A clinical study is conducted to evaluate a novel rapid diagnostic test for a specific bac… — USMLE Step 2 CK

A clinical study is conducted to evaluate a novel rapid diagnostic test for a specific bacterial infection. The study enrolls $1,000$ participants. A gold standard culture method confirms that $100$ participants currently have the infection. The novel rapid test returns a positive result for $90$ of the infected participants. Additionally, the rapid test returns a positive result for $30$ participants who do not have the infection. All other participants tested negative. What is the positive predictive value of this novel rapid diagnostic test, expressed as a percentage?

Answer: 75 %

Answer

The positive predictive value (PPV) is the probability that a patient actually has the disease given a positive test result. It is calculated by dividing the number of true positives (TP) by the total number of individuals who tested positive (TP + FP). In this study,

90

infected participants tested positive (TP =

90

) and

30

uninfected participants tested positive (FP =

30

). The total number of positive tests is

90 + 30 = 120

. Therefore, the

PPV = \frac{90}{120} = 0.75

, which is

75\%

Step-by-Step Solution

Identify the true positive (TP) count.

TP = 90

These are the individuals who actually have the infection and correctly received a positive test result.

Identify the false positive (FP) count.

FP = 30

These are the individuals who do not have the infection but incorrectly received a positive test result.

Calculate the Positive Predictive Value (PPV).

PPV = 90 / (90 + 30) = 90 / 120 = 0.75

PPV measures the proportion of positive test results that are true positives.

Convert the resulting decimal to a percentage.

75%

The question asks for the answer to be expressed as a percentage.

Key Concept

Positive Predictive Value (PPV)

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