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On performance of the 3+3 design and its modified versions for dose finding in phase I clinical trials

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Journal of Data Science 15(2017), 115-128
ON PERFORMANCE OF THE 3+3 DESIGN AND ITS MODIFIED
VERSIONS FOR DOSE FINDING IN PHASE I CLINICAL TRIALS
M. Iftakhar Alam and Md. Ismail Hossain
Institute of Statistical Research and Training, University of Dhaka, Bangladesh
Abstract: Phase I clinical trial is the first step of testing drugs in humans. Clini-
cians often use the rule-based traditional 3+3 design to find the maximum tolerated
dose. Since the design has many potential limitations, some modified versions of it
are available in the literature to tackle those. However, no explicit comparison of
these modified designs exist. In addition of comparing these designs among them-
selves, this paper also compares them with the model-based continual reassessment
method. This is to see whether the modified versions can make a real difference with
the original 3+3 design. Also, we would like to see how the modified versions work
in comparison with the model-based continual reassessment method. Simulation
studies show that all these rule-based designs do not differ much among themselves
and also perform poorly compared to the continual reassessment method.
Key words: Dose finding studies, phase I trial, maximum tolerated dose, 3+3 de-
sign, continual reassessment method.
1. Introduction
Phase I clinical trials are designed to assess safety, tolerability and pharmacokinetics
of a drug. They are usually small, single-arm and open-label. For nontoxic agents,
phase I trials may start with healthy volunteers. But for cytotoxic agents in cancer
treatment, phase I trial starts with the patients for whom standard treatments have
failed. For cytotoxic agents, the highest possible dose is searched, since the benefit of
treatment is believed to increase with dose. Since toxicity also increases with dose, the
challenge is find a dose that will not expose patients to toxicity above the acceptable
level. Such a dose is known as the maximum tolerated dose (MTD).
Since the future of a drug solely depends on the early phases, a careful approach
is essential for dose escalation. A phase I design should be able to identify the MTD
accurately without exposing many patients to either subtherapeutic or toxic doses.
The designs for phase I are usually classified into two broad categories: rule-based and
model-based. The essence of the rule-based designs is that they use some pre-specified
rules to allocate doses to the patients. On the contrary, the model-based designs assume
parametric model and utilise all the available responses to select a dose for the next
patient. Some commonly used rule-based designs include the 3+3 design, Storer’s
up-an-down designs (Storer, 1989), accelerated titration design (Simon et al., 1997),
pharmacologically guided dose-escalation design (Collins et al., 1990), design using
isotonic regression (Leung and Wang, 2001), etc. The model-based designs include
the continual reassessment method (O’Quigley et al., 1990), escalation with overdose
control (Babb et al., 1998), etc. Although the designs above mostly talk about finding
the MTD in cancer treatments, they are equally applicable to the non-cancer drugs.
Although the model-based designs have strong properties, sometimes they get less
attention by the clinicians. According to Kairalla et al. (2012), logistic difficulties and
regulatory concern often limit the use of adaptive model-based designs. Ji and Wang
(2013) developed the modified toxicity probability interval (mTPI) design, which with
116 On Performance of the 3+3 Design and its Modified Versions
matched sample sizes, has lower risks of exposing patients with highly toxic doses than
the 3+3 design. Also, mTPI design is more able to identify the MTD than the 3+3
design. Chiuzan et al. (2015) developed a likelihood-based approach for calculating the
operating characteristics of the 3+3 design. The approach allows consistent inferences
to be made at each dose level, and evidence to be quantified regardless of cohort size.
The method is equally applicable to any design using algorithmic dose-finding rules.
Boonstra et al. (2015) numerically investigated the 3+3 and the continual reassessment
method to quantify how many patients are assigned to the true MTD using a 10 to 20
patient dose expansion cohort. They also found that such an expansion could improve
the identification of the true MTD substantially. Singh et al. (2010) utilised a Bayesian
logistic random effects model to analyze the data from a clinical trial. Liu and Dey
(2015) developed a method for determining sample size when comparing the means in
clinical trials. The essence of the method is that it does not require the pre-estimation
of variation from an external pilot study.
Le Tourneau et al. (2009) discussed some modified versions of the 3+3 design. It
is not clear from their discussion whether these modified versions work well over the
3+3 design. Although the continual reassessment method was compared with the 3+3
design by many authors, it is yet to be compared with the modified versions of the 3+3
design. In this paper, we compare the 3+3 design with its modified versions to find
the MTD. These rule-based designs are also compared with the model-based continual
reassessment method. The remainder of this paper is organised as follows. Section
2 describes the 3+3 design and its variations. The continual reassessment method is
introduced in Section 3. Section 4 discusses the settings of simulation study. Simulation
results comparing all the designs are presented in Section 5. Finally, the conclusion
appears in Section 6.
