Choice of stratification in Poisson process analysis of recurrent event data with environmental covariates

The Poisson process approach for studying the association between environmental covariates and recurrent events depends on the stratification of study period into intervals within which the baseline intensities are assumed constant. In this work we investigate the problem of bias and variance due to misspecification of this stratification. We suggest a cross-validation approach to choosing a stratification model to balance the trade-off between bias and variance. We also establish a connection between the Poisson process approach and case cross-over studies.