Estimating measures of diagnostic accuracy when some covariate information is missing

Many biomedical data sets are concerned with relating the result of screening procedure(s) for a clinical event to the occurrence of that event. The effect of risk factors on measures of accuracy such as positive predictive value and negative predictive value is of great interest for clinicians. In this paper we propose a generic approach to estimate these measures of accuracy in the setting where an explanatory model has been fitted to the joint screening and event outcome data but information on one or more risk factors in the model is not available. We refer to these as conditional rates, i.e. rates conditioned on only a subset of risk factors. We argue that, based upon the joint distribution of the event outcome, the screening result and the risk factor occurrence, a formal expression for such a rate can be obtained. This expression is a function of model parameters and thus can be estimated once the model has been fitted. Inference within the Bayesian framework is particularly attractive since simulation based model fitting straightforwardly yields samples from the posterior distribution of any conditional rate of interest. We perform a simulation study to compare these estimated conditional rates with frequently used ad hoc estimates. Differences can be substantial. We also illustrate the proposed methodology to compute conditional positive predictive value for a screening mammography data set. The proposed approach is also applicable when there are multiple diagnostic screening test outcomes.