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^th December 2013

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 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

Professor

Dept of Anesthesiology and Intensive Care

Nizam’s Institute of Medical Sciences,

Hyderabad 500082 (India)

smantha@srinivasmantha.com