Stratified Methods

Confounding is a major consideration in etiological investigation because it can result in biased estimation

of exposure effects. Control of confounding in data analysis is achieved by stratified analysis or by multivariable analysis. (Control of confounding in research design stage is achieved by matching for observational studies and by randomization for experimental studies.) Stratified analysis is accomplished by stratifying the confounding variable into homogeneous categories and evaluating the association within these strata. Multivariable analysis, on the other hand, involves the use of a regression model and allows the researcher to control for all confounders at the same time while looking at the contribution of each risk factor to the outcome variable. Stratified analysis is a necessary preliminary step to performing regression modeling to control for confounding. Unlike regression models, stratified analysis requires few assumptions.

Here is a simple example of how the stratified method works. In comparing mortality statistics for Mexico and the United States in the 1990s, we observe that Mexico's crude death rate is lower than the crude death rate in the United States. Yet Mexico's age-specific death rates are higher than those of the United States for every age categories. The different age distributions of the two populations explain the direction and magnitude of the difference in the crude death rates between the two countries. The crude death rate may be expressed as Σimiwi, which is a weighted average of the age-specific death rates mi with age distribution wi as weights. The population of Mexico is younger. Mexico has relatively more people in the younger age categories and less people in the older age categories than the United States—wi differs as a function of i between the two countries. There is a strong positive association between age and mortality—mi is an increasing function of i for both countries. Thus, the existence of the confounding variable age i leads to a lower sum of products of mi and wi, the crude death rate for Mexico in the unstratified analysis, whereas a stratified analysis with confounding variable age as the stratification variable provides the true picture—Mexico has higher death rates at every age. Consequently, comparison of directly standardized rates of the two countries will show higher mortality for Mexico.

Generally, epidemiologists consider stratified methods for controlling for confounding to include the following steps:

1. Perform an unstratified analysis by calculating the crude measure of association ignoring the confounding variable (depending on the study design, the measure of association could be risk [Page 1002]difference, rate difference, risk ratio, rate ratio, or odds ratio).

2. Stratify by the confounding variable.

3. Calculate the adjusted overall measure of association.

4. Compare the crude measure with the adjusted measure.

If the crude estimate differs from the adjusted estimate by 10% or more, there is confounding, and the adjusted estimate should then be calculated by stratifying the confounder. If the estimates differ by less than 10%, there is no confounding. If there is confounding, formal significance testing and the calculation of 95% confidence interval may then be carried out to determine the significance of the association between the risk factor and the outcome variable for the different strata.

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