Background
Methods
The EffTox design
EffTox in the Matchpoint trial
Notation | Interpretation | Value |
---|---|---|
N
| Total number of patients | 30 |
m
| Cohort size | 3 |
p
E
| Certainty required to infer dose is threshold efficable | 0.03 |
p
T
| Certainty required to infer dose is threshold tolerable | 0.05 |
\(\underline {{\pi }}_{E}\)
| Minimum efficacy threshold | 0.45 |
\(\overline {{\pi }}_{T}\)
| Maximum toxicity threshold | 0.4 |
\({\pi }_{1, E}^{*}\)
| Required efficacy probability if toxicity is impossible | 0.40 |
\({\pi }_{2, T}^{*}\)
| Permissible toxicity probability if efficacy guaranteed | 0.70 |
Dose-level | Daily ponatinib dose (mg) | Prior Pr(Eff), η
E
| Prior Pr(Tox), η
T
|
---|---|---|---|
1 | 7.5 | 0.2 | 0.025 |
2 | 15 | 0.3 | 0.05 |
3 (start dose) | 30 | 0.5 | 0.1 |
4 | 45 | 0.6 | 0.25 |
multiroot
in the R [29] package rootSolve
[30] to solve the simultaneous equations \(u\left ({\pi }_{3,E}^{*}, {\pi }_{3,T}^{*}\right) = u\left ({\pi }_{4,E}^{*}, {\pi }_{4,T}^{*}\right) = u\left ({\pi }_{5,E}^{*}, {\pi }_{5,T}^{*}\right) = 0\). This yielded a neutral utility curve that intersected (39.6%, 0%) and (100%, 67.9%). We rounded to take \({\pi }_{1,E}^{*} = 0.40\) and \({\pi }_{2,T}^{*} = 0.70\), yielding p=2.07. Our family of contours are illustrated in Fig. 1. The contours are quite steep where efficacy probabilities are less than 70%. We consider alternative contours in the discussion.
Nomenclature for describing outcomes in phase I/II trials
Dose transition pathways
Cohort 2 outcomes | Dose for cohort 3 |
---|---|
2NNN | 3 |
2NNE | 1 |
2NNT | Stop trial |
2NNB | 1 |
2NEE | 1 |
2NET | 1 |
2NEB | 1 |
2NTT | Stop trial |
2NTB | 1 |
2NBB | 1 |
2EEE | 1 |
2EET | 1 |
2EEB | 1 |
2ETT | 1 |
2ETB | 1 |
2EBB | 1 |
2TTT | Stop trial |
2TTB | 1 |
2TBB | 1 |
2BBB | 1 |
clintrials
package can be used to reproduce Table 3. Refer to the Availability of data and software section at the end of this article.Posterior utility
Results
Outcome ambiguity
Dose ambivalence
clintrials
that uses Monte Carlo integration.clintrials
package presents a Matchpoint scenario with dose ambivalence and demonstrates repeated calculation of the dose-decision. Refer to the Availability of data and software section at the end of this article.Changing p E to avoid premature stopping
Dose 1 | Dose 2 | Dose 3 | Dose 4 | |
---|---|---|---|---|
Utility | -0.489 | -0.534 | -0.777 | -0.817 |
Pr(\({\pi }_{E} > \underline {{\pi }}_{E}\)) | 0.079 | 0.037 | 0.060 | 0.200 |
Pr(\({\pi }_{T} < \overline {{\pi }}_{T}\)) | 0.919 | 0.758 | 0.051 | 0.005 |
