A Bayesian approach to estimate and validate the false negative fraction in a two-stage multiple screening test

In estimating sensitivity and specificity of a diagnostic kit it is imperative that all study subjects are verified via a gold standard procedure. However the application of such a procedure to all the study subjects may not be feasible due to associated cost, risk and invasiveness. As a result only a part of the study subjects receive the definitive assessment. The accuracy of a diagnostic kit can also be expressed in terms of its error rates. Our first objective is to estimate the false negative fraction (FNF) under partial verification in a particular case of a two-stage multiple screening test using a beta-binomial model and a Bayesian logistic model. The second objective is to validate the two models in order to determine which fits the data better.

We estimate the FNF from the above mentioned models using Bayesian approach. The validation of the models is based on their out-of-sample predictive capabilities.

For the bowel cancer data that was used in this study we found the median posterior estimate of the FNF, based on the beta-binomial model, to be 26.4% (95% credible interval: 0.123-0.650). The corresponding estimate based on the Bayesian logistic model was 23.3% (95% credible interval: 0.124-0.375). Validation results showed that the betabinomial model gave slightly better predictions compared to the Bayesian logistic model.

Estimation of the FNF can be done by adopting the Bayesian approach. Models fitted can be validated by comparing their performance in terms of their out-of-sample predicitve potential.