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}=Q3-Q1 (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{E+} - CI{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{E+}}{CI{E-}}
  • Prevalence Ratio (PR): PR = \frac{P{E+}}{P{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