I wonder if you have any views on the following?
We shall consider the following decision matrix which crosstabulates positive and negative diagnostic test results and positive and negative observed results:
Non Event (-)
Non Event (-)
Total = n = a+b+c+d
P=Prevalence = (a+c)/n
Sensitivity = a/(a+c)
Specificity = d/(b+d)
We also define
NPV = d/(c+d) (2)
PPV can also be defined:
(Sensitivity x P) / ((Sensitivity x P) + ((1-Specificity)x(1-P))) (3)
NPV can also be defined
(Specificityx(1-P))/( (Specificity x (1-P)) + (P x(1-Sensitivity))) (4)
Now if P in (3) and (4) is (a+c)/n , then (3) and (4) are equivalent to (1) and (2) respectively.
However, what if the real prevalence of the disease (in the population) does not equal (a+c)/n ? i.e. if the value of (a+c)/n in our *study* does not equal the real pre-test probability (of the disease). Am I correct in thinking that we should always use formulas (3) and (4) to calculate PPV and NPV and input P as the real (population) prevalence of the disease (from literature) (rather than assuming that (a+c)/n is an accurate estimate of the real population prevalence of the disease)?
In one document I read that "NPV and PPV should only be used if the ratio of the number of patients in the disease group and the number of patients in the healthy control group used to establish the NPV and PPV is equivalent to the prevalence of the diseases in the studied population, or, in case two disease groups are compared, if the ratio of the number of patients in disease group 1 and the number of patients in disease group 2 is equivalent to the ratio of the prevalences of the two diseases studied". I am not clear as to the reasoning behind this and I'd appreciate any views.
Many thanks, in advance, for your opinion on these issues.
All the best,
Dr Kim Pearce PhD, CStat, Fellow HEA
Faculty of Medical Sciences Graduate School
Ridley Building 1
Queen Victoria Road
Newcastle Upon Tyne
Tel: (0044) (0)191 208 8142
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