It might be the only 200-plus-year-old statistical equation with a cult following, and an engineering consulting company thinks it can help streamline clinical trials for medical devices and drugs.

Named after its discoverer, the 18th century Presbyterian minister Thomas Bayes, the Bayes theorem is a statistical method for gauging the probability that something is true. Even if you don't know what it is, you're exposed to it almost daily. It's used, for example, in your email, to recognize and filter out spam. And if you use some older versions of Microsoft Word, a Bayesian-like code was developed to determine when a talking paperclip would pop up to offer advice.

Now, there's hope that the theorem can save device makers and drug companies money by making clinical trials briefer while involving fewer subjects than with traditional statistical methods.

The push comes in part from the U.S. Food and Drug Administration. In February, they published their long-awaited guidance giving medical device manufacturers the go-ahead to run clinical trials using the Bayesian method.

The problem is that Bayesian analyses tend to be slightly more complex than with traditional statistics, which is where Cambridge Consultants steps in.

A division of Altran, with its UK headquarters in Cambridge, England (true to its moniker, its U.S. office is in Cambridge, Mass.), the 50-year-old consulting company helps drug and medical device companies design medical devices and prepare for clinical trials. They also develop advanced radar systems for the defense industry, and it was in their work for signal processing that they saw the benefits of Bayesian techniques.

CONTINUAL INFERENCE

With their understanding of the method, Cambridge Consultants says it can cut costs of the most expensive part of drug or medical device development - the clinical trial. And it does this because unlike with traditional, or frequentist, statistics, it lets trial planners continually modify their trial plans as new data come in.

"The Bayesian approach considers the prior information and the trial results as part of a continual data stream, in which inferences are being updated each time new data become available. As data continue to accumulate, the uncertainty about the truth (derived from the prior distribution) decreases and predictions derived from the inference become more reliable," write Roger Sewell and Elisabeth Crowe, senior consultants at Cambridge Consultants, in their recent paper, "U.S. FDA Guidance on Using Bayesian Statistics in Medical Device Clinical Trials."

The theorem works, in part, by considering the background probability of whatever's being investigated.

For instance, at Los Alamos National Laboratory in Los Alamos, New Mexico, researchers use Bayesian methods to find out if someone has been exposed to radioactive plutonium on the job. Because these exposures almost never happen, even if a lab worker tests positive for exposure on a urine test, Bayesian analyses would suggest it's more likely due to a test error than actual contact with plutonium, unless the test results are unusually strong.

How does this help medical device trials? Elisabeth Crowe, co-author of the paper on Bayes, says it can help streamline clinical investigations. If the currently available data indicate an acceptable level of certainty of the device's efficacy and safety, the study can be ended sooner. This means recruiting fewer subjects and saving money.

And perhaps more important, it's more flexible.

"The limitations [of traditional studies] are once you planned your trial and started collecting data, you can't change the way you're analyzing depending on what you're learning," she tells DOTmed News. But with Bayes, companies can alter trial plans on the fly to adapt to new information.

And if the prior evidence was weak, that's OK, too. The Bayesian model "self-corrects."

"The model borrows strength from the prior information, and one gets to a conclusion much quicker, but if it looks like the current data are out of sync with the prior, these Bayesian hierarchical models figure that out, and in the process of figuring that out, end up requesting more patients -- basically, to try to figure out why the current data and the prior information are disagreeing," Dr. George Campbell, the head of the FDA's biostatistics division, tells DOTmed.

CAMBRIDGE CONSULTANTS' CONCERNS

Though the FDA believes Bayesian methods could be more cost-effective for some trials, they still require some traditional frequentist-type reporting, even for companies running Bayesian trials, a policy Sewell and Crowe want to see changed.

In essence, they want the FDA to reconsider requiring type 1 error reporting even in Bayesian models. Type 1 errors are "false positive" errors. That is, for medical device testing, a type 1 error would be a study suggesting the device works when it actually doesn't. (Or rather, it passes the statistical tests, even though it's all due to chance.) Typically, these error reports are not relevant for Bayesian models, Crowe says.

"The type 1 error rate is not the appropriate calculation for safeguarding the public; rather, it is the probability being high that the device is good given the data, a question which the Bayesian model answers directly," argue Crowe and Sewell.

But the FDA believes the risk of clearing a defective device is too great to not have these error reports included.

"If the trial concludes, for example, that the device is effective when it's not, that's an error which has implications in terms of the public health.... So it is of concern for the agency to not make those kinds of errors very often, and one way to keep track of that is to ask companies who are doing Bayesian trials... to simulate the type 1 error characteristics in their trial," says Dr. Campbell.

FUTURE OF BAYESIANISM

So far, the method is catching on, but slowly. Crowe says Cambridge Consultants, which only publicly announced their program a few weeks ago, is still working to line up a customer for it.

The FDA hasn't seen too many applications yet, either. An FDA employee recently looked over the figures, and found around 24 pre-market applications using Bayesian designs, admittedly a "relatively small portion of the trials we see," acknowledges Dr. Campbell. But still, it's something that's likely to become more popular.

"[There's] probably a trend to seeing a little more activity in this area," says Dr. Campbell.

But Bayesian analyses have only really taken off over the last 20 years, after mathematicians developed better algorithms, such as the Markov Chain Monte Carlo (MCMC) method, and computing power increased to where the data-dense problems could be tackled. "If you go back 10 or 20 years, there were big mainframe computers that have speeds comparable to people's laptops now," says Dr. Campbell. "We can do things now, that 20 years ago would have been very hard to do."

Further reading: "US FDA Guidance on Using Bayesian Statistics in Medical Device Clinical Trials," Roger Sewell and Elisabeth Crowe,
Regulatory Affairs Journal Devices, March 10th 2010: http://www.rajdevices.com/productsector/medicaldevices/US-FDA-Guidance-on-Using-Bayesian-Statistics-in-Medical-Device-Clinical-Trials-200786?autnID=/contentstore/rajdevices/codex/c09b6183-2c48-11df-9a1d-43f7b12171c7.xml