2. Traditional 3+3 Design and the Modified Versions
As mentioned in the previous section, the 3+3 is a traditional rule-based design
to find the MTD in a phase I clinical trial. Starting with a pre-specified set of doses
X={x(1), . . . , x(d)}, the 3+3 design first assigns the lowest dose x(1) to a cohort of three
patients. Escalation to dose x(2) is carried out if none of the three patients experiences
toxicity. The trial stops if at least two of the three patients have toxicities. The same
dose x(1) is given to three additional patients if one of the initial three patients has a
toxic response. Then, if only one of the six patients has toxicity, escalation to dose x(2)
is made; otherwise, the trial stops. In such a design, the MTD is usually defined as the
highest dose at which the observed toxicity rate is no more than 1/3. Some researchers
claim that the MTD should be the dose at which 2 or fewer toxicities in six patients
are observed. Therefore, it is recommended to check exactly six patients at the MTD,
which may sometimes require a single de-escalation in the 3+3 design.
Simplicity of implementation and safety concerns made the 3+3 design very popular
among the clinicians. The design can also provide some data on inter-patient variability
in pharmacokinetics, as the same dose is assigned to a cohort of patients at each stage
of a trial. However, in this design only information from the current cohort is used to
determine dose for the next cohort. The design is inefficient when the starting dose is
very low and the dose increment is moderate. In such a case, the design requires an
excessive number of steps to reach the desired dose. This in turn means that many
patients are treated at subtherapeutic doses and very few patients receive doses at or
near the MTD. Also, the maximum probability of toxicity that the MTD can have is
fixed once the definition is set. For instance, if we define the MTD as the dose at which
2 or fewer toxicities are observed in six patients, then the toxicity rate at that dose is
less than or equal to 0.33. So, we cannot find a MTD for any other choice of target
toxicity rate in the 3+3 design.
M. Iftakhar Alam and Md. Ismail Hossain 117
Some modified versions of the design, such as 2+4 and 3+3+3 are also available
to accelerate the dose escalation (Le Tourneau et al., 2009). In the 2+4 design, an
additional cohort of size 4 is added if one of the two individuals in the first cohort
shows toxicity. The same stopping rule as the traditional 3+3 design is followed here.
In the 3+3+3 design, the same dose is applied to an additional cohort of size 3 if two
individuals in the first two cohorts experience toxicity. The trial stops if three or more
individuals in three cohorts show toxicity. Although the modified versions are aimed at
accelerating the dose escalation, it is not clear from the discussion in the paper whether
they are completely better than the conservative 3+3 approach or even which is best
out of all these modified versions. No explicit comparison of the designs is available
elsewhere too.
3. Continual Reassessment Method
The continual reassessment method (CRM) (O’Quigley et al., 1990) is a model-
based approach for dose finding in phase I clinical trials. In contrast to the 3+3 design,
the method is capable to identify the MTD for any choice of the target toxicity rate.
Although the design initially carried out under the Bayesian framework, frequentist
extension to it is also available and is known as the continual reassessment maximum
likelihood (CRML) method (O’Quigley and Shen, 1996). Both the methods are ca-
pable to produce similar results. The use of CRML needs enough dose-response data
to facilitate the maximum likelihood estimation of the parameters. It is possible to
implement the method after accumulating information by either a rule-based design or
CRM. As at early stages of a trial data remains small, it is convenient to implement
a design under the Bayesian framework. Therefore, we plan to use the CRM in this
paper.
The initial CRM characterises the dose-toxicity relationship by simple one-parameter
parametric models, such as the hyperbolic tangent model, logistic model, or the power
model. In practical situations, the choice of a model is usually elicited from experts
familiar with drug development. A one-parameter model is easy to implement but
may not depict the dose-response relationship accurately. Since the paper is intended
to illustrate the methodology, the choice of a model carries little importance here. A
logistic model is often preferred because of its appealing S-shaped description of the
dose-toxicity relationship. Here we employ a two-parameter logistic model as shown
below.
ψ(x, θ) = exp(θ1+θ2x)
1 + exp(θ1+θ2x),
where θ= (θ1, θ2) is the vector of dose-response parameters and xis the dose given to
a patient. The parameter θ2is restricted to taking positive values to ensure increasing
dose-toxicity relationship. The original design starts by allocating the initial guess of
the MTD to the first patient. The dose to the each successive patient is allocated
according to the optimisation criterion to be discussed below. Assume that we are at
the kth stage in a trial, which means that kpatients have been treated with different
doses from X. Let xbe a k×1 dose vector with components xland let rbe a k×1
outcome vector with rlas the lth row (l= 1, . . . , k) representing the toxic outcomes
obtained from a patient. Then the likelihood function at the stage kcan be written as
Lk(θ|x,r)
k
Y
l=1
{ψ(xl,θ)}rl{1ψ(xl,θ)}1rl.
Since the available information at the early stages of a trial is small, the design
employs Bayesian approach to estimate the dose-response parameters θ. The posterior
118 On Performance of the 3+3 Design and its Modified Versions
means of the components of θ= (θ1, θ2) at the kth stage are obtained as
ˆ
θik =RΘθig(θ)Lk(θ|x,r)dθ
RΘg(θ)Lk(θ|x,r)dθ, i = 1,2,
where Θ is the parameter space and g(θ) is the prior distribution of the parame-
ters. For simplicity and rapid numerical computation of the posterior means, a bi-
variate uniform density is assumed for the joint distribution of the parameters. The
choice of u1< θ1< u2and u3< θ2< u4, gives a restricted parameter space as
˜
Θ = {θ:u1< θ1< u2, u3< θ2< u4}so that
g(θ) = 1
(u2u1)(u4u3),θ˜
Θ.
