Dichotomizing Screening Measures of Latent Traits at New Cut-Off Values: A Model-Based Approach from Summary Statistics

Screening measures and associated cut-off values are used across different fields of psychology in order to differentiate between two states, e.g., between pathological and non-pathological in clinical assessment. Their diagnostic accuracy can be examined with statistics such as sensitivity and specificity, and cut-offs are chosen to be optimal. However, these statistics are known to be prevalence-dependent. Cut-offs must not be transferred between populations blindly, but chosen in view of the population in question. Popular methods to this end usually require access to primary samples from that population. These might be hard and/or expensive to obtain for certain populations. Summary statistics from such samples are more easily available. In the present work, we (i) adapt a model-based method from the biometric literature to a psychological context which obtains statistics of diagnostic accuracy from a small set of summary statistics, introducing the bivariate normal model. We extend the method (ii) by allowing to compute diagnostic accuracy statistics for varying cut-offs to enable cut-off selection, and (iii) by addressing cases where even less information about the sample is available. To accommodate potentially skewed data obtained in psychological contexts (e.g., clinical questionnaires in sub-clinical populations), we further (iv) generalize the method to a bivariate skew-normal model. We study and compare statistical properties of the suggested method in three simulation studies. With two empirical examples, one examining screening instruments for psychopathy, the other for generalized anxiety disorder, we illustrate how the proposed methods estimate statistics of diagnostic accuracy from sample statistics and inform cut-off selection.