Measuring Health States & Effect Measures

Variables & Data Types

• Variable: measurable characteristic with varying values (e.g., height, DMFT)
• Two main categories
  • Categorical
    • Binary (2 categories, no hierarchy)
    • Nominal (3+ categories, no hierarchy)
    • Ordinal (3+ categories, hierarchical)
    → Summarised by counts, proportions, rates
  • Numerical
    • Discrete (whole numbers)
    • Continuous (decimals allowed)
    → Summarised by means, medians, dispersion

Core Metrics for Measuring Health

• 1) Counts: raw number of cases/events
• 2) Proportions: $\frac{\text{Count}}{\text{Total}} \times 100\%$ (unit-less)
• 3) Rates: $\frac{\text{Count}}{\text{Person\,-time}}$ (includes time unit, e.g. person-years)
• 4) Measures of central tendency for numeric data: mean, median (+ dispersion)

Prevalence

• Existing (old + new) cases at a specific time/period
• Formula: $\frac{\text{Cases at time }t}{\text{Population at time }t}$
• Expressed as proportion or per-population count (e.g. 152/10 000)

Incidence

• Focus on NEW cases during a period
  • Cumulative incidence (Incidence Proportion): $\frac{\text{New cases during }\Delta t}{\text{Population at risk at start}}$
  • Incidence Rate: $\frac{\text{New cases during }\Delta t}{\text{Person\,-years at risk}}$
• Closed population → fixed membership; Open population → gains/losses, differing person-time

Relationship

• Prevalence ≈ Incidence × Duration (plus recurring cases, minus deaths/recoveries)

Mean & Median (Numerical Measures)

• Mean: $\bar{x}=\frac{\sum x_i}{n}$ (sensitive to outliers)
• Median: middle value when ordered; preferred for skewed data/outliers

Measures of Dispersion

• Range: $\text{max}-\text{min}$ (sensitive to extremes)
• Variance: $s^2 = \frac{\sum (x_i-\bar{x})^2}{n-1}$ (sample)
• Standard Deviation: $s = \sqrt{s^2}$ (average deviation from mean)
• Inter-quartile Range: $\text{IQR}=Q<em>3-Q</em>1$ (spread of middle 50 %; robust to outliers)

Epidemiologic Effect Measures (Binary Outcomes)

• Compare outcome between exposed (E+) and unexposed (E−)
• Two scales
  • Absolute (difference)
  • Relative (ratio)

Risk Concept

• Risk = probability (cumulative incidence) of event in a specified period; ranges $0\rightarrow1$

Absolute Measure: Risk Difference (RD)

• $RD = CI<em>{E+} - CI</em>{E-} = \frac{a}{a+b}-\frac{c}{c+d}$
• Retains original units (%); "excess risk" attributable to exposure

Relative Measures

• Risk Ratio / Relative Risk (RR): $RR = \frac{CI<em>{E+}}{CI</em>{E-}}$
• Prevalence Ratio (PR): $PR = \frac{P<em>{E+}}{P</em>{E-}}$ (when only prevalence known)
• Odds Ratio (OR): $OR = \frac{a/b}{c/d}=\frac{ad}{bc}$
  • Approximates RR when outcome is rare (a and c small)

Choosing Measures

• Prevalence studies → PR; Incidence studies → RR/RD
• Skewed numerical data/outliers → report median + IQR
• Effect size interpretation
  • RD = 0, RR/PR/OR = 1 → no effect
  • RD > 0, RR/PR/OR > 1 → exposure increases risk
  • RD < 0, RR/PR/OR < 1 → exposure protective

Key Takeaways

• Select metric based on variable type and study aim
• Counts form the basis for proportions, rates, prevalence, and incidence
• Always pair mean/median with a dispersion measure for numeric data
• Absolute and relative effect measures offer complementary insights; report both when possible