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