Summary
Objectives:
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.
Methods:
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.
Results:
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 beta-binomial
model gave slightly better predictions compared to the Bayesian logistic model.
Conclusions:
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.
Keywords
Bayesian analysis - MCMC - prediction - sensitivity - validation
