Modified case-crossover estimators were unbiased in the presence of temporal trends in the exposure of interest: a simulation study.

OBJECTIVES: Temporal trends in exposure are a common source of bias in the case-crossover design. We evaluated four different estimators of the exposure odds ratio (OR) that adjust for such trends. METHODS: In a simulation study, we simulated 1 million individuals in a 5-year observation period and performed daily Bernoulli-trials to determine exposure status. Exposure probabilities followed a constant, increasing or decreasing trend, or one of three empirical trends based on real-world prescription drug use. The outcome rate was modified by a rate ratio (RR) of 0.5, 1.0 or 2.0. We tested four case-crossover estimators: a naive, unadjusted estimator; two "flipped" estimators modeling the probability of exposure instead of the outcome, adjusting for time linearly or using splines; and a new estimator (self-case-time-control [CTC]), adjusting the naive OR using an estimated trend 1 year prior. For reference, we also applied the CTC design. We performed 2500 simulations for each combination and obtained the mean OR, bias (measured as log (RR)-log(OR)), root mean squared error (RMSE), and coverage. Lastly, we applied all estimators to an empirical example assessing the association between semaglutide and retinal detachment (assumed null-effect) in Danish nationwide health registries. RESULTS: The naive case-crossover estimator was biased under in- or decreasing trends (bias -0.60 to +1.18). The two flipped estimators were unbiased under increasing trends (bias -0.09 to +0.14) but the spline estimator performed better under decreasing trends (bias 0.00 to -0.06). The self-CTC estimator performed similar to the linear estimator. The CTC design was unbiased in all scenarios and yielded the lowest bias. The empirical example yielded biased ORs for the naive estimator, while all other estimators yielded point estimates and 95% confidence intervals (CIs) that were compatible with a null effect. CONCLUSION: The flipped and self-CTC estimators can be used to adjust for temporal trends in the case-crossover design. While the CTC estimator performed better, it requires the use of external time-controls and the assumption that the exposure trend is similar among cases and time controls.