Understanding and expressing “Risk”

Abstract

Making a decision to adopt or reject an intervention based on the evidence driven from medical literature, requires a clear understanding of the risk of adverse outcome and its relation (association) to this intervention. For example to choose a particular anti-arrythemic drug therapy may be based on the relation of this drug in reducing the risk of mortality. Expressing this concept might be done in several methods. Surprisingly, these different methods for expressing the same fact may lead to somewhat different understanding (and hence decisions) by the health practitioners. Assume that the mortality risk related to cardiac event in diabetic patients of average normal weight above 60 years is 20% within 5 years. If this estimation becomes true then in each 100 patients, 20 patients will die within 5 years. That example introduced the first term of risk which is the “event rate” or ER. Let us now consider in these patients a hypothetical condition of overweight where each extra 1 kg above the average weight constitutes a cardiac hazard that leads to an extra 1% increase in mortality (compared to the population with normal weight) related to cardiac event. So if you have a similar group in which each patient has an extra 100 kg weight, this will increases their risk by 100% and their expected ER will be doubled to = 40% i.e., from 100 patients, 40 will die within 5 years. The patient new base line expected risk is 40%. Now, suppose that you are studying certain interventions (like surgical procedure as gastric band versus diet control). If the diet failed to make any weight loss, while gastric band operation lead to loss of 25 kg in weight. There are several methods that the patient can express this weight loss. One may say 1. I Lost 25 kg. This is my absolute weight loss (weight difference). 2. I am now 75% compared to my extra weight before (weight ratio). 3. I have 25% reduction relative to my base line extra weight (relative weight reduction). Similar to these expressions, EBM expression are used to express this decrease risk of outcome as shown in Table 1. Table 1 Hypothetical examples of different risk parameters. 2. Event Rate (ER) The simplest measure of association to understand is the risk (or absolute risk). We often refer to the risk of the adverse outcome in the control group as the baseline risk or the control event rate (CER). When you apply intervention that changes the risk to a new event rate it called experimental event rate (EER). In our example, the risk of death with diet is CER = 40/100 = 0.4 or 40% while the risk of death with gastric band EER = 30/100 = 0.3 or 30% ER=number of events/total number of the group (1) 3. Risk Difference (RD) One way of comparing two risks is by calculating the absolute difference between them. We refer to this as risk difference (RD) or as the absolute risk reduction (ARR). The formula for calculating the RD is: RD=|ER-EER| (2) The symbol | | was used to indicate that this parameter uses absolute rather than relative terms in looking at the proportion of patients who are spared from the adverse outcome. In our example, the RD is 0.4 − 0.0.3 = 0.1. That means a RD of 10%. In this case there is a reduction of 10% which is also called absolute risk reduction (ARR). Let us assume that the intervention (gastric band surgery) caused increase in mortality and made it 60% (the base line was 40%). In this case RD = |CER − EER| = |0.4 − 0.6| = |0.2| = 20% increase in risk or what is called absolute risk increase (ARI). It might be easier for clinicians to avoid the terms ARR and ARI and only stick to RD as it will be able to express both conditions.