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Experimental quantiles of epidemiological indices in case-control studies with non-differential misclassification.

The formulae for some typical epidemiological indices in case-control studies with non-differential misclassification are expressed in terms of two groups (alpha, beta) and (gamma, delta) of misclassification probabilities of exposure E and confounder C, respectively, and the initially estimated frequencies. The parameters alpha and beta denote the probability that subjects exposed to E are classified as non-exposed and the probability that non-exposed ones will be classified as exposed, respectively. Similarly, delta and gamma stand for the probability that those who have been exposed to C will be classified as non-exposed and the probability that non-exposed subjects are classified as exposed, respectively. The non-negativeness of the expressions for the 'true' frequencies in terms of the measured ones and the misclassification probabilities leads to the construction of feasibility regions for alpha, beta, gamma and delta. For a number of 'acceptable' 4-tuples (alpha, beta, gamma, delta), all of which lie inside these feasibility regions, a sequence of feasible values for an epidemiological index is determined, after employing a systematic procedure by means of a 'searching net' with increments delta alpha, delta beta, delta gamma, delta delta. The procedure serves to determine the characteristics of the (experimental) cumulative distribution function for any selected epidemiological index. The final stage in exploiting the structure of feasibility regions for alpha, beta, gamma and delta is to use the cumulative distribution function to calculate quantiles for the index associated with prescribed probabilities.