Correcting the odds ratio in cohort studies of common

Correcting the Odds Ratio in Cohort Studies of Common Outcomes in a Series of Simulated
Cohorts*
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Due to the differences in underlying assumptions between Mantel-Haenszel risk ratio and
logistic regression odds ratio, some discrepancy between the Mantel-Haenszel risk ratio and the
corrected risk ratio is expected (detailed discussion of which is beyond the scope of this work).
More importantly, the validity of the corrected risk ratio relies entirely on the appropriateness of
logistic regression model, ie, only when logistic regression yields an appropriate odds ratio will
the correction procedure provide a better estimate. Therefore, in a cohort study, whenever
feasible, the Mantel-Haenszel estimate should be used.
In summary, in a cohort study, if the incidence of outcome is more than 10% and the odds ratio is
more than 2.5 or less than 0.5, correction of the odds ratio may be desirable to more
appropriately interpret the magnitude of an association.
statistically adjusted
When determining the relationship between two factors, scientists need to take into account
other factors that may affect that relationship. When they do, they statistically adjust their
findings to reflect the impact of these other factors.
Let’s say you need surgery and are asked to choose between two hospitals in which to have it
performed. You have information about post-surgery survival rates in each hospital during the
past two years, and it looks like this:

At first glance, you would likely choose Hospital B for your surgery. After all, your chances of
dying after surgery in Hospital B are only two per cent compared to three per cent in Hospital A.
Scientists may express this to you as an odds ratio (OR). Comparing the risk of dying post-
surgery in the two hospitals (two versus three per cent), they will tell you the odds ratio is 0.66.
In other words, relatively speaking, there is a 34 per cent lower risk of dying in Hospital B than
in Hospital A.
What these scientists will also tell you, however, is that this is an unadjusted or crude odds
ratio. No other factors are taken into account when looking at the relationship between the
hospital and the likelihood of dying. However, other factors may certainly affect the outcome.
How old were the patients at each hospital? Were they in good health before surgery?
These other factors are called confounding variables . They are the “something else” that could
affect the relationship between two other things – in this case, the relationship between the
hospital and post-surgery outcomes.
Let’s look again at the two hospitals and, this time, take into account the health of the patients
going into surgery: either “good” or “poor.”
Good health
Poor health
Hospital A Hospital B
Died 63 (3%) 16 (2%)
Survived 2,037 (97%) 784 (98%)
Total 2,100 (100%) 800 (100%)
Hospital A Hospital B
Died 6 (1%) 8 (1.3%)
Survived 594 (99%) 592 (98.7%)
Total 600 (100%) 600 (100%)
Hospital A Hospital B
Died 57 (3.8%) 8 (4%)
Survived 1,433 (96.2%) 192 (96%)
Total 1,500 (100%) 200 (100%)

With this information, you would be wise to change your mind and choose Hospital A. That’s