Measures of Association

Measures of Association in Epidemiology

Overview

• Presenter: Carrie A. Karvonen-Gutierrez, Ph.D., M.P.H., from the University of Michigan School of Public Health.

Objective of Epidemiologic Studies

• Exposure and Outcome Relationship:

  • The primary question in epidemiologic studies is how to relate information about exposure to outcomes.

  • Key comparisons to make include:

    • Is exposure more common among those who are diseased versus those not diseased (cases vs. controls)?

    • Is the disease more prevalent among the exposed compared to the unexposed?

Resource Allocation in Public Health

• Public health initiatives must operate within limited financial resources. Key considerations include:

  • The need for data to inform decisions (“Data-driven decision-making”).

  • Employing measures of disease and exposure frequency helps to understand population burden.

  • Utilizing measures of association reveals relationships between exposures and outcomes.

Measures of Association

Requirements for Determining Association

1. Identify one variable as the exposure and another as the outcome.

2. Compare at least two groups or analyze a continuous variable.

3. Define comparison groups based on classifications (categories, levels, locations) or a continuous metric of a variable.

4. Conduct comparisons regarding values related to a second variable.

How to Quantify Relationships

• Two main categories of measures of association:

  1. Ratio-based measures:

     • Prevalence ratios

     • Risk ratios

     • Rate ratios

     • Odds ratios

  2. Risk-difference measures:

     • Attributable risk

     • Population attributable risk

Ratio-Based Measures of Association

Definition of Terms

• Risk Ratio: The ratio of the risk of disease in the exposed group to the risk in the unexposed group.

• Rate Ratio: The ratio of incidence rates between two groups (exposed vs. unexposed).

• Prevalence Ratio: Often referred to as Cumulative Incidence Ratio or Incidence Rate Ratio.

Computing Prevalence Ratio

• Formula:
  $\text{Prevalence Ratio} = \frac{\text{Prevalence of outcome in exposed}}{\text{Prevalence of outcome in non-exposed}}$

• Study designs capable of calculating a prevalence ratio include:

  • Cross-sectional study

  • Cohort Study (perhaps after follow-up)

  • Randomized Controlled Trial (RCT) (possibly after follow-up).

Representation of Data

Example Setup for Prevalence Ratio Calculation

• Disease categories:

  • Exposed: a

  • Not Exposed:

    • Disease: b

    • No Disease: c

• Total calculations:

  • Total diseased: a + b

  • Total non-diseased: c + d

  • Total exposed: a + c

  • Total not exposed: b + d

  • Total overall: a + b + c + d.

Prevalence Calculation

• $\text{Prevalence of disease (exposed)} = \frac{a}{(a + b)}$

• $\text{Prevalence of disease (non-exposed)} = \frac{c}{(c + d)}$

Interpretation of Ratio-Based Measures

Key Elements

• Direction: Indicates whether the association is positive or negative.

• Magnitude: The strength of the association is measured quantitatively.

• Statistical Significance: Evaluated post-calculation.

Directions of Measures

• Values range from 0 to infinity.

  • A value of 1.0 indicates no association.

  • A value >1.0 suggests a positive association (i.e., exposure correlates with increased outcome).

  • A value <1.0 suggests a negative/inverse association (i.e., exposure correlates with decreased outcome).

  • In the case of a continuous exposure, higher exposure levels correlate with increased or decreased outcomes as shown by the calculated ratios.

Example Interpretation: Prevalence Ratio

• Example Value: Prevalence Ratio = 1.76

  • Direction: Positive association between exposure and outcome.

  • Magnitude: 1.76 times higher prevalence of the outcome in the exposed group compared to unexposed.

  • Interpretation: Exposed individuals are 76% more likely to have the disease than unexposed individuals during the studied timeframe.

Risk Ratio

Definition

• The risk ratio compares cumulative incidence between exposed and unexposed groups.

Calculation Examples

• Formulated as:
  $\text{Risk Ratio} = \frac{\text{Cumulative incidence in exposed}}{\text{Cumulative incidence in non-exposed}}$

Application

• Suitable study designs include:

  • Cohort Studies

  • Randomized Controlled Trials.

Risk Ratio Interpretation Example

• Example Value: Risk Ratio = 1.25

  • Direction: Positive association (exposed have greater incidence).

  • Magnitude: 1.25 times greater likelihood of disease for the exposed group compared to the unexposed.

Rate Ratio

Definition

• Similar to risk ratio but uses incidence rates instead of cumulative incidence.

Calculation Examples

• Involves cumulative incidence rates and requires consideration of person time.

Rate Ratio Interpretation Example

• Example Value: Rate Ratio = 0.9

  • Direction: Negative association (exposed lower rate compared to unexposed).

  • Magnitude: Rate of disease in the exposed is 10% less than that in unexposed.

Odds Ratio

Definition

• Odds are defined as the probability that an event occurs divided by the probability that it does not.

  • Odds for an event is given as:
    $\text{Odds} = \frac{Y}{1 - Y}$ where Y denotes the probability of the event.

Odds Ratio Calculation

• Applicable particularly in case-control studies where the odds of exposure among cases can be compared with controls.

Interpretation Example

• If the odds ratio equals 1.9, this indicates that cases have 1.9 times the odds of exposure compared to controls, presenting a positive direction in the association.

Risk Differences and Attributable Risk

Definitions

• Attributable Risk (AR): Measure of excess risk in an exposed group compared to an unexposed group.

  • Formula:
    $\text{AR} = \text{Incidence in exposed} - \text{Incidence in unexposed}$

• Population Attributable Risk (PAR): Measures disease occurrence attributable to exposure in the total population.

  • Formula:
    $\text{PAR} = \text{Incidence total} - \text{Incidence unexposed}$

Significance of Attributable Risk

• Provides information on the absolute effect of exposures on disease occurrences.

• Highlights the prevention potential if the exposure were eliminated.

Example of AR and PAR Calculation

• From a hypothetical coronary heart disease (CHD) example, the Attributable Risk and Population Attributable Risk are calculated based on incidence rates among exposed vs. unexposed groups.

Final Thoughts

Summary of Key Takeaways

• Utilize Ratio-based measures (Risk Ratios, Odds Ratios, etc.) for relative risk comparisons.

• Employ Risk Difference measures (AR, PAR) for assessing the absolute impacts of exposures on disease incidence.

• Be cautious of distinctions between types of measures to ensure appropriate interpretation for public health significance.