Dear all,
I thought I'd ask your views on the definition of prevalence in a receiver operator characteristic (ROC) scenario.
We have the 'optimal operating position' on the ROC curve as:
(FPC/FNC) x (P(D-))/(P(D+)) (1)
Where
P(D+) is the prior/pre-test probability of disease (i.e. prevalence of disease)
FPC= average cost associated with false positive diagnosis.
FNC= average cost associated with false negative diagnosis.
The 'cost' can be a financial cost or a health cost.
Also, when defining PPV often packages quote the formula as:
(Sensitivity x P(D+)) / ((Sensitivity x P(D+)) + ((1-Specificity)x(1-P(D+)))) (2)
My question is:
...... texts are quite vague as to the definition of P(D+) in (1) and (2) above. Some say that "depending on the method used to obtain the sample, P(D+) may or may not be estimated from the sample". Now, am I correct in thinking that , if our study is cross sectional, P(D+) can be estimated from the sample (if our sample is truly representative of the population) and, if our study is of a case-control type, then P(D+) must be the population prevalence of disease obtained from literature.
Thus, regardless of whether our study was cross sectional or case-control, if we had a population prevalence of disease from literature it could be used in (1) and (2).
Many thanks for your views on this,
Kind Regards,
Kim
Dr Kim Pearce PhD, CStat
Senior Statistician
Haematological Sciences
Institute of Cellular Medicine
William Leech Building
Medical School
Newcastle University
Framlington Place
Newcastle upon Tyne
NE2 4HH
Tel: (0044) (0)191 282 0451
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