Question

In: Statistics and Probability

Two new tests were developed to test cerebrospinal fluid for presence of cytomegalovirus in neurologically diseased...

Two new tests were developed to test cerebrospinal fluid for presence of cytomegalovirus in neurologically diseased newborns. The table below shows the findings of this trial.

Immunohistochemistry on brain material

PCR

Antigen capture ELISA

Positive

49

52

45

Negative

223

220

227

Total

272

272

272

PCR: sensitivity 95.9%, specificity 97.8%. Antigen capture ELISA sensitivity: 89.8%, specificity 99.6%.

(3 pts.) Choose ONE of the tests and complete a 2x2 table for it.

(4 pts.) A county health department has chosen to modify the exam to use sera, and wants to employ it as a screening test of all newborns. Given the goal of detecting all affected newborns (even those without symptoms), which test would the health department prefer? BRIEFLY explain why.

Solutions

Expert Solution

Two-by-Two table (false-positive, true-positive, false-negative and true-negative results) of the PCR test

The sensitivity of the PCR is given to be 95.9% and specificity of the PCR is given to be 97.8%

The formula for calculating sensitivity is

.........................eq(1)

The formula for calculating specificity is

.........................eq(2)

From the above given we above we have

Positive = TP + FP = 52.........................eq(3)

Negative = TN+FN = 220.........................eq(4)

Solving the 4 simultaneous equations we get,

True positives, TP = 47

False positives, FP = 5

True negatives, TN = 218

False negatives FN = 2

TP (true positives) stands for the number of subjects who have been tested positive given they have the disease.

FP (false positive) stands for the number of subjects who have been tested positive given they don’t have the disease.

FN (false negative) stands for the number of subjects who have been tested negative given they have the disease.

TN (true negative) stands for the number of subjects who have been tested negative given they don’t have the disease

A standard 2 x 2 Standard table for PCR test can be presented as

PCR test CMV present CMV absent Total
Test positive True Positive, TP False positive, FP TP+FP
Test Negative False negative FN True negatives, TN FN+TN
Total TP+FN FP+TN TP+FP+FN+TN

Inserting the values in the above table, we get

PCR test CMV present CMV absent Total
Test positive 47 5 52
Test Negative 2 218 220
Total 49 223 272

A county health department has chosen to modify the exam to use sera, and wants to employ it as a screening test of all newborns. Given the goal of detecting all affected newborns (even those without symptoms), which test would the health department prefer? BRIEFLY explain why.

The data for this question is not provided. details about sera? data of affected newborns (even those without symptoms) is not provided. So, I am unable to answer this question.

Please rate the solution of the first part if it helps you. Thank you.


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