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• W1484155669 abstract "In this issue of Academic Emergency Medicine, Kabrhel and colleagues1 report on factors associated with a positive D-dimer result in patients evaluated for pulmonary embolism. They report both the adjusted odds ratios (OR) for potential predictors obtained from logistic regression and the risk ratio (RR) derived from the OR. For most of the variables, the OR and the RR are relatively close. However, for some, most notably third-trimester pregnancy, the OR and the RR are markedly different. There is a simple statistical reason for this discrepancy that is important for readers and researchers to consider. Both ORs and RRs are used to assess the association between an exposure (risk factor) and an outcome. ORs are reported in case–control studies, because RRs cannot be directly estimated. ORs also are reported in cohort and cross-sectional studies when logistic regression is used to assess the association between the risk factors and an outcome while controlling for confounding variables. When the outcome is rare (<10%), the OR and RR are approximately equal, and the OR can be used to approximate the RR.2 However, when the incidence of the outcome is common (>10%), the OR overestimates the RR.2 It is not inherently incorrect to report the OR in a cohort or cross-sectional study, and some advocate the use of ORs.3 The OR has some properties that are preferable to the RR, although interpretation of the OR may not be intuitive.3, 4 Understanding the interpretation of ORs and RRs is important, in particular, for common outcomes. In general, clinicians and patients tend to think in terms of risk (as a probability), rather than odds. The difference between the two is shown in Figure 1, where the risk (a probability) is 0.20, and the odds are 1:4, or 0.25. If the definition of outcome was inverted, the probability would be 0.8, and the odds would be 4:1, or 4. The odds of an outcome can have a value that may range from considerably less than 1 to considerably greater than 1. The risk of an outcome, as a probability, can only range from 0 to 1. Since the risk of an outcome has a much narrower range of values, the RR typically has a narrower range of possible values. RR vs. OR. The figure on the left depicts risk (a probability), the number of patients with the risk factor and the outcome in the numerator, and all patients with the risk factor in the denominator (Risk = 2/(8 + 2) = 2/10 = 20%). The figure on the right depicts odds, the number of patients with the risk factor and the outcome in the numerator and the number of patients with the risk factor without the outcome in the denominator (Odds = 2/8 = 1/4 = 0.25). RR = relative risk. The overall prevalence of a positive D-dimer in patients evaluated for pulmonary embolism in the study by Kabrhel and colleagues is moderate, at 44%.1 Twenty-three patients in the study had a third-trimester pregnancy. Of these patients, nearly all had a positive D-dimer (22/23, 96%). The multivariate analysis found an adjusted OR of 51.25 for third-trimester pregnancy as a predictor of a positive D-dimer, compared to an adjusted RR of 2.25. Using data from Table 2 of Kabrhel et al., we can illustrate the difference between RRs and ORs by calculating unadjusted RRs and ORs (Table 1).1 In this example, the prevalence of a positive D-dimer in those with the risk factor (third-trimester pregnancy) is 0.96 (22/23). The prevalence of a positive D-dimer in those unexposed to the risk factor (third-trimester pregnancy) is 0.43 (1,881/4,333), similar to the group as a whole. The RR is 0.96/0.43, or 2.2. Therefore, subjects with the risk factor of a third-trimester pregnancy have 2.2 times the risk of a positive D-dimer compared to those without the risk factor. Given the prevalence of 0.43 for a positive D-dimer in the unexposed group, we can see that an estimate of 2.2 is nearly the maximum RR that can be obtained in this comparison. In contrast, the odds of a positive D-dimer in those with a third-trimester pregnancy are 22:1, or 22, and the odds of a positive D-dimer in those without a third-trimester pregnancy are 1,881:2,452, or 0.77. This produces an OR of 22/0.77, or 28.7, which is much higher than the estimate of RR. Therefore, subjects with the risk factor of a third-trimester pregnancy have 28.7 times the odds of a positive D-dimer compared to those without the risk factor. The authors use the method of Zhang and Yu2 to calculate the RRs from the ORs obtained from