Biostatistical And Pharmacoeconomic Measures - NAPLEX

1. What is the formula for standard error of the mean (SEM) using $SD$ and $n$?

   $SEM=\frac{SD}{\sqrt{n}}$. Divides the standard deviation by the square root of sample size to estimate mean variability.

2. What is the formula for a $z$-score for an observation $x$ from mean $\mu$ and $SD$?

   $z=\frac{x-\mu}{SD}$. Subtracts the mean from the value and divides by standard deviation to standardize for normal distribution.

3. What is the formula for specificity of a diagnostic test?

   $\frac{TN}{TN+FP}$. Divides true negatives by all actual negatives to evaluate the test's accuracy in ruling out the condition.

4. What is the formula for prevalence (point prevalence)?

   $\frac{\text{existing cases}}{\text{total population}}$. Represents the fraction of the population affected by the condition at a specific point in time.

5. Find sensitivity if $TP=80$ and $FN=20$.

   $0.80$. Divides true positives by total actual positives to measure the test's detection rate.

6. What is the formula for odds ratio (OR) using a $2\times^2$ table cells $a,b,c,d$?

   $OR=\frac{a\times d}{b\times c}$. Uses the cross-product ratio of a contingency table to estimate relative odds in case-control studies.

7. What is the formula for positive predictive value (PPV)?

   $\frac{TP}{TP+FP}$. Divides true positives by all positive results to determine the probability of disease given a positive test.

8. Find the NNT if $CER=0.20$ and $EER=0.10$.

   $10$. Calculates ARR as 0.10, then takes the reciprocal to find patients needed to prevent one event.

9. What is the formula for number needed to harm (NNH) from absolute risk increase (ARI)?

   $NNH=\frac{1}{ARI}$. Takes the reciprocal of absolute risk increase to find patients needed for one adverse outcome.

10. Which hypothesis test is most appropriate to compare proportions between two independent groups?

    Chi-square test (or Fisher exact if expected counts are small). Tests independence of categorical variables; Fisher exact is used for small sample sizes to ensure accuracy.

11. What is the formula for number needed to treat (NNT) from absolute risk reduction?

    $NNT=\frac{1}{ARR}$. Takes the reciprocal of absolute risk reduction to determine patients needed for one beneficial outcome.

12. What is the formula for sensitivity of a diagnostic test?

    $\frac{TP}{TP+FN}$. Divides true positives by all actual positives to assess the test's ability to detect the condition.

13. What is the formula for absolute risk reduction (ARR) using event rates?

    $ARR=CER-EER$. Subtracts the experimental event rate from the control event rate to find the absolute benefit of treatment.

14. What is the formula for incidence proportion (cumulative incidence) over a period?

    $\frac{\text{new cases in period}}{\text{population at risk at start}}$. Measures the proportion of initially at-risk individuals who develop the condition over the specified time frame.

15. Which hypothesis test is most appropriate to compare means between two independent groups?

    Independent (two-sample) $t$ test. Compares means assuming normality and independence to detect significant differences between groups.

16. What is the formula for the incremental cost-effectiveness ratio (ICER)?

    $ICER=\frac{C_1-C_0}{E_1-E_0}$. Divides the difference in costs by the difference in effectiveness to assess value of the new intervention.

17. What is the formula for negative predictive value (NPV)?

    $\frac{TN}{TN+FN}$. Divides true negatives by all negative results to determine the probability of no disease given a negative test.

18. What is the formula for relative risk (risk ratio, RR) in a cohort study?

    $RR=\frac{\text{risk in exposed}}{\text{risk in unexposed}}$. Divides the probability of the outcome in the exposed group by that in the unexposed to assess association strength.

19. Find the relative risk if exposed risk is $0.12$ and unexposed risk is $0.08$.

    $1.5$. Divides exposed risk by unexposed risk to quantify the relative increase in outcome probability.

20. What is the formula for negative likelihood ratio ($LR^-$) from sensitivity and specificity?

    $LR^-=\frac{1-\text{sensitivity}}{\text{specificity}}$. Divides the false negative rate by specificity to indicate how much a negative result decreases disease likelihood.

21. What is the formula for incidence rate (incidence density)?

    $\frac{\text{new cases}}{\text{person-time at risk}}$. Quantifies the rate of new cases per unit of person-time, accounting for varying durations of risk exposure.

22. What is the formula for relative risk reduction (RRR) using ARR and CER?

    $RRR=\frac{ARR}{CER}=\frac{CER-EER}{CER}$. Divides the absolute reduction by the control rate to express proportional risk decrease due to intervention.

23. What is the formula for positive likelihood ratio ($LR^+$) from sensitivity and specificity?

    $LR^+=\frac{\text{sensitivity}}{1-\text{specificity}}$. Divides sensitivity by the false positive rate to indicate how much a positive result increases disease likelihood.

24. What is the formula for a $95\%$ confidence interval for a mean when $n$ is large?

    $\bar{x}\pm^1.96\times SEM$. Adds and subtracts 1.96 times the standard error from the mean for a 95% confidence range in large samples.

25. Find the ICER if $C_1=\$12{,}000$, $C_0=\$8{,}000$, $E_1=3$ QALYs, and $E_0=2$ QALYs.

    $\$4{,}000\ \text{per QALY}$. Divides the $4,000 cost difference by the 1 QALY gain to find cost per additional quality-adjusted life year.

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