The most popular method used to compute a weighted risk ratio or odds ratio is the Mantel Haenszel method, which can be used for risk ratios or rate ratios.

From the following table

 Cases Total Stratum 1 Exposed a1 Te1 Unexposed c1 Tu1 Total T1 Stratum 2 Exposed a2 Te2 Unexposed c2 Tu2 Total T2

The Mantel Haenszel risk ratio (RRMH) can be computed as follows: In which:
a and c are the number of cases exposed and unexposed in a stratum
Te and Tu are the total number exposed and unexposed in a stratum
T is the total of a stratum
The sums ∑ are calculated for the i strata.

Returning to the example of the cohort study with vaccinated girls and boys:

#### Crude RR

 Gender Cases Total Attack Rate RR Boys 819 1000 82% 4.52 Girls 181 1000 18% ref

#### Stratified RRs

 Gender Cases Total Attack Rate RR Unvaccinated Boys 814 950 86% 1.00 Girls 86 100 86% ref 1050 Vaccinated Boys 5 50 10% 0.95 Girls 95 900 11% ref 950

In our example the crude measure of effect (the risk ratio) was 4.5. The weighted measure of effect calculated with the Mantel Haenszel method is close to 1. It is obtained as follows:

 RRMH = ∑ (aiTui/Ti) = [(814*100)/1050)] + [(5*900)/950] = 82.2 = 0.99 ∑ (ciTei/Ti) [(86*950)/1050)] + [(95*50) / 950)] 82.8

The relative difference between the weighted and the crude measures of effect is more than 15% (4.5/0.99 *100 = 450%) therefore suggesting that, in our hypothetical study, vaccination is confounding (is a confounding factor for) the association between gender and disease. Had a stratified analysis been omitted, the data may lead to the conclusion that being a boy was a risk factor for the disease.

The adjusted RR 0.99 is presented, which concludes that this is the measure of association between gender and disease. This is different from effect modification, where two RRs would be presented.

Mathematically, the adjusted estimate is a weighted average of the stratum specific measures of the risk ratio. It will therefore always lie within the range of the stratum specific measures of the effect. (i.e. in the example above;  0.99 is between the range 0.95 and 1.00 - the stratum specific RRs).

For a case control study the Mantel Haenszel odds ratio (ORMH) can be computed as follows:

 Stratified Risk Factor Cases Controls Totals Stratum 1 Exposed a1 b1 Unexposed c1 d1 T1 Stratum 2 Exposed a2 b2 Unexposed c2 d2 T2 In which:
a and c are the number of cases exposed and unexposed in a stratum,
b and d are the number of controls exposed and unexposed in a stratum.
T is the total for a stratum
The sums ∑ are calculated for the i strata.

It can become customary to 'eyeball' the data: comparing the crude measure to the range of the stratum-specific measures. If the crude measure is not included in the range between stratum-specific measures, confounding may exist.

A watertight method for identifying confounding variables exists. It requires the construction of a causal diagram summarizing the knowledge and assumptions between all exposures, confounders and disease outcome; which is then analysed using graphical algorithms .