# Conducting stratified analyses

## INTRODUCTION

Stratified analysis is a powerful statistical approach that allows you to test for confounding and interaction, but unlike logistic regression, it is quite simple and doesn’t distance you from your data. You can ‘see’ the associations and enjoy the insights gained from analysis.

This approach is useful when you are interested in testing association between two categorical variables – say exposure and disease – by adjusting for a third categorical variable. If done correctly, it also enables you to investigate whether the third variable is a confounder or an effect modifier.

For example, you might be interested in evaluating an association between obesity and cardiovascular disease after stratifying by age or you might want to investigate acceptances rates for males and females in a university program stratified by department. In both these situations you could conduct stratified analysis to identify confounding and interaction.

## A systematic approach for conducting stratified analysis

A systematic approach to stratified analysis involves the following steps:

1. Test crude association of the explanatory variable with the outcome or response variable, i.e. conduct a chi-square test to evaluate significance of the association and calculate a crude odds ratio or relative risk (along with their confidence intervals) to measures the strength of the association.
2. Conduct stratified analysis after stratifying data by the third variable. Similar to the first step, this includes testing the significance and measuring the strength of the association, but for each contingency table created after stratification.
3. Test homogeneity of odds ratios or relative risks to determine whether these measures of association are significantly different. This can be done by conducting a Breslow-Day or Woolf’s test of homogeneity. A significant test indicates a significant interaction or effect modification. If this is the case, then it is preferable to report separate odds ratio and relative risk for each strata.
4. Calculate Mantel- Haenszel odds ratios and relative risk along with their confidence interval, if the test of homogeneity is not significant. This is a weighted measure of association after adjusting for the third variable. The adjusted measure of association can be compared with the crude measure of association calculated in the first step to evaluate percentage change in the measure after adjusting for the third variable. A ‘substantial’ change is indicative of confounding. There are no set rules of deciding what change is substantial but generally more than 20% change is considered important.
5. Conduct a Cochran- Mantel-Haenszel chi-square test to evaluate significance of the adjusted odds ratio or relative risk calculated in the fifth step.

Note that if the test of homogeneity in Step 3 is significant, it is not appropriate to calculate an adjusted odds ratio (Step 4) or test its significance (Step 5).

Also note that many tests are available for testing homogeneity, but most of them have low power, and therefore, non-significance of the test should be interpreted with caution.

## Implementation

Stratified analysis can be conducted using many statistical programs such as Freq procedure in SAS and epiR package in R. Alternatively, you could use a free online program, Statulator, to conduct Steps 2 to 4 in one go: http://statulator.com/stat/StratifiedAnalysis.html.

Crude associations (Step 1) can be similarly evaluated using Statulator’s Chi-square test page.

Statulator not only conducts chi-square and stratified analyses but also interprets the results and provides suggestions about presentation of results in journal articles or technical reports.

Reproduced the article from a LinkedIn article published on May 17, 2015: https://www.linkedin.com/pulse/conducting-stratified-analysis-test-confounding-navneet-dhand/