Objective:
The aim of this dose finding trial is to determine the maximum tolerated dose (MTD) of [agent]
administered [orally, intravenously,..., etc] to patients with [specific disease and other types
of characteristics defining target population]. The MTD is defined to be the dose level of
[agent] that when administered to a patient [method and time of administration] results in a
probability equal to θ = [probability: low for life-threatening and irreversible toxicity, high
for transient, reversible, non-lethal] that a dose limiting toxicity [definition, e.g., grade 4
hematological toxicity] will be manifest within [time to evaluation].
Trail Design:
Introduction
The dose escalation will follow a Bayesian method permitting precise determination of the
therapeutic working-dose while directly controlling the likelihood of an overdose. The method,
known as EWOC (Escalation With Overdose Control), has been used to design many dose
finding clinical trials, a fraction of them being published as peer-reviewed articles (1-17). Babb et
al. (18) provided a comparison of EWOC with alternative phase I design methods. They showed
that up-and-down designs treated only 35% of patients at optimal dose levels, versus 55% for
EWOC, i.e., more patients are treated with doses outside the therapeutic window by up-anddown than by EWOC designs. Babb and Rogatko (19) provide a summary of Bayesian phase I
design methods and Tighiouart et al. (20) studied the performance of EWOC under a rich class
of prior distributions for the MTD. Tighiouart and Rogatko (21) showed that EWOC is coherent.
EWOC was the first dose-finding procedure to directly incorporate the ethical constraint of
minimizing the chance of treating patients at unacceptably high doses. Its defining property is
that the expected proportion of patients treated at doses above the MTD is equal to a specified
value , the feasibility bound. This value is selected by the clinician and reflects his/her level of
concern about overdosing. Zacks et al. (22) showed that among designs with this defining
property, EWOC minimizes the average amount by which patients are under-dosed. This means
that EWOC approaches the MTD as rapidly as possible, while keeping the expected proportion
of patients overdosed less than the value . Zacks et al. (22) also showed that, as a trial
progresses, the dose sequence defined by EWOC approaches the MTD (i.e., the sequence of
recommended doses converges in probability to the MTD). Eventually, all patients beyond a
certain time would be treated at doses sufficiently close to the MTD.
Dose Escalation
The dose for the first patient [or cohort] in the trial will be [initial dose], previous results
indicating this to be a safe dose. The dose for each subsequent patient [or cohort] will be
determined so that, on the basis of all available data, the probability that it exceeds the MTD is
equal to a prespecified value α. In this trial, we set α = [probability, note that a variable α
could also be implemented, e.g., start at α = 0.25 and increase α in small increments
until α = 0.5], this value being a compromise between the therapeutic aspect of the agent and
its toxic side effects [choice of α depends on both the severity of the side effects and θ].
Chu et al. (23) showed that in general, this design provides a better safety protection in limiting
higher dose for patients than four versions of the Continual Reassessment Method designs with
a similar convergence rate.
The dose selected for every patient in the trial will be between the minimum dose [minimum
dose, we suggest that the minimum dose should be less than initial dose] and the
maximum allowable dose [maximum dose, we suggest that the maximum dose should be
higher than the higher dose intended to be given to the patients]. The trial will be
terminated if [number] dose related toxicities are observed for the first [number] patients. The
Figure below shows all the possible dose sequences that could be realized for the first [2 to 5]
patients [use EWOC software to generate the Figure].
Because it takes [number of weeks] weeks to resolve toxicity, a patient may be accrued to the
trial before the responses of all previously treated patients have been determined. It will be at
the PI’s discretion whether to treat the newly accrued patient at the dose level determined on
the basis of the currently available data or to wait until one or more toxicities are resolved. The
maximum number of patients to be treated simultaneously with unresolved DLT status cannot
exceed [number of patients, e.g., three]. In other words, if there are [number of patients,
e.g., three] patients currently under study with unresolved DLT status, a new patient cannot be
treated until at least one patient finishes one cycle of therapy.