Admissible under p
E
=0.05, p
T
=0.05 | 1 | 0 | 1 | 0 |
Admissible under p
E
=0.03, p
T
=0.05 | 1 | 1 | 1 | 0 |
Operating characteristics
Scenario | Dose 1 | Dose 2 | Dose 3 | Dose 4 | Stop | |
---|---|---|---|---|---|---|
Pr(Eff) | 0.20 | 0.30 | 0.50 | 0.60 | ||
1: | Pr(Tox) | 0.03 | 0.05 | 0.10 | 0.30 | |
monotonic, | Utility | -0.33 | -0.17 | 0.16 |
0.22
| |
dose 4 | ESS=0.5 | 0.01 | 0.01 |
0.34
|
0.63
| 0.01 |
optimal | ESS=1.3 | <0.01 | <0.01 |
0.22
|
0.76
| <0.01 |
ESS=1.5 | <0.01 | <0.01 |
0.22
|
0.77
| <0.01 | |
Pr(Eff) | 0.40 | 0.60 | 0.75 | 0.79 | ||
2: | Pr(Tox) | 0.10 | 0.25 | 0.55 | 0.60 | |
monotonic, | Utility | -0.01 |
0.25
| 0.12 | 0.08 | |
dose 2 | ESS=0.5 | 0.06 |
0.59
| 0.32 | <0.01 | 0.03 |
optimal | ESS=1.3 | 0.03 |
0.60
| 0.35 | <0.01 | 0.01 |
ESS=1.5 | 0.03 |
0.57
| 0.39 | <0.01 | 0.01 | |
Pr(Eff) | 0.25 | 0.40 | 0.60 | 0.60 | ||
3: | Pr(Tox) | 0.10 | 0.20 | 0.38 | 0.42 | |
eff. plateau, | Utility | -0.26 | 0.04 |
0.15
| 0.12 | |
dose 3 | ESS=0.5 | 0.03 | 0.10 |
0.70
| 0.13 | 0.04 |
optimal | ESS=1.3 | 0.01 | 0.10 |
0.73
| 0.13 | 0.02 |
ESS=1.5 | 0.01 | 0.09 |
0.73
| 0.15 | 0.02 | |
Pr(Eff) | 0.50 | 0.60 | 0.70 | 0.80 | ||
4: | Pr(Tox) | 0.20 | 0.20 | 0.20 | 0.20 | |
tox. plateau, | Utility | 0.12 | 0.28 | 0.43 |
0.57
| |
dose 4 | ESS=0.5 |
0.02
|
0.03
|
0.61
|
0.34
| <0.01 |
optimal | ESS=1.3 |
<0.01
|
0.02
|
0.47
|
0.50
| <0.01 |
ESS=1.5 |
<0.01
|
0.01
|
0.47
|
0.51
| <0.01 | |
Pr(Eff) | 0.05 | 0.08 | 0.20 | 0.25 | ||
Pr(Tox) | 0.05 | 0.08 | 0.12 | 0.14 | ||
5: | Utility | -0.58 | -0.54 | -0.34 | -0.26 | |
all doses | ESS=0.5 | 0.06 | 0.03 | 0.01 | 0.37 |
0.53
|
inactive | ESS=1.3 | 0.06 | 0.07 | 0.02 | 0.34 |
0.51
|
ESS=1.5 | 0.07 | 0.08 | 0.02 | 0.36 |
0.48
| |
Pr(Eff) | 0.05 | 0.08 | 0.12 | 0.25 | ||
6: | Pr(Tox) | 0.60 | 0.65 | 0.70 | 0.80 | |
all doses | Utility | -0.78 | -0.78 | -0.76 | -0.67 | |
too toxic | ESS=0.5 | 0.09 | 0.01 | 0.01 | 0.01 |
0.88
|
and inactive | ESS=1.3 | 0.06 | 0.01 | 0.01 | 0.01 |
0.91
|
ESS=1.5 | 0.04 | 0.01 | 0.01 | 0.01 |
0.93
|
Design variant | Mean Pr(Optimal decision) |
---|---|
ESS=0.5 | 0.612 |
ESS=1.3 | 0.668 |
ESS=1.5 | 0.65 |
Scenario | Dose 1 | Dose 2 | Dose 3 | Dose 4 | Sum | |
---|---|---|---|---|---|---|
1: | Pr(Eff) | 0.20 | 0.30 | 0.50 | 0.60 | |
monotonic, | Pr(Tox) | 0.03 | 0.05 | 0.10 | 0.30 | |
dose 4 | Utility | -0.33 | -0.17 | 0.16 |
0.22
| |
optimal | ESS=0.5 | 0.7 | 0.6 |
12.1
|
16.4
| 29.8 |
ESS=1.3 | 0.2 | 0.2 |
9.8
|
19.6
| 29.8 | |
ESS=1.5 | 0.1 | 0.1 |
9.5
|
20.1
| 29.8 | |
