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:
| Hospital A | Hospital B | |
|---|---|---|
| Died | 63 (3%) | 16 (2%) |
| Survived | 2,037 (97%) | 784 (98%) |
| Total | 2,100 (100%) | 800 (100%) |
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.”
| 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 because you can now see that, for patients in good health, 1.3 per cent of patients died in Hospital B compared to only one per cent in Hospital A. Interestingly, Hospital B also did worse for patients in poor health, with four per cent dying compared to 3.8 per cent in Hospital A. The confounding variable – condition of the patient – makes a big difference.
(How can Hospital A do better for patients in both good and poor health, yet do worse overall? It could be that Hospital A is a teaching hospital with leading-edge surgeons, which serves seriously ill people from a wide geographic region. It attracts a much higher number of patients in poor health, who are more likely to die. As a result, Hospital A has a higher death rate overall, despite its better performance for each type of patient.)
Again, scientists may express this to you in a different way. This time, they will tell you that the odds ratio has been statistically adjusted to incorporate the effect of patient condition at the time of surgery, and is now 1.14. In other words, there is a 14 per cent higher risk of dying post- surgery in Hospital B than in Hospital A after taking the health of patients into account.
If other potentially confounding factors, such as age of patient, socioeconomic background, etc., are also taken into account, scientists will give you an odds ratio that they call fully adjusted. A fully adjusted odds ratio strips away the effects of other factors, theoretically leaving only the relationship between the two studied factors standing.
Let’s apply these concepts to the health and safety field. Dr. Curtis Breslin, a scientist at the Institute for Work & Health, recently completed a study on learning disabilities and work injury rates among young people (see the Fall 2009 issue of At Work). He reported a crude odds ratio of 2.7 when comparing work injury rates among young people with dyslexia to those without a learning disability; i.e. a 2.7 times greater likelihood of being injured on the job. This represents a straight-forward calculation comparing the number of injuries among youth with and without dyslexia.
After taking school status, age, gender, province of residence, number of working hours and job type into account, the fully adjusted odds ratio stands at 1.9. Even after adjusting for other factors known to increase work injury rates among youth, dyslexia is left standing as the explanation for the 1.9 times greater likelihood of being hurt on the job.
Source: At Work, Issue 58, Fall 2009: Institute for Work & Health, Toronto