Random models for margins of a 2 x 2 contingency table and application to pharmacovigilance

The identification of new adverse drug reactions is often tricky. For a given case, the relationship between drug exposure and symptom occurrence is usually questionable. It could be investigated statistically from a series of drug-event association cases with an independence test between the two variables. Analysing the related 2 x 2 contingency table obviously requires knowledge of its margins. However this information is often not available. We develop a calculation of the P-value by choosing some random models for the unknown margins. Under the hypothesis of independence, a negative binomial distribution for the frequency of the drug-event association cell is obtained, exactly or approximately. This method allows investigation of the causal relationship when some parameters, as incidence of the symptom in the population, are uncertain. An example is presented.