Monday, December 1, 2008

Risk, Risk Reducation and Relative Risk

One of the more common reasons we read clinical trial literature is look at the association between a given treatment, such as spinal adjustment, and the outcome of that treatment (for example, reduced pain or disability). But often we do not delve with any depth into the results, and the concept of relative risk is one that we should be looking at as we assess the outcomes for a research paper.

Let us say we have a paper in which in the course of a randomized trial we are comparing a dichotomous outcome (for example, mortality rates) in patients undergoing either Treatment A or Treatment B. And further, let us say that 36 of 128 patients in Treatment group A died, while 58 of 130 in Treatment group B died. From this, we can construct what is called a 2x2 contingency table (here referring to the columns “Death” and Survival” and the rows “Treatment A” and “Treatment B,” in which we put exposure on the left and the outcome across the top. When we do, we will see that in Treatment Group A, 36 people died and 92 survived, and we will call these "a" and "b"; in Treatment group B, 58 died and 72 survived, and we will label these "c" and "d."

This now allows us to be able to calculate risk. First, we can look at the absolute risk for mortality in both groups. This is defined as the risk of the adverse event in each group, sometimes called baseline risk. So, the risk of mortality in Treatment group A is the number of people who died divided by the total number of people in the group: a/(a+b) = 36/(36+92) = 36/128 = .28 or 28%, and in Treatment group B = 58/130 = .45, or 45%.

The difference between these rates is known as the risk difference, or absolute risk reduction. That is, if we compare these risks, we can see that a patient is less likely to die if they have treatment A. The absolute risk reduction is simply the difference between groups (difference meaning subtraction is involved) = c/(c+d) – a/(a+b). Here, that is .45-.28= .17, or 17%.

Finally, rather than look at the difference between groups, we can also look at the ratio; ratio implies that we will be dividing the rates, rather than subtracting them. When we do this, we calculate the risk ratio, or relative risk. Mathematically, this would be the risk in the Treatment group A divided by the risk in Treatment group B (which is typically a control group), or [a/(a+b) / c/(c+d)]. Here, we can see that the math is .28/.45 = .63, meaning that the risk of death is Treatment group A is about 63% (or about two-thirds) that of Treatment group B.

There are complexities to this assessment, which our next entry will take up. For those who wish to read a bit further on this, let me recommend the “Users’ Guide” as a good resource (1).


1. Guyatt G, Rennie D, Meade MO, Cook DJ. Users’ guides to the medical literature: a manual for evidence-based practice. New York, NY; McGraw Hill;208:87-90

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