Mixed-Frequency Regression Model for Short-Term Environmental Exposure-Response Modelling: A Simulation Study

Background: Extreme environmental events, such as extreme temperatures and air pollution, have become a global concern due to their detrimental effects on human health. Short-term peak exposure episodes, despite lasting only a few hours, are crucial for exposure-response modelling. The use of time-aggregated exposure data often overlooks the impact of peak exposures on human health. However, studies employing high-temporal resolution exposure data are rare due to the limited availability of high-temporal resolution health outcomes across various scenarios. Therefore, to address the limitations associated with exposure-response modelling using aggregated exposure data, we have developed a model referred to as the mixed-frequency distributed lag non-linear model (mf-DLNM). Methods: In this work, a simulation study was conducted to further validate the mf-DLNM for hourly-daily mixed-frequency data, using data on hourly temperature and daily respiratory mortality for the West Midlands, UK. Given that the focus was on extreme exposures, Relative Risks (RR) at the 5th and 95th temperature quantiles were considered as the estimands of interest. Model performance was evaluated based on the bias, empirical standard error (EmpSE), and coverage of these estimands. Additionally, the model was assessed across various scenarios, considering data size (1, 3, 5, and 11 years with a 24-hour lag), lag length (12 and 24 hours with 11 years), seasonal variation (summer months with 11 years and 24-hour lag) and distribution (Poisson and negative binomial). Results: The mf-DLNM effectively captured the true parameters of the model. The model, fitted to 11 years of simulated data, a 24-hour lag and a Poisson distribution, observed a bias of 0.011 (0.0009) and 0.011 (0.001) for the RR at the 5th and 95th temperature quantiles, respectively, with Monte Carlo SEs (MCSEs) in parentheses. Furthermore, the model exhibited coverage of 0.94 and 0.93 for RR at the 5th and 95th temperature quantiles, respectively. In addition, the mf-DLNM with hourly and daily data demonstrated satisfactory performance across all scenarios except for the RR at 95th temperature quantiles in the seasonal analysis. Conclusions: Researchers are encouraged to adopt mf-DLNM in instances where high-temporal resolution exposure data are available alongside low-resolution health data. It serves as an alternative to traditional approaches that aggregate high-frequency exposure data. By preserving the temporal information of environmental exposures, mf-DLNM enables a more precise assessment of exposure-response relationships, thereby improving the accuracy and reliability of health risk estimates. This approach offers a promising opportunity for informed decision-making and the development of effective interventions for vulnerable populations and healthcare facilities to address short-term environmental episodes.