Medical Assessment

BPAS Screen Asthma No Asthma Total

Possible Asthma 30 TP 20 FP 50

No Asthma 10 FN 40 TN 50

Total 40 60 100

Suppose there was no association between a new cheap rapid screen test results(+,-) and true Asthma disease status(D,D^c). (i.e. the test was not able to differentiate between those with or without the disease). The marginal probabilities of test results: P(+)=50/100 and P(-)=50/100, and the marginal probabilities of true disease status: P(D)=40/100 and P(D^c=60/100. Then,how many true positives and true negatives among the sample of 100 do you expect the screen test to reveal if it was indeed independent of the disease status?What would the sensitivity and specificity be under the assumption of independence and compare them with BPAS Test results?

What statistical properties a good screening test must have?