(Published June 2006)

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Risk Calculations

Risk calculations quantify the probability of a particular outcome associated with a specific exposure or hazard. Such calculations allow researchers to hypothesize about a causal link between an exposure and an outcome and allow epidemiologists to calculate the degree to which a disease or event may be attributable to a particular exposure.¹ Risk calculations also allow patients and providers to weigh the pros and cons associated with a treatment intervention. Risk calculations are one of many factors that should be taken into account in making an informed decision among various health care options.

Understanding Odds Ratio

The relative risk can be calculated for cohort studies because the underlying incidence of the condition is known (i.e., the incidence in the unexposed group).1 However, the relative risk cannot be calculated for a case-control study because the underlying incidence of the condition under study (i.e., the incidence in the unexposed group) is unknown. Instead, an odds ratio is calculated. The odds ratio is a risk calculation similar to relative risk that is used to identify an association between an exposure and an outcome in case-control studies. An in-depth discussion of odds ratio is beyond the scope of this report; providers should just be aware that odds ratio quantifies risk for case-control studies in the same way that relative risk quantifies risk for cohort studies.

Understanding the difference between association and causality is essential to a discussion of risk calculations. The existence of a statistical association between an exposure and an outcome does not necessarily mean that the exposure caused the outcome. The association could be due to random chance, bias, an unmeasured variable that may explain or cause both the exposure and the outcome (confounding), or other factors. A number of criteria should be met before one decides that an exposure caused an outcome, including the strength of the association, the consistency of the association over multiple studies, biological plausibility, biological gradient, coherence with existing knowledge, specificity of association, and the presence of an appropriate temporal sequence (i.e., the exposure preceded the outcome).² The bottom line is that a weak association or an association documented only in a single study should not be taken as concrete evidence of a true cause-and effect relationship.²

To communicate effectively with patients, providers should understand three commonly used risk calculations: absolute risk, attributable risk, and relative risk.

Absolute Risk

Absolute risk is the proportion of people in a group at risk for a discrete event who experience that event.^3,4 It is calculated as the number of people with an event divided by the total number of people at risk for the event. Let’s use as an example one of the studies that triggered the “pill scare” of 1995. This study found that of 100,000 women taking third-generation OCs, 30 developed VTE each year.⁵ Thus, the absolute risk of VTE was 30 per 100,000 woman-years.

Attributable risk is the difference in risk of an outcome between those exposed and those not exposed, or between those exposed to two different exposures.^3,6 It reflects the degree of risk associated with exposure and is calculated as the risk in people exposed minus the risk in people unexposed. To continue the example from the pill scare, the absolute risk of VTE in women who took second-generation OCs was 15 per 100,000 woman-years compared with 30 per 100,000 woman-years in those using third-generation OCs.5 Therefore, in women taking thirdgeneration OCs, the attributable risk of VTE was 15 per 100,000 woman-years compared with those taking second-generation (30 per 100,000 womanyears minus 15 per 100,000 woman-years = 15 per 100,000 womanyears). Conversely, the absolute risk reduction is the difference in risk between those exposed (to an intervention) and those unexposed, or between two groups exposed to different interventions. It is calculated the same way as attributable risk but specifically reflects the reduction in risk associated with an intervention, or with one intervention compared with another. In this example, the absolute risk reduction for VTE in women taking second-generation OCs compared with those taking third-generation OCs was 15 per 100,000 woman-years.

Relative Risk

Relative risk is the ratio of frequency of an outcome in people exposed compared with the frequency in people unexposed. It reflects the likelihood of developing an outcome based on an exposure and is used to identify an association between an exposure and an outcome.^1,2 Relative risk is calculated as the outcome rate in the exposed divided by the rate in the unexposed.

To return to the example from the pill scare, relative risk is calculated from the absolute risk of VTE in the exposed group (in this case, women taking third-generation OCs) and the absolute risk in the unexposed group (women taking second-generation OCs). Therefore, the relative risk of VTE for women taking third-generation OCs compared with second-generation OCs is 2.0 (30 per 100,000 woman-years divided by 15 per 100,000 womanyears). A relative risk greater than 1.0 signifies an increased risk of the outcome in the exposed group, as outlined in Table 1 and Figure 3. In this study, women taking third-generation OCs had a risk of VTE two times that of women taking second-generation OCs.

However, even if the risk was correctly stated, the absolute risk of VTE was small. In fact, the risk of VTE with OC use is smaller than the risk associated with pregnancy, as shown in Figure 4.^6,7 Ironically, by stopping third-generation OCs altogether rather than switching to a different contraceptive method, women were potentially exposed to an even greater risk of VTE through unintended pregnancy.

References

1. Hennekens CH, Buring JE. Epidemiology in Medicine. Boston: Little, Brown, and Company; 1987. p. 77.
2. Grimes DA, Schulz KF. Bias and causal associations in observational research. Lancet. 2002;359:248-52.
3. Evidence Based Emergency Medicine at the New York Academy of Medicine. Definitions: absolute risk and its reduction. Available at: http://ebem.org/definitions.html. Accessed February 3, 2006.
4. Misselbrook D, Armstrong D. Thinking about risk: Can doctors and patients talk the same language? Fam Practice. 2002;19:1-2.
5. Mills A. Combined oral contraception and the risk of venous thromboembolism. Human Reprod. 1997;12:2595-8.
6. Shulman LP, Goldzieher JW. The truth about oral contraceptives and venous thromboembolism. J Reprod Med. 2003;48:930-8.
7. Chang J, Elam-Evans LD, Berg CJ, et al. Pregnancy-related mortality surveillance—United States, 1991-1999. In: Surveillance Summaries, February 21, 2003. MMWR. 2003;52(SS-2):1-8.