R ALGORITHM FOR BAYESIAN POWER MODEL OF CONTINUAL REASSESSMENT METHOD TO
Background: I read an article published in July 2013
issue of Anesthesiology Journal on
the above subject.
The journal is widely read, with a
high impact factor.
A, Gupta PK, Zohar S, Chevret S, Hopkins PM. Application
of the Continual Reassessment Method to
Dose-finding Studies in Regional Anesthesia: An Estimate of the ED95 Dose for 0.5%
Bupivacaine for Ultrasound-guided Supraclavicular Block. Anesthesiology. 2013;119 (1):29-35.
The article is currently available on
the Journal’s website for free download.
Please see the following link.
I had a few concerns about the
article and the code for the model, which I communicated to the statistical
co-author of the article, Dr. Sarah Zohar. On October 2, 2013, I
communicated with her through email requesting her to forward the R algorithm that was used for their analysis. In addition, I
requested clarification on some more issues.
I failed to get any
response from the author.
This prompted me to write a formal
letter to Anesthesiology pointing out
an error in Table 2 of the Kant et al
View my submission to the journal Anesthesiology dated 4th
My letter was rejected by
the journal, stating that they would publish a formal correction rather the letter and the
View decision of Anesthesiology dated 22nd November 2013
Looking at the article more closely,
I had a few more concerns related to prior
distribution of alpha. I brought these to the attention of the journal.
View my submission to Anesthesiology dated 28th
second letter was again rejected by the journal, stating that
In summary, errors/fallacies in the article by
Kant et al published in Anesthesiology
are as follows:
is a discrepancy between the data for cohort 3 in the first dose range in
Table 3 and that depicted in Figure 2 related to clinical responses. The
responses were shown as “Failure, Success” in the Table and as “Failure,
Failure” in the figure. When the data were cross- checked for validation
by independent software (bcrm package suited for
R), the results obtained by the authors could be validated when responses
for cohort 3 were Failure, Success” i.e. as depicted in the Table. In other
words, the representation of responses for cohort 3 in the Figure is
any Bayesian approach, the type and distribution of prior is of paramount importance, and they are not clear from
the methods described in the study. In the present context, the parameter
of interest is θ. Two types of
distributions i.e. gamma and lognormal are applicable as negative values
for θ are not compatible with the power model. The exact R algorithm was neither
described nor referred to a web source for readers to get an idea about
the required information about distribution of the prior. By the statement in methods “…where
θ is the model parameter to be estimated, considering as a random
variable with exponential prior ….” Kant et al appeared to use lognormal
prior.3 However, when Kant et al data were examined with a
recently (September 2013) published R package “bcrm’,
the results obtained by the authors could be reproduced when gamma prior
for θ with shape=1 and scale =1 were used for defining prior distribution
of θ, and not with the recommended lognormal prior (mean=0, SD=2).3
Hence the output and the entire sequence dose allocation in cohorts would
more area of concern in Kant et al study is the nomenclature used when
describing the scheme of CRM in Figure 1.
Although the current study is related to determining ED95
dose in post-marketing phase,
the nomenclature appears to be that related to dose-finding studies of
phase 1. For example, the statements in the figure used the phrase “posterior
toxicity probability”. The
nomenclature in this situation should have replaced the word “toxicity”
with “failure”. As described in methods, the study proceeds to compute an
updated probability of failure at each dose level and the failure
probability closest to the 0.05 target is chosen as the current ED95,
and given to the next cohort.
As of June 2014, Anesthesiology did not publish
any such correction. It is obvious that the journal did not care to acknowledge
contribution of diligent readers in recognizing the errors/fallacies of
publications in their journal.
In the meantime, I wanted several
interested people to know the scientific basis of Bayesian power model of
continual reassessment to determine ED95. Hence I presented a poster on the
subject at the Annual meeting of the International Anesthesia
Research Society (IARS) held in Montreal, Canada in May 2014.
R ALGORITHM FOR BAYESIAN POWER
MODEL OF CONTINUAL REASSESSMENT METHOD TO DETERMINE ED95
Srinivas Mantha, MD
of Anesthesiology and Intensive Care
Nizam’s Institute of Medical Sciences,
Hyderabad 500082 (India)