# SS10 – Final Q

Great!

1. Test with 95% specificity, 90% sensitivity, incidence 2%:

Let’s use a population of 10000. Here is a contingency table version:

Overall accuracy = (Test P + Test N) / (total) = 180+9310 / 10000 = 94.9%

2. 90% specificity, 95% sensitivity, incidence 2%:

Incidence remains the same. However not we detect 95% of the 200 true positives -= 190 TP, but only 90% of the true negatives = 8820 TN.

Overall Accuracy = 190+8820/ 10000 = 90.1%

3. 92.5 % specificity, 92.5 sensitivity, incidence 2%

We can already guess that this will be in the middle of those two. However, let’s do the calculation for completeness!

True positives = 92.5% of 200 = 185, True Negatives = 92.5% of 9800 = 9065. Overall = 92.5%

Final Question… its a thinker we’ll do it in three parts

Population health officials don’t just need to think about test accuracy and effectiveness but also cost and ability to process samples to make decisions. For example, during COVID, there were numerous new tests developed (PCR, lateral flow, LAMP etc).

Test 1 is £1, with sensitivity of 99% and specificity of 98%

Test 2 is £10, with sensitivity of 99.9% and specificity of 99%

The standard policy is to use test 1 with anyone with any symptoms related to the disease. If they test positive by that test, confirm with test 2.

What proportion of the population would be correctly identified as being positive following this procedure if the incidence was 10%?