Accurate and concise interpretations of statistical analyses are crucial to the final presentation of clinical research.  In the last decade, a relatively unfamiliar form of statistical analysis, Bayesian analysis, has been used more often.  Many of us who cut our teeth on classical statistics in school have wondered what this Bayesian analysis stuff is all about.  In this brief discussion, I will try to shed a little light on the nature of Bayesian analysis in clinical research, give you a few reasons why this type of statistical analysis might be useful, and provide pointers toward additional information for those inclined to dig deeper.

Trained more years ago than I would like to admit, I was used to the vocabulary of classical (also called frequentist) statistics: mean , median, P value, and so on.  So, when the Bayesians begin to toss around terms like priors, posterior distribution, predictive probability, and so forth, it seemed to me like a whole new ball game.  What's more, I soon discovered that Bayesian methods permit the use of existing data in experimental design and, in fact, encourage the incorporation of accumulating data into the design while the trial is in progress.  This all seems pretty loosey-goosey to me after looking at P values and blinded trial designs for a long time. The Bayesian way of thinking about statistical analysis certainly seemed unfamiliar at a minimum, and looked in some ways almost to classical statistical analysis.

 

In truth, Bayesian methodology logic is quite pragmatic and almost intuitive.  An example may help illustrate the Bayesians' way of thinking about statistical analysis.

 

At the beginning of a coin-toss experiment, the Bayesian statistician has a belief about nature, the prior distribution: the probability of heads in a single flip is 0.5.  If we were to use a biased coin that does not yield heads 50% of the time, perhaps 70% of the trials yield heads.  The Bayesian thinks, "Wait! These data are unlikely, given my prior distribution of the probability of heads!  Incorporating these data gives me a posterior distribution in which the probability of heads is more like 0.65." The Bayesian statistician has "conditioned the prior distribution with the new data."  Now, this revised posterior distribution can serve as a prior distribution for subsequent trials. Ultimately, with enough data accumulation, the estimated values of the parameter of interest (as expressed in the posterior distribution), the probability of heads, will converge.

 

If Bayesian analysis allows us to do cool stuff like watch the experiment in progress, why hasn't it been used all along?

 

Bayesian methods are computationally intensive. In the years before the advent of computers, classical methods were doable, but it was impractical to carry out Bayesian methods. Classical frequentist methods could answer the questions that people were looking to probability and statistics to answer, without the need for extensive computation.

 

 

In this era of increasingly lengthy and costly clinical trials, the main motivation for applying Bayesian methods is to obtain efficiency. Because Bayesian methods can use preexisting data, as well as data being generated, the sample size and trial length can be adjusted after the start of the trial, saving time and money. Adaptive randomization, which allocates subjects to treatment arms that will most quickly bring the trial to a conclusion, can be incorporated into the design.  Similarly, the sample size can be adjusted while the study is in progress, allowing enrollment of the minimum number of subjects needed to reach an endpoint, based on the data from subjects already enrolled. In addition, Bayesian study designs can incorporate features that are difficult to achieve with conventional statistical analysis, such as factorial designs in which multiple treatment combinations are evaluated at the same time.

 

Why would we not want to use Bayesian methods? The main objection to Bayesian analysis is that it is subjective in its use of prior information to modify the estimates of parameters at the study's conclusion.  Use of priors is believed to open the door to bias, which is a particularly sensitive issue in clinical research. Bayesian statisticians often use uninformative prior distributions, or ones biased against a positive outcome, to provide comfort that bias is not creeping into the analysis.  Over the long haul, accumulating data will ultimately overwhelm the bias that existed in the priors. In fact, the ability to use prior information can be advantageous. Using different priors allows modeling of biases that may be preexisting, allowing one to actively cope with bias in the study design.

 

 

How does the FDA feel about Bayesian analyses in clinical studies supporting approval of a new product? The FDA is slowly accepting use of Bayesian methods.  The Center for Device and Radiologic Health has begun to review products based on Bayesian analyses, and several products have been approved based on Bayesian analyses. Currently, the FDA will use Bayesian analysis of trial data in its review process in conjunction with conventional frequentist analysis, and they have hired a cadre of Bayesian-trained statisticians. The Agency has expressed a commitment to move toward the more frequent use of Bayesian analysis, because of the efficiency Bayesian methods bring to the table and the FDA's "least burdensome approach" mandate.

 

About the Author
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6-month, full-time on-site contract in San Francisco

Title:  Clinical Content Specialist (Drug Information)-PUB00002158 Job: Publishing/Editorial

Primary Location: US-CO-Greenwood Village

Organization: Healthcare US

Schedule: Full time

Education Level: Bachelor's Degree (±16 years)

Job Type: Standard

Shift: Day Job

Employee Status: Regular

Description:

 

The healthcare business of Thomson Reuters provides insights -- information, benchmarks, and analysis--that enable organizations to manage costs, improve performance, and enhance the quality of healthcare. The Clinical Content Specialist is responsible for content creation, review, and maintenance, utilizing multiple complex sources of information and editorial technology.

Interested candidates may apply online at http://careers.thomsonreuters.com/.

Comments or questions? Email Susan at caldwell@biotechink.com.