The probability of toxicity at each dose is updated at the end of stage kas
ˆ
ψik =ψ(x(i),ˆ
θk), i = 1,2, . . . , d.
That dose is chosen for the next patient for which the absolute difference between the
updated estimate of probability of toxicity and the target toxicity rate γis minimum.
That is,
xk+1 = arg min
x∈X |ψ(x, ˆ
θk)γ|.
The trial continues until a fixed sample size nis achieved and the MTD is taken
as the dose that would be allocated to patient n+ 1 if he were in the trial. The
CRM has many salient features. For instance, it treats more patients at doses near
the MTD and hence reduces the number of patients treated at low or ineffective dose
levels. It utilises all the available data to fit the dose-toxicity curve. However, the dose
assignment may be too aggressive. Success of a trial utilising the CRM depends on
proper choice of a dose-response model and the prior distribution of the parameter(s).
Unlike the rule-based designs, a computer program is in need to implement this design.
The CRM was not well-accepted in its original form due to safety considerations,
as it could expose patients to unacceptably toxic doses. Consequently, modifications
to the CRM were proposed to add additional safety measures, which are discussed
in Le Tourneau et al. (2009). Two of the modifications are included in this paper:
starting the trial with the lowest dose and increasing the dose by not more than one
pre- specified level at a time.
4. Simulation Settings
We have six dose-response scenarios to investigate in Figure 1. As we move from
Scenario 1 to 4, the steepness in the dose-toxicity curve decreases. Each scenario has
the set of six available doses as X={1,3,...,11}. The acceptable level of probability
of toxicity γis assumed to be 0.33. Doses 3, 5, 7 and 11 are the true MTDs in the
first four scenarios. The last two scenarios are slightly different in the way that the
true MTD is not available in X. That is, the doses at which probabilities of toxicities
are equal to the target, are in the mid way of two available doses in X. Such a set
of doses is not very unlikely to appear in the real trials. As indicated in the previous
section, the uniform prior distribution is used for the parameters θ. More specifically,
we consider a single parameter space ˜
Θ = {θ:4.3< θ1<2.3,0< θ2<1}for all
the scenarios. This parameter space has been chosen, as it has been found to allow a
wide range of dose-response scenarios, including the assumed ones. For instance, if we
choose values at the lower end, like θ1=4.2 and θ1= 0.1, we get a toxicity curve,
where the probabilities at various doses are almost zero. Similarly if we choose values
at the upper end, like θ1=2.4 and θ1= 0.99, the toxicity probabilities at the early
M. Iftakhar Alam and Md. Ismail Hossain 119
0 2 4 6 8 10 12
0.0 0.2 0.4 0.6 0.8 1.0
Scenario 1
Dose
Probability of Toxicity
0 2 4 6 8 10 12
0.0 0.2 0.4 0.6 0.8 1.0
Scenario 2
Dose
Probability of Toxicity
0 2 4 6 8 10 12
0.0 0.2 0.4 0.6 0.8 1.0
Scenario 3
Dose
Probability of Toxicity
0 2 4 6 8 10 12
0.0 0.2 0.4 0.6 0.8 1.0
Scenario 4
Dose
Probability of Toxicity
0 2 4 6 8 10 12
0.0 0.2 0.4 0.6 0.8 1.0
Scenario 5
Dose
Probability of Toxicity
0 2 4 6 8 10 12
0.0 0.2 0.4 0.6 0.8 1.0
Scenario 6
Dose
Probability of Toxicity
Figure 1: Dose-response scenarios for simulation study. The respective parameter
values are: Scenario 1, ϑ= (3.3,0.85); Scenario 2, ϑ= (3.3,0.51); Scenario 3,
ϑ= (3.3,0.37); Scenario 4, ϑ= (3.3,0.23); Scenario 5, ϑ= (3.3,0.43); and
Scenario 6, ϑ= (3.3,0.26). The dotted horizontal line indicates the target toxicity
rate.
doses are very high. So the interval that we consider as prior is wide enough to include
extreme dose-response scenarios. We can think of using other priors such as beta(1,1)
or beta-binomial distribution, since beta distribution is a conjugate prior distribution
of the binomial distribution. The beta(1,1) essentially leads to a constant value for the
probability distribution, something similar to the uniform distribution case. Similar
things happens with the beta-binomial distribution. Since such priors are eventually
similar to the uniform distribution, we can expect similar results like here in those
cases. Following the assignment of a dose to a patient, the binary response is generated
using the true probability of toxicity at that dose.
The 3+3 design and its modified versions are compared with the CRM for varying
values of nand it includes 15, 27, 36 and 48. Notice that the numbers are all multiple of
3, as 3+3 design and its modified versions utilise a maximum of 6 or 9 patients at each
stage to decide on a dose. The CRM stops after reaching nwhile the other designs may
stop early if they already have found the MTD. Sometimes they may fail to identify
the MTD even after reaching n. A trial then stops without any dose recommended for
the next phase. Each of the six scenarios is investigated through 1000 simulated trials
and a self written code in Ris used to produce the results.
