epidemiology-guide

# Epidemiology Guide A skill for designing and analyzing epidemiological studies. Covers study design selection, measures of disease frequency and association, bias assessment, and public health data analysis methods. ## Study Design Selection ### Design Hierarchy ``` Evidence Strength | Systematic Review / Meta-Analysis (Highest) | Randomized Controlled Trial | Cohort Study (Prospective) | Case-Control Study | Cross-Sectional Study | Case Report / Case Series (Lowest) ``` ### When to Use Each Design | Design | Research Question | Time | Cost | Bias Risk | |--------|------------------|------|------|-----------| | RCT | Does intervention X prevent outcome Y? | Years | Very high | Lowest | | Prospective Cohort | Does exposure X increase risk of Y? | Years | High | Moderate | | Retrospective Cohort | Historical exposure-outcome relationship? | Months | Moderate | Moderate-High | | Case-Control | What exposures are associated with rare disease? | Months | Low | High | | Cross-Sectional | What is the prevalence of X? | Weeks | Low | High | | Ecological | Do population-level factors correlate with disease? | Weeks | Very low | Very high | ## Measures of Disease Frequency ```python import numpy as np def compute_measures(cases: int, population: int, person_time: float = None, period_years: float = 1.0) -> dict: """ Compute basic epidemiological measures. Args: cases: Number of new cases (for incidence) or existing cases (for prevalence) population: Population at risk person_time: Person-years of follow-up (for incidence rate) period_years: Time period in years (for cumulative incidence) """ measures = {} # Point prevalence measures['prevalence'] = { 'value': cases / population, 'per_1000': (cases / population) * 1000, 'formula': 'cases / population at a point in time' } # Cumulative incidence (risk) measures['cumulative_incidence'] = { 'value': cases / population, 'per_1000': (cases / population) * 1000, 'period_years': period_years, 'formula': 'new cases / population at risk during time period' } # Incidence rate (if person-time available) if person_time: measures['incidence_rate'] = { 'value': cases / person_time, 'per_1000_py': (cases / person_time) * 1000, 'formula': 'new cases / person-time at risk' } return measures ``` ## Measures of Association ### Risk Ratio, Odds Ratio, and Attributable Risk ```python def measures_of_association(a: int, b: int, c: int, d: int) -> dict: """ Compute epidemiological measures of association from a 2x2 table. Disease+ Disease- Exposed+ a b a+b Exposed- c d c+d a+c b+d N Args: a: Exposed with disease b: Exposed without disease c: Unexposed with disease d: Unexposed without disease """ # Risk in exposed and unexposed risk_exposed = a / (a + b) risk_unexposed = c / (c + d) # Risk Ratio (Relative Risk) rr = risk_exposed / risk_unexposed ln_rr = np.log(rr) se_ln_rr = np.sqrt(1/a - 1/(a+b) + 1/c - 1/(c+d)) rr_ci = (np.exp(ln_rr - 1.96*se_ln_rr), np.exp(ln_rr + 1.96*se_ln_rr)) # Odds Ratio or_val = (a * d) / (b * c) ln_or = np.log(or_val) se_ln_or = np.sqrt(1/a + 1/b + 1/c + 1/d) or_ci = (np.exp(ln_or - 1.96*se_ln_or), np.exp(ln_or + 1.96*se_ln_or)) # Attributable Risk (Risk Difference) ar = risk_exposed - risk_unexposed se_ar = np.sqrt(risk_exposed*(1-risk_exposed)/(a+b) + risk_unexposed*(1-risk_unexposed)/(c+d)) ar_ci = (ar - 1.96*se_ar, ar + 1.96*se_ar) # Attributable Fraction in Exposed af_exposed = (rr - 1) / rr # Population Attributable Fraction prevalence_exposure = (a + b) / (a + b + c + d) paf = prevalence_exposure * (rr - 1) / (prevalence_exposure * (rr - 1) + 1) return { 'risk_ratio': {'value': round(rr, 3), 'ci_95': tuple(round(x, 3) for x in rr_ci)}, 'odds_ratio': {'value': round(or_val, 3), 'ci_95': tuple(round(x, 3) for x in or_ci)}, 'risk_difference': {'value': round(ar, 4), 'ci_95': tuple(round(x, 4) for x in ar_ci)}, 'attributable_fraction_exposed': round(af_exposed, 3), 'population_attributable_fraction': round(paf, 3), 'number_needed_to_harm': round(1/ar, 1) if ar > 0 else None } # Example: smoking and lung cancer result = measures_of_association(a=80, b=920, c=10, d=990) print(f"RR: {result['risk_ratio']['value']} ({result['risk_ratio']['ci_95']})") print(f"OR: {result['odds_ratio']['value']} ({result['odds_ratio']['ci_95']})") print(f"PAF: {result['population_attributable_fraction']}") ``` ## Bias Assessment ### Types of Bias and Mitigation | Bias Type | Description | Mitigation Strategy | |-----------|------------|-------------------| | Selection bias | Non-random sample selection | Random sampling, matching | | Information bias | Measurement error in exposure/outcome | Validated instruments, blinding | | Recall bias | Differential recall by disease status | Use records, not self-report | | Confounding | Third variable affects both exposure and outcome | Stratification, regression, matching | | Lead-time bias | Earlier detection misinterpreted as longer survival | Use mortality, not survival | | Healthy worker effect | Workers are healthier than general population | Use employed comparison group | ### Confounding Assessment ```python def assess_confounding(crude_rr: float, adjusted_rr: float, threshold: float = 0.10) -> dict: """ Assess whether a variable is a confounder. """ pct_change = abs(crude_rr - adjusted_rr) / crude_rr * 100 return { 'crude_RR': crude_rr, 'adjusted_RR': adjusted_rr, 'percent_change': round(pct_change, 1), 'is_confounder': pct_change > threshold * 100, 'interpretation': ( f"{'Confounder detected' if pct_change > threshold * 100 else 'Not a confounder'}: " f"adjusting changed the RR by {pct_change:.1f}% " f"(threshold: {threshold*100:.0f}%)" ) } ``` ## Survival Analysis For time-to-event data, use Kaplan-Meier estimators for descriptive analysis, log-rank tests for group comparisons, and Cox proportional hazards regression for multivariable analysis. Always check the proportional hazards assumption using Schoenfeld residuals and report median survival times with 95% confidence intervals. ## Reporting Standards Follow STROBE (observational studies), CONSORT (trials), or RECORD (routinely collected data) reporting guidelines. Report all measures with 95% confidence intervals. Present both crude and adjusted estimates to show the impact of confounding adjustment.