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Implications of the Bayesian Odds Model for Imputation Methods Design

In the event of a positive test result, the likelihood ratio for a dichotomous test must be greater than 1 as long as both test sensitivity and specificity are >0.5. Hence, appropriately selected, positive tests increase the posterior odds favoring pro-duct-AE causality regardless of the prior odds value. This implies that imputation screening would logically be directed toward finding cases in which the summary likelihood ratio for that case is greater than one. Screening for AEs likely to have a high prior odds due to, for example, a low non-causal incidence rate, is also an appealing strategy, but does not involve individual case diagnostic information, and is therefore not a form of imputation screening. Thus, an examination of the Bayesian odds model suggests that imputation screening methods are essentially procedures that look for "interesting" product-AEs by finding individual AE reports that possess one or more diagnostically relevant tests for causality.

In contrast, case series imputation methodology represents a pre-epidemiologic approach to the summarization of causal evidence in a product-AE case series. Such methods depend on both the prior odds (epidemiologic data) and the summary likelihood ratios (individual case testing) for all cases in the case series. In designing and using case series imputation methods, safety evaluators will need to focus both on the refinement of estimates affecting the prior odds (e.g. background incidence rates), as well as estimates for the sensitivity and specificity of tests for causality that were performed for all cases in the case series. Since empirical data pertaining to these quantities are often not available, case series imputation frequently becomes an exercise in which analogous and simulated data are used to support a product-AE causal argument (Lane et al., 1987; Ghajar et al., 1989).

Tests for Event Versus Tests for Causality

The Bayesian odds model underscores the fundamentally conditional nature of diagnostic testing in case series imputation procedures (Naranjo and Lanctot, 1991). Such testing is a two-step process in which diagnostic tests for an AE are first applied to establish a product-AE case, following which diagnostic tests for causality are interpreted (see Figure 18.1). Tests for the event (AE) establish reports as cases, while interpretation of tests for causality alter the conditional probabilities that pertain to at least two potential causes for such cases. In AE surveillance, two alternative causes, the monitored product versus all other (background) causes, are usually considered.

Both the identification of a product-event (acceptance of a report as a case), and the summarization of evidence concerning product versus non-product causality are quantitatively dependent on the sensitivity and specificity of the aggregate testing that was used by the evaluator for those purposes. Since summary tests for event are generally quite accurate, physician diagnoses that are provided in AE reports are often taken at face value, as long as reasonable supporting descriptions are available. In contrast, tests for causality can be more difficult to interpret, and frequently lack empirical validation data concerning their sensitivity and specificity. As a consequence, the results of tests for causality are usually carefully scrutinized by product monitors prior to their acceptance.

Tests for causality can be further divided into chronological tests (time to onset, dechallenge, rechallenge tests), tests based on clinical manifestations (features of the case that suggest product rather than background causation), and tests based on physical-chemical linkage of the AE with the monitored product (Kramer et al., 1979). Physical-chemical linkage can be directly accomplished, in particular, by high suspect product serum levels or the presence of a product moiety in pathologic specimens, but would also encompass immunologic testing such as in vitro challenge tests, skin tests, and antibody-related testing that have an appropriate positive predictive value for product causality. Risk factors could also be used as tests for causality, provided that their ability to differentiate product causality from other causes for the AE was adequate. Although the assumed sensitivities and specificities of tests for causality are difficult to formulate explicitly, the safety analyst should carefully weigh any evidence that might influence the derivation of a best estimate, since the summary likelihood ratio for each AE occurrence is a function of these quantities.

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