### INTRODUCTION

^{1)}Relative risk is a scale showing how many times higher the incidence of an event is in the group exposed to the risk factors of the event than in the group not exposed by calculating the ratio of the incidence in the exposed group to that in the non-exposed group.

^{2)}Odds ratio is a scale used often in medical research reports because it has a number of useful characteristics. First of all, odds ratio provides uniform (regular) values in both retrospective and prospective studies.

^{2,}

^{3)}Unlike relative risk, odds ratio treats the two variables being compared symmetrically, and can be estimated using some type of non-random samples. For this reason, many case-control studies report odds ratio.

^{2,}

^{3)}

^{4,}

^{5)}Moreover, odds ratio can be derived easily even through more complicated calculation under the condition that confounding variables are controlled as in logistic regression analysis.

^{6)}

^{3)}Relative risk itself allows intuitive interpretation. That is, if the relative risk is A, we can say "the risk of an event is A times higher in those exposed to certain risk factors: than in unexposed ones." Because odds ratio is just 'ratio of odds' it may not be interpreted intuitively.

^{2,}

^{3)}

^{3)}In addition, odds ratio is easily mistaken for relative risk by lay people or media personnel without expert knowledge about the definitions of relative risk and odds ratio or difference between the two concepts. Odds ratio is reported in many newspaper articles on academic studies, and many of them are misinterpretations of relative risk. For example, a research result saying "The odds ratio for disease A is B if one eats C" is often described wrongly as "The risk of disease A increases B times higher if one eats C much." Even in some theses, odds ratio is mistaken for relative risk. As mentioned above, however, in order for odds ratio to be similar to relative risk, the odds ratio should be close to 1 or the incidence of the event should be low.

^{4,}

^{5)}According to Zhang and Yu,

^{1)}if

*P*

_{0}, namely, the incidence of an event in the non-exposed group is higher than 0.1 or the odds ratio is higher than 2.5 or lower than 0.5, difference between the odds ratio and the relative risk is expected to be large. Thus, although odds ratio should not be mistaken for relative risk,

^{1)}such a mistake can be made easily and this may lead to wrong interpretation and application of research results.

^{3)}

^{1)}and assessed difference between the odds ratio and the estimated relative risk. The objective of this study was 1) to investigate cases misinterpreting odds ratio, 2) to assess difference between odds ratio and estimated relative risk when possible.

### METHODS

^{7)}The search keyword was 'odds ratio.' For theses before 1994, we manually searched the Korean Journal of Family Medicine.

*P*

_{0}(the incidence of disease in the group not exposed to risk factors) was reported or when it could be derived from data presented in the theses, we excluded theses for which estimated relative risk was not calculable from the analysis that required the estimation of relative risk.

*P*

_{0}is the incidence of disease in the group not exposed to risk factors and

*P*

_{1}is that in the exposed group. For odds ratio, however, we used the value reported in the theses as in the research by Holcomb et al.

^{3)}and if correction was made for confounding variables the final corrected value was used.

^{1)}in 1998. The formula is as follows.

*P*

_{0}means the incidence of disease in the unexposed group. The validity of this formula was proven in a simulation using virtual cohorts, and as expected, the difference between odds ratio and relative risk was larger when

*P*

_{0}was high.

^{1)}In order for odds ratio to be similar to relative risk, the incidence of disease should be low. This formula can be applied to prospective cohort studies and clinical trials, and to retrospective studies with known prevalence.

^{4,}

^{5)}

_{10}(

*odds ratio*)|

### RESULTS

^{1)}based on

*P*

_{0}. For the remaining 77 theses, we calculated estimated relative risk, and analyzed the difference between estimated relative risk and odds ratio using data from these theses (Figure 1).

_{10}(

*odds ratio*)| was over 20%.

### DISCUSSION

^{3)}We observed a decreasing trend in the frequency of misinterpretation over time. With the exception of a small number of theses, odds ratio was different from estimated relative risk and odds ratio was larger than estimated relative risk (Figure 3). In around 60% of the theses, difference between odds ratio and estimated relative risk was over 20%. This result suggests the possibility that readers may mistake odds ratio for relative risk even if the thesis itself does not misinterpret odds ratio.

*P*

_{0}is quite large, the authors need to prevent such a misinterpretation of odds ratio. Based on medical reports, physicians or ordinary people may make medical or health-related decisions. For example, if a treatment effect calculated as relative risk indicates improvement of 20% but is interpreted as improvement of 40%, doctors and patients may overestimate the effect of the corresponding drug and such a decision can have an adverse effect on the patients.

^{8)}we can reduce the room for misinterpretation by reporting both odds ratio and relative risk at the same time, if possible. In case relative risk is not calculable, the report of estimated relative risk using 'relative risk estimation method'

^{1)}with well-proven validity can remind the readers of the limitations of odds ratio.

^{1-}

^{3)}In particular, guidelines in the field of medicine have been established through meta-analysis that analyzes the results of multiple studies together.

^{9)}

^{3)}the percentage of theses misinterpreting odds ratio in the Korean Journal of Family Medicine was relatively low and decreased continuously. The reasons for the decreasing pattern could not be found in this study, but they may be related to the improved quality of medical studies and statistical education. Considering the health-related effects of misinterpretation on general readers of medical reports, however, there should be continuous caution against the misinterpretation of odds ratio, and further efforts by researchers to reduce the possibility of misinterpretation.