6 30
31.1
8.2
8.5
8.4
8.0 3
0.25
5.8
2.1
19.1
4.9
5.6
0.7
5.3 4
0.3
1.3
12.0
2.0
3.8
0.1
7.2
1.0
4.5
4.4
3.7
3.3
65.0 88 42
95.8
12.3
11.8
3.2
7.1
4.3
4.0
1.1
2.3
0.6
Starting dose is dose level 1. Sample size of 27 and cohort size of 3 are used

21. Discussion Extended mTPI and TEQR designs:
The optimal dose is the MTD or the peak efficacy dose.
The extended mTPI design does well in predicting the optimal dose.
The design is an early phase design that assumes a moderate sample size will be used to determine the optimal dose accurately.
Proposed 2D TEQR design:
The 2D TEQR design is simple, easy to understand and implement with no complex computations. Although the design is less accurate than the TEPI design in optimal dose selection, the accuracy can be increased, in many cases, with a moderate increase in cohort size.
We have not explored the effect of using different utility functions on the accuracy of optimal dose selection.

22. Thank for your kind attention