A New Mixed Frequency Regression Model For Environmental Epidemiology

Background: In the absence of high-resolution response data, exposure-response modelling often relies on aggregated low-frequency exposure data, leading to loss of high-resolution information. Mixed Data Sampling (MIDAS) from econometrics offers an alternative but is limited due to its inability to make high-resolution predictions, inflexible likelihoods and penalised nonlinear functions, and limited visualization options. We propose a mixed-frequency Distributed Lag Non-linear Model (mf-DLNM) which can eliminate the need to aggregate exposure data in environmental epidemiology and provide high resolution predictions for time series studies. Methods: We evaluated the inference and predictive performance of the mf-DLNM. To evaluate its ability to estimate exposure-response relationships, we applied mf-DLNM and same-frequency (sf)-DLNM using data from the West Midlands, UK. Additionally, we compared the predictive performance of mf-DLNM with sf-DLNM and MIDAS across nine regions of England. As MIDAS cannot predict at the resolution of the predictor (daily), we compared the predictive performance of mf-DLNM and MIDAS at weekly resolution. To test the model's ability to predict high temporal resolution risk (daily), we compared sf-DLNM (with access to daily mortality counts) with mf-DLNM (with access only to weekly mortality counts). Results: In the West Midlands example, mf-DLNM performed comparably to sf-DLNM in estimating daily risk of temperature on respiratory mortality. Furthermore, mf-DLNM and MIDAS exhibited similar performance for weekly predictions. For high-resolution predictions, mf-DLNM and sf-DLNM showed nearly similar performance, despite mf-DLNM having access only to low-resolution response data. Conclusion: This mixed-frequency approach in environmental epidemiology overcomes the limitations of predicting health risks using aggregated exposure data and provides estimates of high-resolution outcomes in the absence of high-frequency health outcome datasets.