STAT 2023 Due (a 2:45 pm-May 8, 2017 uestio The tables below refer to a two-step

Question

STAT 2023 Due (a 2:45 pm-May 8, 2017 uestio The tables below refer to a two-step test for Lyme Disease. This is the most common vector-borne disease in the United States. The CDC's Association of State and Territorial Public Health Laboratory Directors (ASTPHLD recommend a two-step approach to diagnosis of Lyme Disease, which suggests that a positive or indeterminate serology test be followed by the more specific Western Blot Test. A positive or negative result for the two-step test procedure is then provided Table A -Vermont Table B-Vermont Lyme Disease Lyme Disease (Overall) (Forestry Workers) Blot & Result Present ores Absent (No) Test Serology & Western Absent (No) Blot Test Result Present CYes) Positive Positive 999 (-)WW 27 29 98893 Negative 428 Negative a. Calculate the following for the Serology & Western Blot two-step test (using Table A above) Sensitivity Specificity Positive Predictive value (PPV)

Explanation / Answer

For Table A -

Sensitivity = 79/(79+29) * 100 = 73.15%

Specificity = 98893/(98893+999) * 100 = 99%

Positive predictive value = 79/(79+999) * 100 = 7.3 %

Negative predictive value = 98893/(98893+29) *100 = 99.97%

For Table B -

Sensitivity = 73/(73+27) * 100 = 73 %

Specificity = 428/(428+4) * 100 = 99%

Positive predictive value = 73/(73+4) * 100 = 94.8 %

Negative predictive value = 428/(428+27) *100 = 94 %

(c) We see sensitivity and specificty are almost same for both the tables.

Sensitivity is same, because the test is independent of whether it is tested on Forestry workers or not. 73% of the people (whether they are forestry workers or not) with disease will be tested positive.

Same applies for Specificity. Specificity is same, because the test is independent of whether it is tested on Forestry workers or not. 99% of the people (whether they are forestry workers or not) with no disease will be tested negative.

(d) We see positive predictive value and negative predictive value are different for both the tables.

Positive and negative predictive values are influenced by the prevalence of disease in the population that is being tested. If we test in a high prevalence setting, it is more likely that persons who test positive truly have disease than if the test is performed in a population with low prevalence.

As positive predictive value is greater for table B than for table A, prevalence of disease is high in forestry workers.

(e) Probability of negative results when having a disease (as per Table A) = 29/(29+79) = 0.2685

Probability of getting negative results twice when having a disease (as per Table A) = 0.2685 * 0.2685 = 0.0721

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