Methods/Statistics
Quasi-U-shaped Generalized Additive Model Wenhui Zhu* Wenhui Zhu Zhu Peking University
Incorporating shape constraints into models is widely recognized to enhance both accuracy and interpretability of results by leveraging epidemiologically shape priors. However, existing shape-constraint methods cannot effectively account for the prior following a quasi-U shape—a composite pattern encompassing monotonic increase, monotonic decrease, and U-shaped curves, as exemplified by the exposure-response relationship between temperature and mortality. In this work, we developed a new method called quasi-U-shaped generalized additive model (qUGAM) and theoretically demonstrate its advantages in integrating the quasi-U-shaped priors. Simulation studies showed that qUGAM considerably outperformed conventional generalized additive model (GAM) in estimating quasi-U-shaped exposure-response associations. Specifically, qUGAM achieved comparable or superior performance in root mean squared error (RMSE), relative RMSE, mean absolute error (MAE), relative MAE, coverage percentage of 95% confidence interval, and interpretability. These improvements were particularly pronounced at both ends of the exposure range with threshold effects and under a small sample size. A case study examining temperature-mortality associations further supported these findings. Given the wide existence of quasi-U-shaped priors, qUGAM holds substantial potential for broad application across diverse scientific and public health practice.