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Sensitivity, Specificity, Prevalence and Predictive Values - Statswork

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The following 2 x 2 table shows the results obtained in a screening test for diabetes used on 10,000 persons. A random blood glucose value of 180 mg/dl or above as was established as the cutoff point to identify a person as positive for diabetes.

Screening Test Results True Characteristic Diabetic True Characteristic Not Diabetic Total
Positive 34 (a) 20 (b) 54
Negative 116 (c) (1.17%) 9830 (d) (98.8%) 9946
Total 150 (x) 9850 (y) 10,000

Calculate sensitivity, specificity, and positive predictive value of this screening test. Show how you set up the equations.

Sensitivity: probability that a test result will be positive when the disease is present (true positive rate, expressed as a percentage)

Sensitivity
= a / (a + c)
= 34 / (34 + 116)
= 0.227

Specificity: probability that a test result will be negative when the disease is not present (true negative rate, expressed as a percentage).

Specificity
= d / (b + d)
= 9830 / (20 + 9830)
= 0.998

Positive predictive value: probability that the disease is present when the test is positive (expressed as a percentage).

Positive Predictive Value
= a / (a + b)
= 34 / (34 + 20)
= 0.629

Negative predictive value: probability that the disease is not present when the test is negative (expressed as a percentage).

Negative Predictive Value
= d / (c + d)
= 9830 / (116 + 9830)
= 0.988

Using the cutoff above, discuss whether a random glucose lab value of 180 mg/dl represents a true negative or false negative. Is the cutoff value appropriate?

False Negative = 116 (1.5%); True Negative = 9830 (98.8%) The above random glucose 180mg/dl had high specificity (99%) and high negative predictive value (99%) for correctly identifying disease-free individuals; however it had low sensitivity (23%) and low positive predictive value (63%) for detecting diabetes. Hence the cut-off of 180mg/dl was not appropriate. To identify appropriate cut-off, sensitivity and specificity should be matched or else the optimum cut-off point was defined as the closest point on the ROC curve to the point (0, 1) i.e., false positive rate of zero and sensitivity of 100%.

Based on the above table, what is the point prevalence of diabetes for this population?

Prevalence = x / x+y


X is the number of individuals in the population with the disease at a given time, and Y is the number of individuals in the population at risk of developing the disease at a given time, not including those with the disease, since they are not at risk of developing it

The point prevalence of diabetes is 1.5%.

The screening test cutoff point was lowered to a blood glucose value of 120 mg/dl. In the clinic 300 total persons were now screened with positive results for diabetes. However, 250 of these 300 persons do not actually have diabetes.

Complete the 2 x 2 table below using the new information (assuming that the point prevalence remains the same for this group)

Screening Test Results True Characteristic Diabetic True Characteristic Not Diabetic Total
Positive 100 (a) 200 (b) 300
Negative 50 (c) 9650 (d) 9700
Total 150 (x) 9850 (y) 10,000

Calculate sensitivity, specificity, and positive predictive value for the new screening test cutoff point of 120 mg/dl.

Sensitivity: probability that a test result will be positive when the disease is present (true positive rate, expressed as a percentage)

Sensitivity = a / (a + c)
= 100 / (100 + 50)
= 0.667

Specificity: probability that a test result will be negative when the disease is not present (true negative rate, expressed as a percentage).

Specificity = d / (b + d)
= 9650 / (200 + 9650)
= 0.979

Positive predictive value: probability that the disease is present when the test is positive (expressed as a percentage).

Positive Predictive Value = a / (a + b)
= 100 / (100 + 9650)
= 0.010

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