Epidemiological Reasoning - Eppp Knowledge

1. What is the false positive rate in terms of specificity?

   $P(T+\mid \neg D)=1-\text{specificity}$. False positive rate is the complement of specificity, representing the probability of a positive test result in the absence of the disorder.

2. Calculate $LR+$: sensitivity $=0.80$, specificity $=0.90$.

   $LR+=\frac{0.80}{0.10}=8$. LR+ is derived as sensitivity divided by the false positive rate, indicating an 8-fold increase in odds with a positive test.

3. What is prevalence in diagnostic reasoning, expressed as a probability?

   Population probability of the disorder at a given time, $P(D)$. Prevalence quantifies the existing proportion of a population with a disorder, serving as the prior probability in Bayesian diagnostic assessments.

4. Identify the key effect of low prevalence on PPV when sensitivity and specificity are fixed.

   Lower prevalence decreases PPV (more false positives among $T+$). In low-prevalence scenarios, the proportion of false positives rises relative to true positives, thus lowering the predictive value of a positive test.

5. What is the prior odds form of Bayes for a positive test using likelihood ratio $LR+$?

   Posterior odds $=$ prior odds $\times LR+$. Bayes' theorem in odds form multiplies prior odds by the positive likelihood ratio to yield posterior odds after a positive test.

6. What is the total probability formula for $P(T+)$ using sensitivity, specificity, and prevalence?

   $P(T+)=P(T+\mid D)P(D)+P(T+\mid \neg D)P(\neg D)$. The law of total probability decomposes the probability of a positive test into contributions from true and false positives weighted by prevalence.

7. What is the conversion from odds $o$ to probability in diagnostic calculations?

   Probability $=\frac{o}{1+o}$. This formula transforms odds back to probability, enabling interpretation of posterior odds after applying likelihood ratios.

8. What is the false negative rate in terms of sensitivity?

   $P(T-\mid D)=1-\text{sensitivity}$. False negative rate is the complement of sensitivity, indicating the likelihood of a negative test result when the disorder is present.

9. What is sensitivity of a diagnostic test in probability notation?

   True positive rate, $P(T+\mid D)$. Sensitivity measures the test's ability to correctly identify those with the disorder, critical for minimizing false negatives in diagnostics.

10. What is $LR+$ in terms of sensitivity and specificity?

    $LR+=\frac{\text{sensitivity}}{1-\text{specificity}}$. LR+ quantifies how much a positive test increases the odds of the disorder, as the ratio of true positive to false positive rates.

11. What is the conversion from probability $p$ to odds in diagnostic calculations?

    Odds $=\frac{p}{1-p}$. This conversion expresses probability as the ratio of success to failure, facilitating odds-based Bayesian updates in diagnostics.

12. State the formula for PPV using sensitivity, specificity, and prevalence.

    $\frac{\text{sens}\cdot P(D)}{\text{sens}\cdot P(D)+(1-\text{spec})\cdot(1-P(D))}$. This formula applies Bayes' theorem by dividing true positives by the total positives, incorporating prevalence to adjust predictive value.

13. What is the negative predictive value (NPV) in probability notation?

    Probability of no disorder given $T-$, $P(\neg D\mid T-)$. NPV indicates the conditional probability of absence of disorder given a negative test, depending on prevalence and test characteristics.

14. Identify the key effect of higher prevalence on NPV when sensitivity and specificity are fixed.

    Higher prevalence decreases NPV (more false negatives among $T-$). Elevated prevalence increases false negatives among negative tests, reducing the reliability of ruling out the disorder with a negative result.

15. State the formula for NPV using sensitivity, specificity, and prevalence.

    $\frac{\text{spec}\cdot(1-P(D))}{\text{spec}\cdot(1-P(D))+(1-\text{sens})\cdot P(D)}$. This expression uses Bayes' rule to compute the proportion of true negatives among all negative results, adjusted for disease prevalence.

16. What is $LR-$ in terms of sensitivity and specificity?

    $LR-=\frac{1-\text{sensitivity}}{\text{specificity}}$. LR- measures the reduction in odds of the disorder given a negative test, as the ratio of false negative to true negative rates.

17. What is the positive predictive value (PPV) in probability notation?

    Probability of disorder given $T+$, $P(D\mid T+)$. PPV represents the conditional probability that the disorder is present given a positive test, integrating base rate and test accuracy.

18. What is specificity of a diagnostic test in probability notation?

    True negative rate, $P(T-\mid \neg D)$. Specificity assesses the test's accuracy in identifying those without the disorder, vital for reducing false positives in probability calculations.

19. State Bayes' theorem for post-test probability of disorder given a positive test.

    $P(D\mid T+)=\frac{P(T+\mid D)P(D)}{P(T+)}$. Bayes' theorem updates the prior probability of a disorder using test sensitivity and the marginal probability of a positive result.

20. What is base rate in diagnostic probability problems (as used on the EPPP)?

    Prior probability of the condition before testing, $P(D)$. Base rate denotes the pre-test likelihood of a condition in the population, essential for accurate probabilistic diagnosis using Bayes' theorem.

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