The existence of effect modifiers or confounding factors requires measuring an effect in subgroups (strata) of the study population. We perform a stratified analysis. The effect modifier or confounding factor can have two or several categories. Each of them is a stratum in the stratified analysis. We measure the effect between exposure and outcome in each of the various levels taken by the effect modifier or the confounding factor.

The relevant table looks as follows

 Cases Total Attack Rate Risk Ratio Stratum 1 a1 Te1 Re1 RR1 c1 Tu1 Ru1 Stratum 2 a2 Te2 Re2 RR2 c2 Tu2 Ru2 Stratum 3 a3 Te3 Re3 RR3 c3 Tu3 Ru3 Stratum 4 a4 Te4 Re4 RR4 c4 Tu4 Ru4 TOTAL Sa STe Re RR Sc STu Ru

To conduct a stratified analysis we can identify six major steps which have a specific chronology:

### 1.      Conduct a crude analysis

Measure the effect (RR or OR) of the exposure of interest on the outcome in our study. Compute the confidence limits of this effect.

### 2.      Identify the potential effect modifiers or confounding factors

Those variables are identified from the crude analysis of the data or identified a priori from literature review. They include the other identified risk factors (variables which are associated with outcome) and variables which can be sub-divided in several sub groups of public health interest (age, gender, etc.). When the effect modifier or confounding factor is not binary (Yes-No) we create as many strata as there are categories of exposure in that variable.

### 3.      Measure the effect of exposure on outcome within each stratum

Measure the effect of the exposure on outcome within each of the strata (RR2 to RR4 above).

### 4.      Look for effect modification

If the effect differs between strata, we then suggest that effect modification is present. This should be supported by a test for homogeneity between strata and a reflection on the biological plausibility of the varying effect among strata. Since effect varies among strata we need to present the results by stratum. An overall effect (crude effect) is less informative since not illustrating the information given by the effect measured in each stratum.

### 5.      Look for confounding

Compare the crude measure of effect to a weighted measure (e.g. Mantel-Haenszel).

If the crude and weighted measures differ by more than 15-20%, the crude measure of effect may have been confounded. The weighted measure of effect is therefore more appropriate than the crude measure of effect. The crude measure of effect can be compared to the range of value taken by the stratum specific effects: if it lies outside the range of stratum-specific values, then confounding is likely.

### 6.      Are effect modification and confounding present?

If both effect modification and confounding are present, the interpretation of a measured effect is complicated (a variable can be both a confounding factor and an effect modifier). In that event a multivariable analysis taking into account confounding and interaction is needed [1].

## References

1. Hosmer DW, Lemeshow S. Model-Building Strategies and Methods for Logistic Regression. 2nd ed. New Jersey, USA: John Wiley & Sons Inc; 2000.