Exposure-response relationship for a dichotomized response when the continuous underlying variable is not measured.

Abstract

Radiological assessment of pneumoconiosis is an example of a dichotomized variable, namely one that is analysed as a binary response but in fact has an underlying continuum, which in this case is not measurable. Estimates of exposure-response relationships vary greatly for different observers of a dichotomized response variable because of random error of measurement and differences in the threshold implicitly chosen by each observer for categorizing cases. We present a method of using the biserial correlation coefficient and normal distribution theory to estimate exposure-response relationships at any required threshold for each observer. Exposure-response relationships can also be corrected for random observational error using the reliability coefficient, calculated as the tetrachoric correlation between repeat observations by readers.