5. Simulation Findings
The true MTD in the first scenario is 3. When n= 15, the designs 3+3, 2+4 and
3+3+3 can identify the true MTD in 25.3%, 22.1% and 19.6% of the trials, respectively.
The CRM can identify the dose 3 correctly in 93.4% of the trials. The identification of
the MTD does not change much, as nincreases in the 3+3 and 2+4 designs. However,
identification improves for the 3+3+3 design. As nincreases, the correct identification
of the MTD also increases for the CRM. The rule-based designs do not treat that many
patients at the MTD. However, majority of the patients are treated at the MTD during
120 On Performance of the 3+3 Design and its Modified Versions
the trials in the CRM.
Scenario 2 gets dose 5 as the true MTD. This dose is recommended in 60.8% of
the trials by the CRM. The corresponding percentages for the rule-based designs are
much smaller than this figure. Unlike the first scenario, the CRM is less efficient here
in finding the MTD and it is because of the location of the MTD. Fifteen patients
probably is not enough to learn the dose-response relationship much accurately in this
scenario. As nincreases, the correct identification of the MTD increases for the rule-
based designs and so does for the CRM. The 3+3 design is more efficient in finding
the MTD than the other two rule-based designs. Of the rule-based designs, the 3+3+3
design exposes less patients to the subtherapeutic doses. However, it exposes relatively
more patients to the toxic doses.
Dose 7 is the true MTD in Scenario 3. If nmoves from 15 to 27, the improvement
in the MTD selection is notable for the rule-based designs. However, the changes in
response to the other values of nare not that appreciable for the rule-based designs. On
the contrary, as nincreases, the identification of the MTD increases quite appreciably
for the CRM. The number of patients treated at the MTD in the rule-based designs is
not as good as that of the CRM.
It is important to mention that as our rule-based designs can stop without recom-
mending a MTD, the total percentage of the MTDs at each row in Tables 1-6 does
not make 100. But the total percentage of the patients is always 100 for the rule-
based designs, since only allocated doses in the simulated trials are considered in the
calculation.
The traditional designs perform worst in Scenario 4. Many trials recommend sub-
therapeutic doses as the MTD in the 3+3 and 2+4 designs. The 3+3+3 design does
not recommend lower doses as the MTD many times, but it fails to identify the MTD
accurately. The designs may stop without a MTD because of the restriction in n. Per-
haps more recruitment of patients in the trials could lead to a improved identification
of the MTD. The CRM is still doing very well even with the recruitment of 15 patients.
The next two scenarios differ from the rest in the way that the true MTD is not
available in the dose vector X. Investigating the behavior of a design for these scenarios
is important, as they are likely to happen in reality. The true MTD is 6 in Scenario 5
and it lies between 5 and 7. These two doses are identified as the MTD in most of the
trials by the CRM. The rule-based designs are not working as well as the CRM.
In the last scenario, the true MTD lies between doses 9 and 11. For the CRM,
these doses are selected as the MTD in 29.3% and 44.1% of the trials, respectively. The
selection of the MTD by the other designs are not as good as the CRM. The traditional
designs completely fail to identify the MTD if nis 15. However, if we increase the
number of patients, the designs become more able to identify the MTD.
For the various scenarios, it is clear that subtherapeutic doses appear as the MTD
in the 3+3 design in more than half of the trials. Similar thing happens with the 2+4
design. The 3+3+3 design is much better than the 3+3 and 2+4 designs in this aspect.
The CRM is the best in the way that it limits the occurrence of subtherapeutic doses
as the MTD considerably. Of all the rule based designs, highly toxic doses appear as
the MTD most often in the 3+3+3 design. So the 3+3 and 2+4 are more conservative
approaches than the 3+3+3 design. The CRM can identify the MTD more accurately
than the considered rule-based designs. Also, it appreciably limits the occurrence of
toxic doses as the MTD.
6. Conclusion
The whole purpose of this paper was to investigate the performance of the 3+3
design compared to that of its modified versions. To explore the differences, some
plausible dose-response scenarios have been studied in great detail. These rule-based
M. Iftakhar Alam and Md. Ismail Hossain 121
designs are also compared with the model-based CRM. The CRM has been found to
work nicely in Scenario 1. For small number of patients, the 3+3 design is better than
the other two rule-based designs. But when we are considering large number of patients
then the 3+3+3 design is doing comparatively better than 3+3 and 2+4 designs. In
the second scenario, the CRM is doing the best. There is not much difference across
the traditional designs. The CRM is working nicely in the remaining scenarios as well.
We have seen that as the true MTD moves to the upper end of dose region, the correct
identification of the MTD gradually decreases both for the CRM and the rule-based
designs.
