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Blood, 15 August 2001, Vol. 98, No. 4, pp. 1275-1275
CORRESPONDENCE
To the editor:
Alternate designs for conduct and analysis of phase I
cancer
trials
We have read with interest the paper by Press et
al1 that reported a phase I/II trial of
iodine-131-tositumomab in combination with etoposide, cyclophosphamide,
and autologous stem cell transplantation for relapsing B-cell lymphomas. Objectives, design, and analysis of the trial are very accurately
reported, as well as the data (with the actual doses and toxicities of
all 52 treated patients). The main objective of the trial was to
estimate the maximum tolerated dose (MTD) of iodine-131-tositumomab,
defined as the dose associated with a 25% toxic rate. Design
and analysis of the trial were based on a grouped up-and-down scheme,
using cohorts of 4 patients. The principal advantage of this method is
its simplicity and its great ease of application. But we have some
ethical and statistical concerns with the use of such a design in
evaluating the MTD. First, the observed toxic rate associated with the estimated MTD was
0.174 (4 of 23), as reported in Table 3. But such a statistical conclusion involves uncertainty. It should have been informative to
give an estimate of the 95% confidence interval of the toxic rate
associated with MTD, which can be exactly computed from the paper
results at [0.05-0.388]. In addition, the estimated MTD was
empirically defined by the dose received by 20 patients (ie, 5 cohorts), provided that the lower limit of the 80% one-sided confidence interval associated with the observed toxicity rate did not
exceed the 25% target toxicity rate. This latter statistical restriction should be more clearly explained and justified. Second, these up-and-down designs poorly address ethical concerns (such
as minimal sample size) that have become a major issue in the conduct
and analysis of dose-ranging phase I oncology trials. Several new
approaches have been introduced that more explicitly address these
concerns. They are usually derived from the continual reassessment
method (CRM), a sequential Bayesian approach that allows, in defining
the dose to be administered to the next patient (or the next cohort of
patients), for incorporating evidence from previous experience and
previous experiments jointly with information accumulated along the
trial.2 Patients are entered sequentially, and the toxic
probability associated with each dose level is updated, using Bayes
formula together with the available information on doses and observed
toxicities. Each patient of the next cohort is then treated at the dose
level for which the updated toxicity rate is closest to the target
(here, 25%). It facilitates a commonsense interpretation of
statistical conclusions by allowing for direct probability statements,
such as the probability that the toxic rate of a dose level is in some
interval around the target. Moreover, this Bayesian (probability)
interval for an unknown toxic rate can be regarded as having high
probability of containing the unknown quantity, in contrast to a
confidence interval, which may strictly be interpreted only in relation
to a sequence of similar inferences that might be made in repeated
practice. Additionally, Bayesian approach enables calculations of
probabilities of future observations, from which several stopping rules
can be derived, allowing an easy and reproducible decision either to
continue patient accrual or to stop inclusions.3 We have
retrospectively applied the CRM to the available data on the 47 patients who were actually administered the tositumomab. Using either
23 Gy (dose 2) or 25 Gy (dose 3) as the initial guess of MTD (as
required by the Bayesian paradigm), we found from the updated
dose-toxicity relationship that 25 Gy was the estimate of the MTD, with
posterior toxic rate associated with MTD at 0.216 (95% Bayesian
interval: [0.108-0.352], Figure 1A) or
0.188 ([0.089-0.316], Figure 1B), respectively. Our findings confirm
the results of Press et al. Nevertheless, the sequential computation
after each cohort of 4 patients of stopping rules based on the
predictive distribution of the number of toxicities observed in the
next 4 patients would have yielded to an earlier stopping of the
accrual, at most after 36 patients.
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| Figure 1.
Updating of the initial guess of dose-toxicity
relationship after enrollment of 47 patients.
