Abstract
BackgroundVarious methods exist for statistical inference about a prevalence that consider misclassifications due to an imperfect diagnostic test. However, traditional methods are known to suffer from truncation of the prevalence estimate and the confidence intervals constructed around the point estimate, as well as from under-performance of the confidence intervals’ coverage.MethodsIn this study, we used simulated data sets to validate a Bayesian prevalence estimation method and compare its performance to frequentist methods, i.e. the Rogan-Gladen estimate for prevalence, RGE, in combination with several methods of confidence interval construction. Our performance measures are (i) error distribution of the point estimate against the simulated true prevalence and (ii) coverage and length of the confidence interval, or credible interval in the case of the Bayesian method.ResultsAcross all data sets, the Bayesian point estimate and the RGE produced similar error distributions with slight advantages of the former over the latter. In addition, the Bayesian estimate did not suffer from the RGE’s truncation problem at zero or unity. With respect to coverage performance of the confidence and credible intervals, all of the traditional frequentist methods exhibited strong under-coverage, whereas the Bayesian credible interval as well as a newly developed frequentist method by Lang and Reiczigel performed as desired, with the Bayesian method having a very slight advantage in terms of interval length.ConclusionThe Bayesian prevalence estimation method should be prefered over traditional frequentist methods. An acceptable alternative is to combine the Rogan-Gladen point estimate with the Lang-Reiczigel confidence interval.
Highlights
Various methods exist for statistical inference about a prevalence that consider misclassifications due to an imperfect diagnostic test
The confidence interval for the slope estimate, (0.938, 0.941), does not include the diagnonal revealing that overall the Bayesian estimator performs slightly better than the Rogan-Gladen estimate
A linear regression analysis for both estimators suggests that the residual estimation error after adjusting prevalence estimates for diagnostic sensitivity and specificity does depend on the application scenario as represented by our design variables for sample sizes, true prevalence, true sensitivity and true specificity, but that the effects are only very minor for the whole model, the individual parameters, as well as their first-order interactions
Summary
Various methods exist for statistical inference about a prevalence that consider misclassifications due to an imperfect diagnostic test. Flor et al BMC Public Health (2020) 20:1135 have derived an estimator for prevalence with adjustment for diagnostic misclassification [4]. This approach requires that unbiased estimates of the diagnostic accuracy be available for the given application (reviewed in [5]). We present a comparison of Bayesian and frequentist methods for prevalence estimation taking into account all relevant uncertainties associated with the study- and meta-data, e.g. the diagnostic test performance. The probability that a test applied to a random individual from such a population yields a positive result is called the apparent prevalence, AP = Pr T+ = Pr T+|D+ Pr D+ + Pr T+|D− Pr D−
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