Approximate Bayesian inference for case-crossover models

A case-crossover analysis is used as a simple but powerful tool for estimating the effect of short-term environmental factors such as extreme temperatures or poor air quality on mortality. The environment on the day of each death is compared to the one or more "control days" in previous weeks, and higher levels of exposure on death days than control days provide evidence of an effect. Current state-of-the-art methodology and software (integrated nested Laplace approximation [INLA]) cannot be used to fit the most flexible case-crossover models to large datasets, because the likelihood for case-crossover models cannot be expressed in a manner compatible with this methodology. In this paper, we develop a flexible and scalable modeling framework for case-crossover models with linear and semiparametric effects which retains the flexibility and computational advantages of INLA. We apply our method to quantify nonlinear associations between mortality and extreme temperatures in India. An R package implementing our methods is publicly available.