A maximum of [number of patients] patients will be accrued to the trial. Procedures for
determining the number of patients needed in a dose finding trial using a Bayesian framework
depends on the investigators, goal and sets of criteria such as precision of the estimate of the
MTD and frequency of DLTs. Tighiouart and Rogatko (24) conducted extensive simulations
under several scenarios (true values of the MTD, probability of toxicity at the initial dose and
target probability of DLT) and tabulated values on the number of patients needed to achieve a
given accuracy (measured as posterior standard deviation or average length of highest posterior
density – HPD - credible interval) of the estimate of the MTD. [number of patients] will achieve
[a mean posterior standard deviation of , or length of 90 or 95% HPD credible interval of
– search value in Table 1, Figures 1 or 2).
[The trial will be terminated after the maximum number of patients were evaluated; or
when the length of the HPD credible interval for the MTD, or the posterior standard
deviation falls below a specified value; or when the magnitude of change in the MTD
estimate (mean, median and mode of the posterior distribution of the MTD) is smaller
than some threshold for 1, 2, 3, ... successive patients.]
Upon completion of the trial, the MTD will be estimated as the median [or mode, or mean] of
the marginal posterior distribution of the MTD. The computation of the dose to be administered
to each patient and the 95% highest posterior density credible interval estimate of the MTD will
be carried out by [statistician in charge] with the computer program EWOC Version 3.1 (userfriendly, dialog-based, stand-alone application and the self-extracting file can be downloaded
from http://biostatistics.csmc.edu/ewoc/(25, 26) or Web-EWOC(27)
Design Operating Characteristics
Trials were simulated under [number of scenarios, e.g., 3] scenarios to study the safety and
efficiency of the proposed trial design, with [description of scenarios; e.g., θ=0.33, α=0.05,
Variable Alpha Increment=0.04, Cohort size=1, Sample Size for each Trial=30, Minimum
Dose=10, and Maximum Dose=400, using Continuous Dose scenario with Probability of
DLT at the Minimum Dose= 0.05, True MTD= 50, 150 and 250, and Number of Simulated
Trials=1000].
Table 1 shows the summary statistics for safety and efficiency of the proposed EWOC design
based on [Number of trials, e.g., one thousand] trials. Overall, the design is safe and efficient.
[Table 1 with Design Operating Characteristics]
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Table 1. Average posterior standard deviation and average length of HPD of
the posterior distribution of the MTD that are achieved for a given sample size
for θ = 0.3.
n
Mean SD Length of 90% HPD Length of 95% HPD
6
0.2453
0.7386
0.8161
8
0.2399
0.7238
0.8040
10
0.2351
0.7111
0.7925
12
0.2309
0.6985
0.7818
14
0.2281
0.6913
0.7755
16
0.2248
0.6821
0.7678
18
0.2221
0.6748
0.7608
20
0.2197
0.6673
0.7546
22
0.2176
0.6624
0.7500
24
0.2153
0.6557
0.7439
26
0.2136
0.6505
0.7395
28
0.2119
0.6455
0.7352
30
0.2102
0.6410
0.7313
32
0.2085
0.6350
0.7257
34
0.2072
0.6313
0.7221
36
0.2057
0.6262
0.7176
38
0.2050
0.6240
0.7162
40
0.2036
0.6200
0.7123
STD
0.2600
θ=0.2
0.2500
θ=0.25
θ=0.3
Mean SD
0.2400
θ=0.4
0.2300
0.2200
0.2100
0.2000
0.1900
0.1800
6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Sample size
Figure 1. Estimated mean posterior standard deviation as a function of the number of patients
accrued to the trial for different target probabilities of DLT θ.
95% HPD
0.8400
θ=0.2
θ=0.25
0.8200
θ=0.3
θ=0.4
0.8000
Length
0.7800
0.7600
0.7400
0.7200
0.7000
0.6800
6
8
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Sample size
Figure 2. Estimated mean length of HPD of the posterior distribution of the MTD as a function of
the number of patients accrued to the trial for different target probabilities of DLT θ.