The future of an investigational drug depends on the correct identification of the
MTD. Although the 3+3 design and its modified versions are easy to implement, they
behave very similarly. So not much improvement over the 3+3 design is possible by the
modified versions. Also, the modified designs do not have more attractive properties
than the CRM. The CRM is a model-based approach and it utilises all the available
information to decide on a dose level. Of course the accuracy of the CRM depends on
the location of the MTD. The CRM is much more capable in the identification of the
MTD than the modified versions of the 3+3 design. To conclude, the findings in the
paper can make the investigators careful in using the modified 3+3 designs.
Acknowledgements
The authors wish to thank the referees for their constructive comments, which have
led to a much improved paper.
Appendix A: Simulation Results
122 On Performance of the 3+3 Design and its Modified Versions
Table 1: The MTD selection and dose allocation for Scenario 1.
Dose
1 3 5 7 9 11
nDesign Toxicity probability : 0.08 0.32 0.72 0.93 0.99 1
15 3+3 % patients 39.5 47.6 12.7 0.2 0.0 0.0
% MTD 37.1 25.3 1.7 0.0 0.0 0.0
27 3+3 % patients 35.1 48.9 15.7 0.3 0.0 0.0
% MTD 49.2 27.1 1.1 0.0 0.0 0.0
36 3+3 % patients 33.1 49.5 17.0 0.4 0.0 0.0
% MTD 53.5 26.0 0.4 0.0 0.0 0.0
48 3+3 % patients 31.7 50.5 17.5 0.3 0.0 0.0
% MTD 55.7 24.8 0.8 0.0 0.0 0.0
15 2+4 % patients 37.1 45.5 16.7 0.8 0.0 0.0
% MTD 21.2 22.1 0.7 0.0 0.0 0.0
27 2+4 % patients 34.8 46.8 17.6 0.8 0.0 0.0
% MTD 49.1 23.4 1.2 0.0 0.0 0.0
36 2+4 % patients 33.4 46.1 19.4 1.0 0.0 0.0
% MTD 53.7 22.7 0.3 0.0 0.0 0.0
48 2+4 % patients 31.9 45.9 21.2 1.0 0.0 0.0
% MTD 54.9 22.7 0.5 0.0 0.0 0.0
15 3+3+3 % patients 27.4 52.0 20.2 0.4 0.2 0.0
% MTD 6.4 19.6 11.2 0.0 0.0 0.0
27 3+3+3 % patients 21.5 50.3 27.5 0.7 0.0 0.0
% MTD 26.3 30.3 11.4 0.2 0.0 0.0
36 3+3+3 % patients 19.3 49.4 30.5 0.8 0.0 0.0
% MTD 32.0 31.7 12.9 0.2 0.0 0.0
48 3+3+3 % patients 16.5 50.6 32.1 0.8 0.0 0.0
% MTD 34.5 33.4 13.8 0.2 0.0 0.0
15 CRM % patients 6.86 75.71 15.33 1.98 0.0 0.12
% MTD 0.8 93.4 5.8 0.0 0.0 0.0
27 CRM % patients 4.1 85.24 9.48 1.11 0.007 0.06
% MTD 0.3 98.3 1.4 0.0 0.0 0.0
36 CRM % patients 3.1 88.37 7.65 0.8 0.003 0.04
% MTD 0.7 98.5 0.8 0.0 0.0 0.0
48 CRM % patients 2.28 91.22 5.84 0.63 0.006 0.03
% MTD 0.1 99.8 0.1 0.0 0.0 0.0
M. Iftakhar Alam and Md. Ismail Hossain 123
Table 2: The MTD selection and dose allocation for Scenario 2.
Dose
1 3 5 7 9 11
nDesign Toxicity probability : 0.06 0.15 0.32 0.57 0.78 0.91
15 3+3 % patients 27.4 35.2 29.3 7.8 0.3 0.0
% MTD 11.4 23.5 17.9 1.3 0.0 0.0
27 3+3 % patients 20.4 31.3 34.2 13.2 0.9 0.0
% MTD 18.8 37.2 23.3 4.2 0.1 0.0
36 3+3 % patients 17.8 30.0 35.7 15.2 1.3 0.0
% MTD 18.7 41.3 26.5 3.7 0.0 0.0
48 3+3 % patients 15.9 28.0 37.4 17.2 1.5 0.0
% MTD 21.9 40.2 26.8 3.8 0.1 0.0
15 2+4 % patients 29.6 33.8 28.8 7.8 0.0 0.0
% MTD 4.7 11.1 10.3 0.0 0.0 0.0
27 2+4 % patients 20.8 29.9 31.7 15.3 2.2 0.1
% MTD 14.2 31.8 19.4 5.0 0.1 0.0
36 2+4 % patients 19.5 28.3 32.9 16.9 2.3 0.1
% MTD 21,0 35.6 22.2 3.8 0.2 0.0
48 2+4 % patients 18.8 27.6 33.8 17.5 2.2 0.1
% MTD 25.3 39.4 23.3 1.5 0.1 0.0
15 3+3+3 % patients 24.1 31.6 33.6 10.5 0.3 0.0
% MTD 1.0 2.7 12.8 7.9 0.0 0.0
27 3+3+3 % patients 14.6 20.9 35.9 26.1 2.5 0.0
% MTD 3.7 12.2 23.1 19.8 2.0 0.0
36 3+3+3 % patients 12.1 18.0 34.3 31.8 3.8 0.0
% MTD 7.4 17.7 24.2 22.7 3.0 0.0
48 3+3+3 % patients 10.5 15.8 34.0 34.9 4.7 0.1
% MTD 10.4 22.6 27.4 20.8 3.1 0.1
15 CRM % patients 6.67 28.93 44.29 16.25 1.58 2.29
% MTD 0.0 24.7 60.8 13.9 .4 0.2
27 CRM % patients 3.70 25.69 53.93 14.23 1.12 1.34
% MTD 0.0 20.3 71.6 8.0 .1 0.0
36 CRM % patients 2.78 23.01 59.15 13.10 0.95 1.00
% MTD 0.0 15.5 78.1 6.4 0.0 0.0
48 CRM % patients 2.08 21.77 64.69 10.01 0.68 0.76
% MTD 0.0 13.5 82.8 3.7 0.0 0.0
124 On Performance of the 3+3 Design and its Modified Versions
Table 3: The MTD selection and dose allocation for Scenario 3.
