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

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

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

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.