A least squares algorithm for estimating epidemiological indices in case-control studies with non-differential...

A least squares method for determining two integer 4-tuples representing, in a non-differentially misclassified case-control study with exposure factor E and confounder C, the 'true' case and control frequencies respectively, is presented. Each of the four integer frequencies in the 4-tuple related to cases represents the number of patients whose exposure status to the factors E and C is characterized by one of the four possible combinations of occurrence or non-occurrence of E and C, while quite analog remarks hold for the meaning of the elements of the 4-tuple which is related to controls. As an additional product of the relevant algorithm the two groups (alpha, beta) and (gamma, delta) of the 'true' misclassification probabilities referring to exposure E and confounder C respectively, are calculated. 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 final objective of the method is to use the above determined least squares substitutes of the true case and/or control frequencies in the formulas giving the epidemiological indices, in the hope to compute values for these parameters conforming as far as possible with the real ones. A numerical experiment illustrates such a use of the method and indicates the deviations which may be observed between epidemiological indices when no correction for misclassification is taken into account and those computed by means of the method outlined in this paper.