Dose
1 3 5 7 9 11
nDesign Toxicity probability : 0.05 0.10 0.19 0.33 0.51 0.68
15 3+3 % patients 24.4 28.5 29.2 15.7 2.2 0.0
% MTD 4.5 13.1 15.3 6.7 0.0 0.0
27 3+3 % patients 16.3 21.0 28.1 24.6 9.0 1.0
% MTD 6.5 21.5 28.1 21.9 5.8 0.2
36 3+3 % patients 14.3 18.9 26.8 26.5 11.8 1.8
% MTD 9.4 23.1 29.8 23.0 5.2 0.4
48 3+3 % patients 12.8 17.0 25.9 28.5 13.8 2.0
% MTD 8.5 24.5 34.2 22.9 5.6 0.1
15 2+4 % patients 28.4 31.0 28.4 12.3 0.0 0.0
% MTD 2.9 7.3 9.0 0.0 0.0 0.0
27 2+4 % patients 17.8 20.9 26.9 22.7 9.8 1.9
% MTD 6.5 13.3 22.4 16.7 4.0 0.5
36 2+4 % patients 15.7 19.9 25.1 25.1 12.0 2.2
% MTD 9.4 23.2 28.0 17.3 4.4 0.7
48 2+4 % patients 14.2 18.9 25.0 25.9 13.6 2.5
% MTD 11.1 25.6 32.6 18.2 3.8 0.7
15 3+3+3 % patients 23.5 26.9 30.0 17.4 2.1 0.0
% MTD 0.2 1.1 3.5 5.7 0.0 0.0
27 3+3+3 % patients 13.2 15.8 21.6 29.9 17.3 2.2
% MTD 0.8 3.4 7.7 18.5 15.9 1.6
36 3+3+3 % patients 10.5 12.8 18.4 29.5 23.7 5.0
% MTD 2.7 5.8 11.2 20.5 21.0 5.4
48 3+3+3 % patients 8.7 11.0 15.8 28.2 29.0 7.3
% MTD 2.8 8.8 15.4 23.0 24.1 7.2
15 CRM % patients 6.67 10.88 31.41 29.24 11.24 10.57
% MTD 0.0 6.4 30.1 39.8 20.6 3.1
27 CRM % patients 3.82 39.71 31.77 17.88 4.44 2.38
% MTD 0.0 3.2 27.3 55.2 13.2 1.1
36 CRM % patients 2.78 5.59 29.97 45.08 12.13 4.46
% MTD 0.0 1.0 24.6 64.1 10.0 0.3
48 CRM % patients 2.08 5.16 27.95 49.93 11.46 3.42
% MTD 0.0 0.5 20.3 71.1 8.1 0.0
M. Iftakhar Alam and Md. Ismail Hossain 125
Table 4: The MTD selection and dose allocation for Scenario 4.
