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In previous blogs, I promised that I would come back to the subject of superiority trials of antibiotics and the use of Bayesian statistical methods as the basis for designing such trials. I have been discussing this approach with a number of infectious diseases clinical trialists for the last year or two. But I am not a sophisticated enough statistician to actually put such a plan into practice. On the other hand, I think I now have enough of a basic understanding of the Bayesian method (first described in a posthumous publication by Thomas Bayes in 1763) to conceptualize the approach. The one article that was the most helpful to me was written by Roger Lewis and Robert Wears and published in 1993.

First, it is useful to understand the distinction between classical statistical approaches and the Bayesian approach. Basically, in the classical approach, we compare pre-existing hypotheses and attempt to rule out one of them – usually the so-called null hypothesis which is the negative of the hypothesis to be tested. Such an approach will require a specific population of patients to reach the appropriate statistical conclusion – accepting or rejecting the null hypothesis. Mostly, a positive study provides a low probability that the null hypothesis is true (P=<0.05). It does not provide information on the likelihood that the hypothesis that we are actually trying to test is true or not. We just reject the idea that it is not true. In taking care of patients, who thinks like that? We would all be going crazy dealing with double negatives.

Another problem with the classical approach is that the conclusion depends on exactly why you take certain steps within a trial. The example used by Lewis and Wears is the following. Suppose you expect a mortality of 30% for a given disease. After treating 10 patients you stop the trial because only one has died giving a mortality of 10%. But the P value is only 1.49. But – if the trial were run differently, a totally different conclusion might be drawn. Suppose the investigators decided that they would continue enrolling patients in the treatment arm until they had a death? In that case, the P value reflects the probability of having to have enrolled 10 patients before seeing the first death – P=0.04!

In complete contrast to the classical method, Bayesian approach actually allows one to calculate the probability of a defined outcome. This probability is expressed as a distribution over a population. In the Bayesian approach, prior knowledge is utilized to provide an a priori probability distribution for the effect under consideration. Usually, there is little prior knowledge, but in the case of many bacterial infections, we may have some advantage based on prior animal testing, human PK and approaches involving PK/PD.

Data is then acquired in a study or trial. Using the Bayesian approach, interim analyses are permitted and in fact may ultimately reduce the population required for study by increasing the probability that the effect being studied is real. These “posterior” estimates are therefore extremely useful and informative during the conduct of the trial.

In fact, Bayesian statistics closely resembles clinical reasoning. When a patient comes in with a set of co-morbidities and an acute infection, we try and assimilate this information to provide a probability of some outcome. The PORT score for determining risk of mortality in community acquired pneumonia that is commonly used to determine whether patients can be appropriately treated as outpatients or whether they require admission is just one example of this sort of approach. There are many others – when should one obtain which diagnostic tests to rule out a pulmonary embolism is another good example.

So how can we apply such an approach to superiority trials for antibiotics? That will have to await the next blog.