Question

nfatal disease akin to leprosy. This test can identify patients before the onset of symptoms in order to begin early treatment. The group tested 50,000 people across different villages from the Stormlands and recorded their findings in the table below. The presence of the disease was validated by later onset of symptoms. Disease Present Disease Not Present Tested Positive 54 36 Tested Negative 9 49,901 Calculate the following, showing all calculations: 1) Disease Prevalence 2) Sensitivity 3) Specificity 4) Positive Predictive Value 5) Negative Predictive Value Would you consider this a good diagnostic test? Justify your answer.

Answer 1

The table is as follows:

	Disease Present	Disease Not Present	Total
Tested Positive	54	36	90
Tested Negative	9	49901	49910
Total	63	49937	50000

1) Disease prevalence = Disease Present/50000 = 63/50000 = 0.00126

2) Sensitivity = TP/(TP + FP) = 54/63 = 0.857

3) Specificity = TN/(TN + FN) = 49901/49937 = 0.9993

4) Positive Predicted Value = TP/(TP + FP) = 54/90 = 0.6

5) Negative Predicted Value = TN/(TN + FN) = 49901/49910 = 0.9998

Although the specificity of the test is quite high, a high sensitivity is really important in the above diagnostic test because if a person has the disease and the test identifies it, the treatment can begin early. But if sensitivity is low, the test won't identify the person has the disease (100 - 85.7)% = 14.3% of the time which is quite serious. Hence, we won't consider it a good diagnostic test. The sensitivity should be more than 95% for a fatal disease.