2: | Pr(Eff) | 0.40 | 0.60 | 0.75 | 0.79 | |
monotonic, | Pr(Tox) | 0.10 | 0.25 | 0.55 | 0.60 | |
dose 2 | Utility | -0.01 |
0.25
| 0.12 | 0.08 | |
optimal | ESS=0.5 | 1.5 |
11.5
| 16.0 | 0.4 | 29.4 |
ESS=1.3 | 0.8 |
11.6
| 16.9 | 0.6 | 29.9 | |
ESS=1.5 | 0.7 |
10.3
| 18.2 | 0.7 | 29.9 | |
3: | Pr(Eff) | 0.25 | 0.40 | 0.60 | 0.60 | |
eff. plateau, | Pr(Tox) | 0.10 | 0.20 | 0.38 | 0.42 | |
dose 3 | Utility | -0.26 | -0.04 |
0.15
| 0.11 | |
optimal | ESS=0.5 | 1.1 | 2.8 |
21.8
| 3.7 | 29.4 |
ESS=1.3 | 0.5 | 2.5 |
22.2
| 4.4 | 29.6 | |
ESS=1.5 | 0.4 | 2.0 |
22.1
| 5.2 | 29.7 | |
4: | Pr(Eff) | 0.50 | 0.60 | 0.70 | 0.80 | |
tox. plateau, | Pr(Tox) | 0.20 | 0.20 | 0.20 | 0.20 | |
dose 4 | Utility | 0.12 | 0.28 | 0.43 |
0.57
| |
optimal | ESS=0.5 |
0.5
|
1.0
|
19.3
|
9.2
| 30.0 |
ESS=1.3 |
0.1
|
0.7
|
15.9
|
13.3
| 30.0 | |
ESS=1.5 |
0.1
|
0.3
|
15.9
|
13.7
| 30.0 | |
5: | Pr(Eff) | 0.05 | 0.08 | 0.20 | 0.25 | |
all doses | Pr(Tox) | 0.05 | 0.08 | 0.12 | 0.14 | |
inactive | Utility | -0.58 | -0.54 | -0.34 | -0.26 | |
ESS=0.5 | 2.4 | 2.4 | 4.7 | 14.1 | 23.6 | |
ESS=1.3 | 1.5 | 1.9 | 4.7 | 15.3 | 23.4 | |
ESS=1.5 | 1.4 | 1.7 | 4.5 | 16.0 | 23.6 | |
6 | Pr(Eff) | 0.05 | 0.08 | 0.12 | 0.25 | |
all doses | Pr(Tox) | 0.60 | 0.65 | 0.70 | 0.80 | |
too toxic | Utility | -0.78 | -0.78 | -0.76 | -0.67 | |
and inactive | ESS=0.5 | 2.6 | 3.0 | 4.0 | 0.9 | 10.5 |
ESS=1.3 | 1.1 | 2.8 | 5.2 | 0.8 | 9.9 | |
ESS=1.5 | 1.0 | 2.8 | 5.3 | 0.9 | 10.0 |
Discussion
clintrials
[34].Conclusion
Acknowledgements
Funding
Availability of data and materials
trialr
R-package and clintrials
python package [34], both developed by KB. Code is available with absolutely no warranty under the GNU3 licence atclintrials
. A snapshot of the version used is posted on Zenodo at https://zenodo.org/record/164621.clintrials
, we provide tutorials on dose-transition pathways, posterior dose utility and dose ambivalence in the form of IPython notebooks. These let you reproduce some of the tables and figures in this manuscript. They are available to download and execute or to simply view online. Go toclintrials
is written in Python and will run on Mac, Linux and Windows. It requires that Python be installed and that the numpy, scipy and pandas packages (amongst others) are installed. The simplest way to achieve this is to install Anaconda, a Python distribution aimed at researchers that bundles each of these packages and many more.clintrials
is developed using 64 bit Python 3.5. Efforts are made to maintain compatibility with Python 2.7.