## A simple imperfect gold standard computation

## gilles.hunault "at" univ-angers.fr

## Reference

Exceeding the limits of liver histology markersShruti H. Mehta, Bryan Lau, Nezam H. Afdhal, David L. Thomas

Journal of Hepatology, Volume 50, Issue 1, January 2009, Pages 36-41.

## Programmed formula

D+ and D denote the true stage of disease; B+ and B indicate biopsy diagnosed disease;M denotes the value on a continuous scale of a marker;μ_{B:D}and γ_{B:D}are the sensitivity and specificity of the biopsyrelative to true disease, respectively; p_{D}is be the prevalence of true disease.

prob[ M>c | D+ ] and prob[ M>c | D- ] are the sensitivity of marker vs. truedisease at cut-off c and 1-specificity of marker vs. true disease at cutoff c.

For example, for a perfect marker panel where the sensitivity and specificitywith respect to true disease are 100% (AUROC = 1), a disease prevalence of 40%and the sensitivity and specificity of the biopsy vs. true disease both equal to 90%,the observed sensitivity and specificity of the marker panel vs. biopsy will beequal to 0.86 and 0.93, respectively.

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