**R ALGORITHM FOR BAYESIAN POWER MODEL OF CONTINUAL REASSESSMENT METHOD TO
DETERMINE ED95**

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.

Kant
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.

__http://journals.lww.com/anesthesiology/Fulltext/2013/07000/Application_of_the_Continual_Reassessment_Method.12.aspx__

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*
article.

View my submission to the journal *Anesthesiology* dated 4^{th}
October 2013

My letter was rejected by
the journal, stating that they would publish a formal correction rather the letter and the
authors’ reply.

View decision of *Anesthesiology* dated 22^{nd} 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 28^{th}
November 2013

My
second letter was again rejected by the journal, stating that

it would publish an author correction regarding that
article in an upcoming issue of the journal. View decision letter
of Anesthesiology dated 11 |

In summary, errors/fallacies in the article by
Kant et al published in *Anesthesiology*
are as follows:

- There
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
incorrect.
- In
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 be different. - One
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 ED
_{95}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 ED_{95}, 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

Professor

Dept
of Anesthesiology and Intensive Care

Nizam’s Institute of Medical Sciences,

Hyderabad 500082 (India)

www.srinivasmantha.com