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

J Clin Epidemiol. 2026 Apr 29:112291. doi: 10.1016/j.jclinepi.2026.112291. Online ahead of print.

ABSTRACT

BACKGROUND: 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 five-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 naïve, unadjusted estimator; two “flipped” estimators modelling the probability of exposure instead of the outcome, adjusting for time linearly or using splines; and a new estimator (self-case-time-control), adjusting the naïve OR using an estimated trend one year prior. For reference, we also applied the case-time-control design. We performed 2500 simulations for each combination and obtained the mean odds ratio, bias (measured as log(RR)-log(OR)), root-mean squared error, 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 naïve 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-case-time-control estimator performed similar to the linear estimator. The case-time-control design was unbiased in all scenarios and yielded the lowest bias. The empirical example yielded biased odds ratios for the Naïve estimator, while all other estimators yielded point estimates and 95% confidence intervals that were compatible with a null-effect.

CONCLUSION: The flipped and self-case-time-control estimators can be used to adjust for temporal trends in the case-crossover design. While the case-time-control 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.

PMID:42066966 | DOI:10.1016/j.jclinepi.2026.112291