6.2 Sensitivity, specificity, and predictive values

Screening and diagnostic tests are crucial tools in epidemiology. They help identify diseases and guide public health decisions. Understanding how well these tests perform is key to using them effectively.

Sensitivity, specificity, and predictive values are essential measures of test accuracy. These metrics help us gauge how reliable a test is in different situations. They also show us how disease prevalence affects test results.

Sensitivity, Specificity, and Predictive Values

Defining Test Performance Metrics

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• Sensitivity is the proportion of people with the disease who test positive, or the probability that a test result will be positive when the disease is present (true positive rate)
  • Sensitivity measures how well a test identifies individuals with the disease
  • A highly sensitive test will correctly identify most people with the disease, minimizing false negatives
• Specificity is the proportion of people without the disease who test negative, or the probability that a test result will be negative when the disease is not present (true negative rate)
  • Specificity measures how well a test identifies individuals without the disease
  • A highly specific test will correctly identify most people without the disease, minimizing false positives
• Positive predictive value (PPV) is the probability that a person has the disease given that they test positive, or the proportion of people with positive test results who have the disease
  • PPV indicates the likelihood that a positive test result is a true positive
  • PPV is influenced by the prevalence of the disease in the population being tested
• Negative predictive value (NPV) is the probability that a person does not have the disease given that they test negative, or the proportion of people with negative test results who do not have the disease
  • NPV indicates the likelihood that a negative test result is a true negative
  • NPV is also influenced by the prevalence of the disease in the population being tested
• Sensitivity and specificity are intrinsic properties of a test, while predictive values depend on the prevalence of the disease in the population being tested
  • Sensitivity and specificity remain constant across different populations
  • Predictive values can vary depending on the prevalence of the disease in the population

Relationship Between Test Performance Metrics

• Sensitivity and specificity are inversely related, meaning that increasing one often leads to a decrease in the other
  • Highly sensitive tests may have lower specificity, leading to more false positives
  • Highly specific tests may have lower sensitivity, leading to more false negatives
• PPV and NPV are also inversely related and depend on the prevalence of the disease in the population
  • As prevalence increases, PPV increases and NPV decreases, assuming sensitivity and specificity remain constant
  • As prevalence decreases, PPV decreases and NPV increases, assuming sensitivity and specificity remain constant

Calculating Test Performance Metrics

Using 2x2 Contingency Tables

• Data for calculating sensitivity, specificity, and predictive values are typically presented in a 2x2 contingency table
  • The table has disease status (present or absent) on one axis and test result (positive or negative) on the other
  • The four cells of the table represent true positives, false positives, true negatives, and false negatives
• Sensitivity is calculated as: True Positives / (True Positives + False Negatives)
  • This formula represents the proportion of people with the disease who test positive
• Specificity is calculated as: True Negatives / (True Negatives + False Positives)
  • This formula represents the proportion of people without the disease who test negative
• Positive Predictive Value (PPV) is calculated as: True Positives / (True Positives + False Positives)
  • This formula represents the proportion of people with positive test results who have the disease
• Negative Predictive Value (NPV) is calculated as: True Negatives / (True Negatives + False Negatives)
  • This formula represents the proportion of people with negative test results who do not have the disease

Example Calculation

• Consider a hypothetical 2x2 contingency table for a screening test:
  • True Positives: 80, False Positives: 20, False Negatives: 20, True Negatives: 880
  • Sensitivity = 80 / (80 + 20) = 0.80 or 80%
  • Specificity = 880 / (880 + 20) = 0.978 or 97.8%
  • PPV = 80 / (80 + 20) = 0.80 or 80%
  • NPV = 880 / (880 + 20) = 0.978 or 97.8%

Implications for Public Health Decisions

Balancing Test Performance Metrics

• The optimal balance of sensitivity, specificity, and predictive values depends on the purpose of the test, the prevalence of the disease, and the relative costs of false positives and false negatives
  • High sensitivity is important when the consequences of missing a case are severe, such as in screening for a serious disease, as it minimizes false negatives
  • High specificity is important when the consequences of incorrectly identifying someone as having the disease are severe, such as in diagnostic tests for conditions with significant psychological or financial costs, as it minimizes false positives
• High PPV is desirable when the disease is rare, as it indicates that a positive test result is more likely to be a true positive
  • In low prevalence settings, even highly specific tests can have low PPV due to the high number of false positives relative to true positives
• High NPV is desirable when the disease is common, as it indicates that a negative test result is more likely to be a true negative
  • In high prevalence settings, even highly sensitive tests can have low NPV due to the high number of false negatives relative to true negatives

Choosing Appropriate Tests

• Public health professionals must consider the trade-offs between sensitivity, specificity, and predictive values when selecting tests for different purposes
  • Screening tests prioritize high sensitivity to minimize false negatives, as the goal is to identify potential cases for further testing
  • Diagnostic tests prioritize high specificity to minimize false positives, as the goal is to confirm the presence of the disease with a high degree of certainty
• The prevalence of the disease in the population being tested should also inform test selection and interpretation
  • In low prevalence settings, tests with high specificity are preferred to minimize false positives
  • In high prevalence settings, tests with high sensitivity are preferred to minimize false negatives

Prevalence vs Predictive Values

Impact of Prevalence on Predictive Values

• Prevalence is the proportion of people in a population who have the disease at a given time
  • Prevalence can vary across different populations and subgroups
  • Prevalence is a key factor in determining the predictive values of a test
• As prevalence increases, PPV increases and NPV decreases, assuming sensitivity and specificity remain constant
  • In high prevalence settings, a higher proportion of positive test results will be true positives, increasing PPV
  • In high prevalence settings, a higher proportion of negative test results will be false negatives, decreasing NPV
• As prevalence decreases, PPV decreases and NPV increases, assuming sensitivity and specificity remain constant
  • In low prevalence settings, a higher proportion of positive test results will be false positives, decreasing PPV
  • In low prevalence settings, a higher proportion of negative test results will be true negatives, increasing NPV

Interpreting Test Results Based on Prevalence

• Understanding the relationship between prevalence and predictive values is crucial for interpreting test results and making appropriate public health decisions
  • In low prevalence settings, positive test results should be interpreted with caution, as there is a higher likelihood of false positives
  • In high prevalence settings, negative test results should be interpreted with caution, as there is a higher likelihood of false negatives
• Public health professionals should consider the prevalence of the disease in the population when communicating test results and making recommendations
  • In low prevalence settings, positive test results may require confirmatory testing to rule out false positives
  • In high prevalence settings, negative test results may require additional testing to rule out false negatives