PH 45 wk 8

Regression Models

Help understand relationships between variables and predict outcomes; commonly used in public health research to study risk factors, protective factors, and intervention effectiveness

Regression Analysis in Epidemiology

Foundational tool used to understand relationships between exposures and health outcomes

Linear Regression

Predicts a continuous outcome variable

Logistic Regression

Predicts a categorical outcome variable

Multiple Regression

Regression with multiple predictor variables; can apply to both linear and logistic regression

Independent Variable (Predictor Variable)

The variable believed to influence or predict the outcome

Dependent Variable (Outcome Variable)

The variable being predicted or explained

Continuous Variable

A variable that can take many numerical values (ex: BMI, blood pressure, cholesterol)

Categorical Variable

A variable divided into groups or categories (ex: smoker/non-smoker, disease/no disease)

Linear Regression Outcome Type

Continuous

Logistic Regression Outcome Type

Categorical

Examples of Continuous Outcomes

Blood pressure, cholesterol levels, BMI, air pollution levels

Examples of Categorical Outcomes

Disease present/not present, vaccinated/unvaccinated, smoker/non-smoker

Purpose of Linear Regression

Examines how changes in predictor variables affect a continuous outcome

Purpose of Logistic Regression

Estimates probability of an outcome occurring

Regression Line

Represents the average change in the dependent variable for each unit increase in the independent variable

Positive Regression Coefficient

Indicates a positive relationship; as one variable increases, the other increases

Negative Regression Coefficient

Indicates a negative relationship; as one variable increases, the other decreases

Large Regression Coefficient

Indicates a stronger relationship between variables

Example of Linear Regression in Public Health

Predicting cholesterol based on exercise, diet, and socioeconomic status

Example of Logistic Regression in Public Health

Predicting vaccine uptake using health literacy, insurance status, and side effect experiences

Logistic Regression Output

Probabilities that are converted into binary outcomes

Odds Ratio (OR)

Measure used in logistic regression to describe odds of an outcome occurring

OR > 1 Meaning

Increased odds of the outcome occurring

OR < 1 Meaning

Decreased odds of the outcome occurring

Formula for Increased Odds Percentage

(OR − 1) × 100

Formula for Decreased Odds Percentage

(1 − OR) × 100

OR of 2.67 Means

167% increased odds of the outcome

OR of 0.25 Means

75% decreased odds of the outcome

Choosing the Correct Regression Model

Continuous outcomes use linear regression; categorical outcomes use logistic regression

Why Variable Type Matters

Using the wrong regression model can produce misleading or inaccurate conclusions

Correlation

Measures association between two variables

Regression vs Correlation

Correlation measures association only, while regression suggests a directional relationship

Does Regression Prove Causation?

No; causation requires assumptions and additional evidence

Multivariate Analysis

Analysis that includes multiple variables to account for confounders

Confounding Variable

A third variable that may distort the relationship between two variables

Why Use Multivariate Analysis?

To control for confounders and improve accuracy of results

Example of Confounding

Exercise may appear related to lower blood pressure, but diet could influence the relationship

Bivariate Analysis

Examines relationship between two variables only

Limitation of Bivariate Analysis

Can be misleading if confounders are not controlled

Advantage of Multivariate Analysis

Provides adjusted estimates that better reflect true relationships

Comparative Statistics

Statistical tests used to compare characteristics between populations or changes over time

Hypothesis Testing

Process used to determine whether there is evidence of a difference between groups

Difference-Seeking Tests

Comparative tests are designed to detect differences, not sameness

Null Hypothesis (H₀)

Assumes there is no difference between groups or conditions

Alternative Hypothesis (Hₐ)

Assumes there is a difference between groups or conditions

When p ≥ α

Fail to reject the null hypothesis

When p < α

Reject the null hypothesis

Statistically Significant Result

Evidence suggests a real difference between groups or conditions

Alpha Level (α)

Threshold used to determine significance; commonly set at 0.05

Meaning of α = 0.05

5% chance of incorrectly concluding there is a difference when there is not

P-Value

Probability that observed results occurred by chance

Two-Sided Test

Looks for a difference in either direction

One-Sided Test

Looks for a difference in one specific direction only

Why Two-Sided Tests Are Common

They allow researchers to detect differences regardless of direction

Why One-Sided Tests Are Rare

Used only when there is strong evidence expecting change in one direction

Importance of Choosing the Correct Statistical Test

The test must match the research question and variable types

Assumptions in Statistics

Conditions data must meet for test results to be valid

Examples of Statistical Assumptions

Normal distribution, equal variability, independence of observations

Positive Correlation

As one variable increases, the other increases

Negative Correlation

As one variable increases, the other decreases

No Correlation

No clear relationship between variables

Pearson’s r

Statistic measuring strength and direction of correlation

What Determines Significance in Correlation?

The p-value

Independent Samples T-Test

Compares means of two separate independent groups

When to Use Independent Samples T-Test

When comparing means between two groups

When NOT to Use Independent Samples T-Test

When comparing three or more groups

T Statistic

Measures how far apart the group means are

What Determines Significance in a T-Test?

The p-value

ANOVA (Analysis of Variance)

Compares means between three or more groups

Purpose of ANOVA

Determines whether at least one group mean differs from others

F Statistic

Measures strength of evidence that group means differ

What Determines Significance in ANOVA?

The p-value

Chi-Squared (χ²) Test

Determines whether there is an association between two categorical variables

Data Type Used in Chi-Squared Tests

Categorical data only

Chi-Squared Test Compares

Observed frequencies versus expected frequencies

χ² Statistic

Measures how different observed frequencies are from expected frequencies

What Determines Significance in Chi-Squared Tests?

The p-value

Most Important Statistic Across Tests

The p-value