Comparison of Estimates of False Negative Fraction (FNF) and Predictions when different Non-informative Priors are used in a two-stage Screening Test
Abstract
Summary measures of the performance of a diagnostic kit require all study subjects to be verified via a gold standard procedure. However the subjection of all subjects to such a procedure may not be possible due to associated risks, invasiveness and cost. In normal practice only those who register at least one positive test result undergo the confirmatory procedure. Over the recent past different models have been proposed to estimate the false negative fraction (FNF) in this partial verification scenario using Maximum Likelihood and Bayesian techniques. In the Bayesian framework different priors have been proposed for the parameter of a Bernoulli distribution. In this work we compared the estimates of FNF obtained when three different non-informative priors are assigned to the probability of an individual testing positive and further did some validation by comparing the predictions with the actual observed data. Results show that the estimates of the FNF under three selected non-informative priors are largely similar. We conclude that though different forms of non-informative priors for the parameter of the Bernoulli distribution are in existence they do lead to similar results. The choice of the non-informative prior to use does not really matter. However, it was found that the predictions based on each of the three selected non- informative priors did not fit the observed data quite well.
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