Biostatistics, Epidemiology, and Population Health
Screening metrics move with prevalence
Sensitivity = TP/(TP+FN); specificity = TN/(TN+FP); positive and negative predictive values depend on prevalence, while sensitivity and specificity do not (for a fixed cutoff). High sensitivity is good for ruling out (SnNout); high specificity is good for ruling in (SpPin). Positive likelihood ratio = sensitivity/(1 − specificity).
Study designs and bias
Randomized trials best support causality; cohorts yield incidence and relative risk; case-control studies yield odds ratios and are efficient for rare disease; cross-sectional studies give prevalence, not incidence; ecologic designs are weakest for individual-level inference. Know selection bias, recall bias, lead-time bias (screening appears to prolong survival without changing mortality), and length-time bias (slowly progressive disease is over-represented). Confounding is handled by randomization, restriction, matching, stratification, or multivariable adjustment; effect modification is reported as stratum-specific effects rather than adjusted away.
Measures of frequency and effect
Incidence = new cases/population at risk/time; prevalence = all cases/total population. RR = incidence in exposed ÷ incidence in unexposed. The odds ratio approximates RR only when the outcome is rare (roughly under 10%). ARR = control rate − treatment rate; NNT = 1/ARR. Case fatality = deaths ÷ cases. Age standardization permits fair comparison across populations with different age structures.
Inference
Type I error is alpha (false positive); type II is beta (false negative); power = 1 − beta. A p-value is not the probability that the null hypothesis is true. A 95% CI excluding the null corresponds to p < 0.05, and the CI conveys magnitude as well as precision. Chi-square for categorical comparisons, t-test for two means, ANOVA for three or more means, correlation for association between two continuous variables.
Worked example
Of 1000 patients, 90 have disease and 910 do not. The test is positive in 81 diseased and 91 healthy patients. Sensitivity = 81/90 = 90%; specificity = 819/910 = 90%; PPV = 81/(81 + 91) ≈ 47%. If prevalence fell to 1% with the same test, PPV would drop to roughly 8%.