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# Sensitivity, Specificity, Predictive for a Positive Test

The following table shows results obtained in a new screening test for disease X used on 10,000 persons based on a serum marker. The cut off level was a serum marker value of 180mg or above as positive for this disease:

Results of screening test for Disease X

Test result Disease present Disease absent Total
Positive 34 20 54
Negative 116 9830 9946
Total 150 9850 10000

a.Calculate sensitivity, specificity, positive and negative predictive value for a positive test.

b) When screening cut off point was lowered to a value of 130 instead, there were 164 persons who then tested positive. Of these 98 were false positives. Remember that 9850 in total did not have the disease. Calculate sensitivity, specificity, positive and negative predictive value for a positive test.

c. What effect do you get from lowering the screening cut off point in terms of false-positive and false-negative findings and predictive value of a positive test?

d. How does this affect the sensitivity?

e. If the cut off is set higher than 180 then how would you expect this to affect the specificity and sensitivity of the test?

f. What effect this will have on the number of false-negative and false-positive findings?

g. Assuming the prevalence of disease X increases from 1.5% to 2%. Given the same sensitivity and specificity (as in part a) calculate the predictive value of a positive test.

#### Solution Preview

The following table shows results obtained in a new screening test for disease X used on 10,000 persons based on a serum marker. The cut off level was a serum marker value of 180mg or above as positive for this disease:

Results of screening test for Disease X

Test result Disease present Disease absent Total
Positive 34 20 54
Negative 116 9830 9946
Total 150 9850 10000

a.Calculate sensitivity, specificity, positive and negative predictive value for a positive test.

Sensitivity=34/150=0.2267
Specificity=9830/9850=0.9980
Positive predictive value=34/54= 0.6296
negative predictive value= 9830/9946=0.9883

b) When screening cut off ...

#### Solution Summary

The solution gives detailed steps on calculating sensitivity, specificity, positive and negative predictive value for a given postive test under various conditions. All formula and calcuations are shown and explained.

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