Dear Jacob,
On 05-Mar-02 Jacob Puliyel wrote:
> Ordinarily we say 'false positive' if test is positive but
> person is not diseased.
> Assume population of 100 persons. Suppose 10 tested positive to a
> screening test and of these only 5 had the disease then the
> false positive rate in 50%
>
> Why is it then, that when we look at a screening test like triple
> test or nuchal translucency in Downs syndrome, people talk of 80%
> detection for a 5% false positive rate meaning 5% of the population
> will be positive. (Wald NJ & Hackshaw AK, Prenat Diagn 1997;
> 17:821-9)
This is not what "5% false positive" means. The 5% is the frequency
with which the test gives a positive result when applied to a
patient without the disease, and it is independent of the proportion
in the population who have the disease, since it is defined only in
terms of the results for non-diseased patients.
Similarly, 80% detection rate means that the test gives a positive
result for 80% of cases when the patient does have the disease.
As you pointed out, the proportion of positives when the test
is applied to a population does depend on the proportion of the
population who have the disease. Say it is P with the disease,
(1-P) without it. Then you get 0.8*P + 0.05*(1-P) positives,
and 0.2*P + 0.95*(1-P) negatives (note that these add to 1).
The proportion of the positives who really have the disease
is (0.8*P)/(0.8*P + 0.05*(1-P)), which can be small if P is small.
e.g. P = 0.001 gives 0.0158, or less than 2 per cent of
positives have the disease. Rougly speaking, if the false
positive rate for the test is greater than the disease incidence,
then the majority of the positive results will be false positives
(this is only approximate, and assumes that false positive
rate for the test is small, and that detection rate for the
test is large).
I'm afraid I couldn't follow the arithmetical argument in
your example of Downs syndrome.
I hope this helps.
> Downs syndrome occurs 1 per 1000 deliveries.
> For purposes of simplicity let us assume 100 % pick up by the test.
> If there are 100,000 deliveries we can expect 5000 (5%)
> to be identified by the screening test.
> 100 among the 5000 identified by the test, will have Downs(1%).
> In other words 4900 of those identified by the test did not have
> disease and 100 had disease. The false positive rate is 4900/5000
> multiplied by 100 = 98% false positive.
> It does not sound like a good test if we say it has 98% false
> positvity.
> Is that we say the test has a 5% false positive rate?
> Sincerely
> Jacob M. Puliyel
> _____________________________
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Date: 05-Mar-02 Time: 20:58:07
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