Data available on the 47 treated patients were modeled using CRM. The
results are presented as the initial guesses ( ) of probability of
toxicity at each dose level, updated ( ) after enrollment of 47 patients, using either 23 Gy (A) or 25 Gy (B) as the initial candidate
for MTD. Modeling used a 1-parameter logistic model with the scale
parameter fixed at 3 and a unit exponential prior for the shape
parameter.
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We conclude that sequential Bayesian approaches may provide useful
information on the dose-toxicity relationship so that its use in
planning further phase I/II trials should be encouraged among
investigators in hematology, as it has been done in other fields.4
Vincent Lévy, Sarah Zohar, Raphaël Porcher, and Sylvie Chevret
Correspondence: Vincent Lévy, Département de
Biostatistique et Informatique Médicale, Hôpital Saint
Louis, 1 avenue Claude Vellefaux, 75475 Paris cedex 10 and INSERM U444,
France; levy{at}dbim.jussieu.fr
References
1.
Press OW, Eary JF, Gooley T, et al.
A phase I/II trial of iodine-131-tositumomab (anti-CD20), etoposide, cyclophosphamide, and autologous stem cell transplantation for relapsed B-cell lymphomas.
Blood.
2000;96:2934-2942[Abstract/Free Full Text].
2.
O'Quigley J, Pepe M, Fisher L.
Continual reassessment method: a practical design for phase I clinical trials in cancer.
Biometrics.
1990;46:33-48[CrossRef][Medline]
[Order article via Infotrieve].
3. Zohar S, Chevret S. The continual reassessment method: comparison of
bayesian stopping rules for dose-ranging studies. Stat Med. In press.
4.
Fabre E, Chevret S, Piechaud JF, et al.
An approach for dose finding of drugs in infants: sedation by midazolam studied using the continual reassessment method.
Br J Clin Pharmacol.
1998;46:395-401[Medline]
[Order article via Infotrieve].
Response:
Statistical designs for clinical trials of
radioimmunotherapy
We agree with Vincent Levy et al that there are "newer"
designs for dose-finding studies that may prove preferable to the more
standard designs that are commonly employed, particularly when the more
standard designs define an MTD with as few as 3 to 6 patients. In
fact, we have ongoing dose-finding studies that utilize these
alternate designs. But we believe that the design that was employed in
the phase I/II trial of iodine-131-tositumomab in combination with
etoposide, cyclophosphamide, and autologous stem cell transplantation
for relapsing B-cell lymphomas that we reported had operating
characteristics that were more than acceptable, and this provided us
with sufficient confidence to implement this design in practice. Levy et al point out that the observed toxicity rate at the estimated
MTD involved uncertainty and that confidence intervals should have been
provided. Any estimate of an MTD will involve uncertainty, of course,
regardless of the method used. We chose not to provide estimates of a
confidence interval, however, as the observed toxicity rate at the
defined MTD would be biased since the dose-finding rules
restrict what could be observed in order to deem a dose as the MTD. The
restriction of requiring the MTD to have an associated lower limit to
the corresponding one-sided 80% confidence interval that does not
exceed 25% was largely based on heuristic grounds. Nonetheless, this
rule led to operating characteristics that were more than adequate for a wide range of assumed-true dose-response relationships. The greater
precision of the Bayesian confidence intervals reflects to a large
extent the information that has been added to the statistical model
through the choice of an initial guess at the MTD and a prior
distribution, even before any data have been collected. Whether this is
a strength or weakness of the Bayesian approach is a continuing
philosophical debate that need not be addressed here.
Theodore Gooley, Barry Storer, and Oliver W. Press
Correspondence: Oliver W. Press, Fred Hutchinson Cancer Research
Center, C-3-190, 1100 Fairview, Seattle, WA 98109
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Related Article in Blood Online:
-
A phase I/II trial of iodine-131-tositumomab (anti-CD20), etoposide, cyclophosphamide, and autologous stem cell transplantation for relapsed B-cell lymphomas
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Blood 2000 96: 2934-2942.
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