Recently, Brenner and Gefeller presented calculations in which the basic efficacy measures of diagnostic tests, sensitivity, specificity and likelihood ratios, vary strongly with disease prevalence. The calculations are based upon the situation where the disease classification is made by means of a dichotomization of a continuous trait subject to measurement error. In short, X denotes the true value of the continuous trait and is assumed to follow a Normal distribution with mean and variance 1. The disease is defined as present if X*C. An approximate measurement of X is given by Z"X#e, where e is the measurement error. It is assumed that X and e are independent and that e is Normally distributed with mean 0 and variance C . Hence, Z is Normally distributed with mean and variance 1# C . Without loss of generality the diagnostic cutpoint is chosen as C"0. To investigate the association between the efficacy measures of the diagnostic test based on the variable Z and the disease prevalence, the mean is varied between !3 and #3, producing populations with a range of disease prevalence from 0)1 per cent to 99)9 per cent. Within this model, the expected sensitivity and specificity as well as the expected predictive values can be expressed as direct functions of and C . Under the above assumptions it was shown that sensitivity, specificity, and likelihood ratios strongly vary with disease prevalence, and that the association of the predictive values with disease prevalence is lower than one would expect if sensitivity and specificity were constant between populations. These results are interpreted as a 'methodological framework for quantitative assessment of the importance of disease prevalence'.
Brenner and Gefeller address an important issue. Defining and diagnosing a disease by means of the same continuous trait observed with measurement error involves some problems. However, we think that the results of their calculations are misinterpreted in so far as the simple model used has no practical relevance. To investigate the accuracy of a diagnostic test, two classifications are required: one ideally based on the truth (for example, variable X of the paper) orif X is not observablebased on the gold standard (for example, variable Z of the paper) and one classification based on a diagnostic variable ½. In the model described above either the diagnostic variable ½ or the gold standard is missing. Hence, an evaluation study of a diagnostic test as described in the paper will never be performed in practice. The authors do not use the terms 'sensitivity'' and 'specificity' as it is usually the case, that is, with respect to a diagnostic test as an indicator for a known ('truth') or assumed (gold standard) disease status; they rather use these terms to describe the impact of measurement error of a quantitative test on its precision at the tails of the underlying distribution.
The fact that a diagnostic classification of patients depends on whether a continuous trait is above or below some defined cutpoint does not automatically mean that the disease itself is defined by means of a dichotomized continuum. For example, diabetes is often diagnosed by means of the 2 hour plasma glucose value (oral glucose tolerance test). Nevertheless, there is the idea that diabetes is inherently binary although the true state is not directly observable. For example, Engelau et al. define the true diabetes states theoretically by means of two components of a bimodal distribution fitted to 2 hour glucose values. The historical background for defining cutpoints of 2 hour plasma glucose values was to predict the development of microvascular complications associated with diabetes, not to define diabetes itself.
Most importantly, the formulation used by the authors that sensitivity and specificity strongly vary with the disease prevalence is misleading. At first, the event A"B is stochastically independent of B by definition. This means that the event 'test positive"disease present' is stochastically independent of the event 'disease present'. As sensitivity only refers to the subgroup of ill subjects one can get an unbiased estimate of