logistic regression using the formula where P0 is the probability of the outcome in the unexposed group.2 This method is simple, convenient, and widely used (JAMA’s website lists 911 citations as accessed on March 19, 2010). It is useful if a reader wants to get an approximate estimate of the RR from a reported OR in a published paper. However, the method does not produce a consistent estimator for RR,4-7 and the confidence intervals (CIs) around this RR are inaccurately narrow.4-6, 8, 9 Various approaches have been proposed to directly estimate adjusted RRs in cohort and cross-sectional studies for common events, and they are easily implemented using standard statistical packages. Reviews and comparison of these approaches and their implementation in statistical packages are available.5, 7, 8, 10 There are advantages and disadvantages for different approaches, and an explanation of these is technically detailed. Interested researchers are encouraged to read these reviews and consult with a statistician to determine the best approach to model common events for their particular study. We will briefly discuss two commonly recommended approaches and provide a general description of their use in Stata (StataCorp, College Station, TX) and SAS (SAS Institute, Cary, NC). For rare events, a logistic regression should still be used. First, RRs can be estimated in cohort or cross-sectional studies using a generalized linear model with a log link and binomial distribution. This approach has been called log-binomial model.4, 5, 7, 9, 10 In Stata, this can be implemented using the glm command with the following syntax:7 glm dv iv1 iv2 iv3, family(binomial) link(log) eform difficult where dv is the dependent variable and iv is an independent variable. Sometimes, this model will fail to converge and produce valid estimates. In these cases, Stata users can use the binreg command, which modifies the convergence algorithm, as follows:7 binreg dv iv1 iv2 iv3, rr The binreg command may achieve convergence when the glm command will not; however, sometimes both approaches will fail to converge. In SAS, proc genmod is used to implement the log-binomial model, as follows:10 proc genmod; model dv = iv1 iv2 iv3/dist = bin link = log; run; The second commonly described approach uses the generalized linear model with log link and a Poisson distribution.4, 5, 7, 10 Because the Poisson distribution overestimates the variation in binary data, a robust variance estimator (also known as the sandwich estimator) is used to obtain correct standard errors for model coefficient estimates. In Stata, this is implemented using the Poisson command:7 poisson dv iv1 iv2 iv3, irr nolog vce(robust) or, equivalently, glm dv iv1 iv2 iv3,link(log) eform vce(robust) family(Poisson) where the option vce(robust) requests the robust variance estimates. In SAS, the Poisson model is again fitted using proc genmod:10 proc genmod; class id; model dv = iv1 iv2 iv3/dist = poisson link = log; repeated subject=id/type = ind; run; where id is the variable that uniquely identifies each subject. The above code usually works for clustered data with multiple observations from each cluster. In this case, it gives robust variance estimates. In addition, a SAS macro has been developed to fit a log-binomial or Poisson model based on convergence status, and information to obtain this macro is provided in Spiegelman and Hertzmark.10 Usually the Poisson model does not have the convergence problem and produces robust estimates, while the estimates from the log-binomial model, when available, are more efficient, producing narrower CIs. With all models, it is possible to produce fitted probability of the outcome that is greater than 1. This will not occur using logistic regression. We commend Kabrhel and colleagues for paying special attention to the interpretation of ORs and making the effort to convert the ORs to RRs to facilitate the interpretation of results. ORs will be higher than RRs for common outcomes and must not be interpreted as RRs when they are reported in cohort and cross-sectional studies. Models that allow direct calculation of adjusted RRs provide more accurate estimates than those obtained from the approach of Zhang and Yu2 and should be considered when it is needed to estimate RRs for common events." @default.
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• W1484155669 title "Risk Ratios and Odds Ratios for Common Events in Cross-sectional and Cohort Studies" @default.
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