Dose
1 3 5 7 9 11
nDesign Toxicity probability : 0.04 0.07 0.1 0.16 0.23 0.32
15 3+3 % patients 23.3 24.7 25.5 19.4 7.1 0.0
% MTD 3.3 6.1 6.9 6.5 0.0 0.0
27 3+3 % patients 14.7 15.8 18.0 20.6 20.2 10.6
% MTD 3.4 5.2 10.7 18.8 17.5 6.2
36 3+3 % patients 13.1 14.5 17.0 19.8 21.2 14.3
% MTD 2.5 5.7 11.2 17.7 14.9 4.7
48 3+3 % patients 12.5 13.4 16.0 19.1 22.2 16.8
% MTD 2.9 5.2 11.2 16.9 13.6 2.3
15 2+4 % patients 27.6 29.0 27.3 16.0 0.0 0.0
% MTD 2.0 3.2 4.6 0.0 0.0 0.0
27 2+4 % patients 16.4 17.6 19.6 20.4 17.1 9.0
% MTD 2.0 5.0 9.8 12.0 11.2 5.3
36 2+4 % patients 14.3 15.2 17.3 20.5 19.7 13.1
% MTD 1.7 4.7 10.1 14.7 13.8 8.2
48 2+4 % patients 13.2 14.3 16.8 19.7 21.1 14.9
% MTD 1.5 5.5 11.1 15.7 15.4 3.5
15 3+3+3 % patients 22.7 24.4 25.9 20.2 6.8 0.0
% MTD 0.2 0.3 0.6 1.5 0.0 0.0
27 3+3+3 % patients 13.4 14.4 15.9 19.0 21.9 15.4
% MTD 0.0 0.5 0.9 2.3 4.7 6.2
36 3+3+3 % patients 11.7 12.5 14.1 16.8 22.0 22.8
% MTD 0.0 0.5 1.4 3.0 5.1 4.4
48 3+3+3 % patients 11.1 12.1 13.5 16.1 21.3 26.0
% MTD 0.1 0.4 1.4 2.7 2.8 1.8
15 CRM % patients 6.67 4.13 15.49 17.81 12.36 43.53
% MTD 0.0 0.5 5.5 11.1 23.2 59.7
27 CRM % patients 3.70 2.74 10.00 14.7 16.80 52.05
% MTD 0.0 0.2 1.5 8.9 21.8 67.6
36 CRM % patients 2.78 2.00 7.01 11.57 17.52 59.12
% MTD 0.0 0.1 0.6 3.5 22.9 72.9
48 CRM % patients 2.08 1.41 5.81 9.8 19.41 61.49
% MTD 0.0 0.0 0.3 3.0 21.3 75.4
126 On Performance of the 3+3 Design and its Modified Versions
Table 5: The MTD selection and dose allocation for Scenario 5.
Dose
1 3 5 7 9 11
nDesign Toxicity probability : 0.05 0.12 0.24 0.43 0.64 0.81
15 3+3 % patients 25.6 30.4 30.3 12.5 1.3 0.0
% MTD 6.4 16.3 19.0 4.5 0.0 0.0
27 3+3 % patients 17.8 25.0 32.3 20.7 4.0 0.2
% MTD 10.2 30.4 32.1 11.7 1.1 0.0
36 3+3 % patients 15.7 23.0 32.1 23.9 5.0 0.3
% MTD 14.4 31.9 31.9 14.0 0.7 0.0
48 3+3 % patients 14.3 20.8 33.1 25.7 5.9 0.3
% MTD 14.0 34.6 32.8 13.1 0.8 0.0
15 2+4 % patients 28.7 32.4 28.7 10.2 0.0 0.0
% MTD 3.6 9.5 10.6 0.0 0.0 0.0
27 2+4 % patients 19.0 24.7 28.8 20.7 6.1 0.7
% MTD 8.0 24.5 22.7 11.1 1.6 0.0
36 2+4 % patients 17.0 23.4 29.9 22.4 6.6 0.7
% MTD 13.6 28.8 30.9 9.1 1.2 0.0
48 2+4 % patients 15.9 22.5 29.8 23.2 7.8 0.8
% MTD 16.3 34.5 30.8 9.6 1.3 0.1
15 3+3+3 % patients 23.4 28.7 31.9 15.0 1.0 0.0
% MTD 0.3 2.1 7.3 7.7 0.0 0.0
27 3+3+3 % patients 13.8 17.8 27.4 31.2 9.5 0.4
% MTD 2.0 7.0 13.3 22.9 8.4 0.1
36 3+3+3 % patients 11.1 14.3 23.8 36.3 13.5 1.0
% MTD 3.5 10.5 19.3 24.9 13.4 1.1
48 3+3+3 % patients 9.4 12.8 21.7 37.7 17.0 1.3
% MTD 4.5 15.4 25.4 23.0 13.5 1.6
15 CRM % patients 6.67 16.09 40.82 25.98 5.34 5.1
% MTD 0.0 10.5 52.1 32.8 4.2 0.4
27 CRM % patients 3.70 13.78 45.71 29.75 4.68 2.98
% MTD 0.0 7.2 54.2 37.1 1.5 0.0
36 CRM % patients 2.78 11.16 48.83 31.64 3.54 2.04
% MTD 0.0 3.5 59.1 36.4 1.0 0.0
48 CRM % patients 2.08 9.49 51.72 32.46 2.69 1.56
% MTD 0.0 2.1 62.5 35.3 0.1 0.0
M. Iftakhar Alam and Md. Ismail Hossain 127
Table 6: The MTD selection and dose allocation for Scenario 6.
