Part 1: Two simple and inexpensive screening methods have been developed to iden

Question

Part 1: Two simple and inexpensive screening methods have been developed to identify individuals with HIV infection at routine medical check-ups. To study the sensitivity and specificity, both methods were tested on 12,860 persons who underwent a simultaneous and thorough clinical examination that was considered to give an accurate diagnosis. There were 1,900 cases of disease as diagnosed by clinical methods. The Screening test #1 was positive for a total of 1,000 people, including 800 with active HIV infection. The screening method #2 was positive for 2,444 individuals. This method also detected 800 individuals diagnosed with active HIV as positive.

a) Calculate the sensitivity of each screening method.

b) Calculate the specificity of each screening method.

c) What is the positive predictive value of each screening method?

d) What is the negative predictive value of each screening method?

e) Which screening method would you recommend? Give your reason for this recommendation.

Part 2: In a mass screening aimed at early diagnosis of HIV infection in Pennsylvania, the screening method you recommended above is used. Of 25,000 individuals attending the screening, 6,843 were found to be positive. Calculate the prevalence of HIV in the city.

Explanation / Answer

Part1:

Compute a confusion matrix:

Excel formula:

a) Calculate the sensitivity of each screening method.

Method -1 & Method-2 both have sensitivity= 0.421

b) Calculate the specificity of each screening method.

Method-1: 0.98

Method-2: 0.85

c) What is the positive predictive value of each screening method?

Method-1: 1000

Method-2: 2444

d) What is the negative predictive value of each screening method?

Method-1: 11860

Method-2: 10416

e) Which screening method would you recommend? Give your reason for this recommendation.

Method-1.

Part2:

Using excel Add-in Solver.

There are approx 12500 HIV+

Confusion Matrix Predicted Actual +ve -ve +ve TP FN Total Actual Positive -ve FP TN Total Actual Negative Confusion Matrix Confusion Matrix Method-1 Method-2 Predicted Predicted Actual +ve -ve Actual +ve -ve +ve 800 1100 1900 +ve 800 1100 1,900 -ve 200 10,760 10,960 -ve 1,644 9,316 10,960 1000 11860 12,860 2,444 10416 12,860 Sensitivity=True Positive Rate (TPR) Sensitivity=True Positive Rate (TPR) =(True Positive)/(Total Positive) =(True Positive)/(Total Positive) 0.4210526 0.421053 Specificity=True Negative Rate (TNR) Specificity=True Negative Rate (TNR) =(True Negative)/(Total Positive) =(True Negative)/(Total Positive) 0.9818 0.8500

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