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


  • L. M. Irwig,

    1. Institute for Biostatistics of the South African Medical Research Council, P.O. Box, 17555, Hillbrow, 2038, South Africa
    Current affiliation:
    1. Department of Public Health, Building A27, University of Sydney, New South Wales 2006, Australia (address for reprint requests and correspondence
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  • H. T. Groeneveld

    1. Department of Statistics, University of Pretoria, Brooklyn, Pretoria, South Africa
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  • Based on a thesis accepted for the degree of Doctor of Philosophy at the University of the Witwatersrand.


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.