Article type
Year
Abstract
Background: When an outcome is dichotomous and investigators are concerned about potential confounding or effect modification across subgroups (e.g. diabetics versus non-diabetics), they often report both the crude (unadjusted) odds ratio and the stratum-specific odds ratios (or adjusted odds ratios). When the stratum-specific odds ratios are different from each other in the absence of bias in either observational studies or randomized controlled trials, authors often interpret this as causal effect modification (biological interaction).
Objectives: To illustrate that between stratum-specific odds ratios are actually expected to be different if the variable of interest affects the prevalence of the outcome, even when both causal effect modification and bias are absent.
Methods: We demonstrate how and why this phenomenon occurs using hypothetical data from a randomized trial where the one-year untreated mortality was 52%, and the proportion of diabetics (a cause of the outcome) was 30% in each group.
Results: In our example, the relative risk was 50% in all patients, in non-diabetic patients, and in diabetic patients. However, the odds ratio was 0.32 in all patients, 0.38 in non-diabetic patients and 0.17 in diabetic patients, with the interaction term from the statistical model being statistically significant. Remembering that the odds ratio becomes more extreme compared to the relative risk as the prevalence increases, our results are a truism since diabetes affects the outcome in our example. The difference between the stratum-specific odds ratios is dependent on the combined effect of the variable that affects the outcome prevalence (proposed effect modifier), and the baseline risk.
Conclusions: Although logistic regression is an important tool and reporting adjusted odds ratios (or Cox regression and rate ratios) is appropriate in many contexts, investigators and readers should be wary of claims of effect modification or biological interaction when the covariate is known to be an independent cause of the outcome, and the disease is common.
Objectives: To illustrate that between stratum-specific odds ratios are actually expected to be different if the variable of interest affects the prevalence of the outcome, even when both causal effect modification and bias are absent.
Methods: We demonstrate how and why this phenomenon occurs using hypothetical data from a randomized trial where the one-year untreated mortality was 52%, and the proportion of diabetics (a cause of the outcome) was 30% in each group.
Results: In our example, the relative risk was 50% in all patients, in non-diabetic patients, and in diabetic patients. However, the odds ratio was 0.32 in all patients, 0.38 in non-diabetic patients and 0.17 in diabetic patients, with the interaction term from the statistical model being statistically significant. Remembering that the odds ratio becomes more extreme compared to the relative risk as the prevalence increases, our results are a truism since diabetes affects the outcome in our example. The difference between the stratum-specific odds ratios is dependent on the combined effect of the variable that affects the outcome prevalence (proposed effect modifier), and the baseline risk.
Conclusions: Although logistic regression is an important tool and reporting adjusted odds ratios (or Cox regression and rate ratios) is appropriate in many contexts, investigators and readers should be wary of claims of effect modification or biological interaction when the covariate is known to be an independent cause of the outcome, and the disease is common.