Dose
1 3 5 7 9 11
nDesign Toxicity probability : 0.05 0.07 0.12 0.19 0.28 0.39
15 3+3 % patients 23.7 25.3 26.2 18.9 5.8 0.0
% MTD 3.5 7.2 9.8 7.2 0.0 0.0
27 3+3 % patients 14.9 16.3 19.9 22.2 19.2 7.5
% MTD 3.6 8.0 16.3 21.1 17.6 3.8
36 3+3 % patients 12.8 14.5 17.5 21.6 22.3 11.4
% MTD 3.3 6.9 17.5 21.6 16.8 5.6
48 3+3 % patients 12.0 13.5 16.6 21.5 23.7 12.7
% MTD 3.5 7.8 17.9 22.7 14.3 2.3
15 2+4 % patients 27.5 29.3 27.5 15.7 0.0 0.0
% MTD 1.7 4.4 5.6 0.0 0.0 0.0
27 2+4 % patients 16.5 18.1 20.1 21.2 16.4 7.6
% MTD 2.1 7.8 10.8 15.3 10.9 4.3
36 2+4 % patients 14.3 15.5 18.3 21.7 19.7 10.5
% MTD 3.8 6.4 14.2 19.1 15.8 6.4
48 2+4 % patients 12.9 14.5 17.9 21.8 20.9 12.0
% MTD 3.2 8.8 17.7 20.2 15.0 4.5
15 3+3+3 % patients 22.8 24.9 26.8 19.9 5.6 0.0
% MTD 0.2 0.3 1.5 2.1 0.0 0.0
27 3+3+3 % patients 13.0 14.5 16.7 20.8 22.6 12.5
% MTD 0.1 0.6 1.4 4.3 10.7 8.1
36 3+3+3 % patients 11.2 12.1 13.9 17.7 24.1 21.0
% MTD 0.1 0.6 2.9 6.6 9.8 8.7
48 3+3+3 % patients 9.8 10.9 13.1 16.0 24.1 26.1
% MTD 0.2 1.6 3.1 5.7 7.3 4.5
15 CRM % patients 6.67 5.83 17.65 19.96 13.92 35.97
% MTD 0.0 1.6 6.9 18.1 29.3 44.1
27 CRM % patients 3.70 3.3 12.56 19.94 21.6 38.9
% MTD 0.0 0.9 3.6 16.6 36.8 42.1
36 CRM % patients 2.78 2.74 10.52 19.08 27.53 37.35
% MTD 0.0 0.2 1.8 14.3 44.6 39.1
48 CRM % patients 2.08 1.96 7.11 16.79 32.97 39.09
% MTD 0.0 0.1 0.8 9.2 49.5 40.4
128 On Performance of the 3+3 Design and its Modified Versions
References
Babb, J., A. Rogatko, and S. Zacks (1998). Cancer phase I clinical trials: Efficient dose
escalation with overdose control. Statistics in Medicine 17 (10), 1103–1120.
Boonstra, P. S., J. Shen, J. M. Taylor, T. M. Braun, K. A. Griffith, S. Daignault, G. P.
Kalemkerian, T. S. Lawrence, and M. J. Schipper (2015). A statistical evaluation
of dose expansion cohorts in phase I clinical trials. Journal of the National Cancer
Institute 107 (3), dju429.
Chiuzan, C., E. Garrett-Mayer, and S. D. Yeatts (2015). A likelihood-based approach
for computing the operating characteristics of the 3+ 3 phase I clinical trial design
with extensions to other A+ B designs. Clinical Trials 12 (1), 24–33.
Collins, J. M., C. K. Grieshaber, and B. A. Chabner (1990). Pharmacologically guided
phase I clinical trials based upon preclinical drug development. Journal of the Na-
tional Cancer Institute 82 (16), 1321–1326.
Ji, Y. and S.-J. Wang (2013). Modified toxicity probability interval design: A safer
and more reliable method than the 3+ 3 design for practical phase I trials. Journal
of Clinical Oncology 31 (14), 1785–1791.
Kairalla, J. A., C. S. Coffey, M. A. Thomann, and K. E. Muller (2012). Adaptive trial
designs: A review of barriers and opportunities. Trials 13 (1), 145.
Le Tourneau, C., J. J. Lee, and L. L. Siu (2009). Dose escalation methods in phase I
cancer clinical trials. Journal of the National Cancer Institute 101 (10), 708–720.
Leung, D. H.-Y. and Y.-G. Wang (2001). Isotonic designs for phase I trials. Controlled
Clinical Trials 22 (2), 126–138.
Liu, J. and D. K. Dey (2015). A type of sample size planning for mean comparison in
clinical trials. Journal of Data Science 13 (1), 115–125.
O’Quigley, J., M. Pepe, and L. Fisher (1990). Continual reassessment method: A
practical design for phase I clinical trials in cancer. Biometrics 46 (1), 33–48.
O’Quigley, J. and L. Z. Shen (1996). Continual reassessment method: A likelihood
approach. Biometrics 52 (2), 673–684.
Simon, R., L. Rubinstein, S. G. Arbuck, M. C. Christian, B. Freidlin, and J. Collins
(1997). Accelerated titration designs for phase I clinical trials in oncology. Journal
of the National Cancer Institute 89 (15), 1138–1147.
Singh, K., A. Bartolucci, and S. Bae (2010). The Bayesian multiple logistic random
effects model for analysis of clinical trial data. Journal of Data Science 8 (3), 495–504.
Storer, B. E. (1989). Design and analysis of phase I clinical trials. Biometrics 45 (3),
925–937.
M. Iftakhar Alam
Institute of Statistical Research and Training
University of Dhaka
Dhaka-1000, Bangladesh
iftakhar@isrt.ac.bd
Md. Ismail Hossain
Institute of Statistical Research and Training
University of Dhaka
Dhaka-1000, Bangladesh
ihossain1@isrt.ac.bd
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