/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 19 Refer to the accompanying table ... [FREE SOLUTION] | 91Ó°ÊÓ

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Refer to the accompanying table showing results from a Chembio test for hepatitis Camong HIV-infected patients (based on data from a variety of sources). $$\begin{array}{|l|c|c|} \hline & \text { Positive Test Result } & \text { Negative Test Result } \\ \hline \text { Hepatitis C } & 335 & 10 \\ \hline \text { No Hepatitis C } & 2 & 1153 \\ \hline \end{array}$$ Positive Predictive Value Find the positive predictive value for the test. That is, find the probability that a subject has hepatitis \(C\), given that the test yields a positive result. Does the result make the test appear to be effective?

Short Answer

Expert verified
The Positive Predictive Value is 99.41%. The high value suggests the test is effective.

Step by step solution

01

Identify the Given Data

From the table, note the following: - True Positives (TP): 335 - False Positives (FP): 2 - True Negatives (TN): 1153 - False Negatives (FN): 10
02

Understand Positive Predictive Value

The Positive Predictive Value (PPV) measures the probability that subjects with a positive test result actually have the disease. The formula for PPV is: \(PPV = \frac{TP}{TP + FP} \)
03

Apply the Data to the Formula

Substitute the known values into the formula: \(PPV = \frac{335}{335 + 2} \)
04

Simplify the Expression

Calculate the denominator: \(335 + 2 = 337 \) Then divide the numerator by the denominator: \(PPV = \frac{335}{337} \approx 0.9941 \)
05

Convert to Percentage

To express the PPV as a percentage, multiply by 100: \(0.9941 \times 100 = 99.41\text{\text{%}} \)
06

Conclusion

The Positive Predictive Value is 99.41%. This high value indicates that the test is very effective in correctly identifying those with hepatitis C when the test result is positive.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

statistical analysis
Statistical analysis is a critical tool in understanding complex data sets. In the context of hepatitis C diagnosis, statistical analysis helps us evaluate the effectiveness of diagnostic tests. For instance, analyzing the data allows us to calculate the Positive Predictive Value (PPV), which reveals how accurately the test can identify true positive cases when a positive result is obtained.
First, we gather and categorize the results into true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). Using these categories, we can apply statistical formulas to derive meaningful metrics such as the PPV. Detailed analysis like this ensures decisions in medical diagnostics are based on reliable data and statistical computations.
probability
Probability is a measure of the likelihood that a particular event will occur. When evaluating a diagnostic test for hepatitis C, probability helps us understand the chances of a patient having the disease given certain test results.
For example, the Positive Predictive Value (PPV) is essentially a probability measure. It tells us the probability that a person who tests positive actually has hepatitis C, calculated using the formula: \(PPV = \frac{TP}{TP + FP} \). This formula incorporates the true positives and false positives from the test to give a precise likelihood, enhancing our understanding of the test's accuracy.
diagnostic test evaluation
Diagnostic test evaluation is crucial for determining the reliability of tests used in medical practice. Evaluating a diagnostic test for hepatitis C involves measuring its sensitivity and specificity, and understanding values like the Positive Predictive Value (PPV).
Sensitivity measures how often the test correctly identifies those with the disease (true positives), while specificity measures how often the test correctly identifies those without the disease (true negatives). high sensitivity and specificity indicate an effective test. The PPV, as calculated from our example, is high at 99.41%. This suggests that the test is highly reliable in predicting the presence of hepatitis C when a positive result is found.
hepatitis C diagnosis
Hepatitis C is a liver infection caused by the hepatitis C virus (HCV). Diagnosing it accurately is vital for effective treatment and patient management. Diagnostic tests for hepatitis C aim to detect the virus's presence in the patient's blood through various means, such as antibody or RNA tests.
The data used here comes from a Chembio test for diagnosing hepatitis C in HIV-infected patients. By calculating the Positive Predictive Value (PPV), we gauge the test's effectiveness. A PPV of 99.41% means that when the test result is positive, there's a 99.41% chance the patient truly has hepatitis C. This high PPV ensures confidence in the diagnosis and subsequently aids in prompt and appropriate medical intervention.

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Most popular questions from this chapter

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