1 Department of Epidemiology, School of Public Health, University at Albany, State University of New York, Rensselaer, NY.
2 Department of Epidemiology and Population Health, Albert Einstein College of Medicine, Bronx, NY.
3 Departments of Pulmonary and General Internal Medicine, Samuel S. Stratton Department of Veterans Affairs Medical Center, Albany, NY
We thank Dr. Cummings (1) and Drs. Deddens and Petersen (2) for their observations on our paper (3). Many cohort studies focus on disease or death as the outcome. These events typically occur infrequently enough in a study period to be considered mathematically rare (i.e., <10 percent). Researchers in such studies utilize logistic regression when approximately equal follow-up occurs, and they correctly use the adjusted odds ratio to estimate relative risk. A growing number of recent studies have investigated common outcomes such as health symptoms, health care utilization, and disease in high-risk populations. Cross-sectional studies of prevalent symptoms, behaviors, and conditions are also on the rise. Many researchers, including well-trained epidemiologists, continue to estimate adjusted relative risks in studies of common outcomes using adjusted odds ratios computed with logistic regression. This highlights the need to focus attention on the correct methods for analysis of such data.
Analytical methods are discussed in the letters by Cummings (1) and Deddens and Peterson (2). Relative risks can also be estimated using other methods, such as the probabilities computed in logistic regression (48). These methods are largely ignored, while a method proposed by Zhang and Yu (9) has become popular for a wide variety of research. It is puzzling that many investigators choose methods that overestimate the adjusted relative risk when appropriate methods of statistical analysis are available. We hypothesize two likely reasons for the continued use of these approaches: accessibility and a lack of education.
The Zhang and Yu method (9) was introduced in the clinical literature in 1998 and provided a simple formula written in a style that was understandable to nonstatisticians. This combination worked well to disseminate the method. A similar approach should be used to educate researchers on statistical methods for study designs that have grown in prominence or for which new statistical methods have become available.
Now that many researchers are studying common outcomes, graduate courses in statistics and epidemiology should cover this topic more thoroughly. Review articles published in the public health, epidemiology, medicine, and social science literature would be useful for researchers who have completed formal training yet find the statistical literature unapproachable. Despite multiple concerns about the quality of complex statistical analysis undertaken by persons who have not been thoroughly trained for such work, the reality is that they are major players in the analysis of data. Since this is unlikely to change in the near future, working to translate statistical methods for researchers who conduct data analysis is a worthwhile goal. We believe that the Practice of Epidemiology section of the Journal is an important place for such discussions and thus chose to submit our paper for publication in that section (3).
Because a substantial number of researchers, including epidemiologists, lack the resources to access complex computer programs, more user-friendly statistical software is needed. Logistic regression is available in user-friendly formats in most statistical software packages, which may explain its popularity. The log-binomial model is available in several statistical packages, although it is somewhat less accessible. Fortunately, we have found that the log-binomial model is easily taught and is well received when the instruction is given from both a conceptual and a mathematical perspective.
We concur with Cummings (1) and Deddens and Petersen (2) that the statistical methods discussed in our paper are not new. The methodological issues pertaining to estimation of adjusted relative risks in studies of common outcomes have been discussed in the statistical and epidemiologic literature for many years. The purpose of our paper was to focus attention on frequent errors made in the analysis of studies with common outcomes and to suggest alternatives that can be readily implemented. We believe that we met this goal, and we welcome continued discussion of these important topics.
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