Unbiased estimates using temporally aggregated outcome data in time series analysis: generalization to different outcomes, exposures and types of aggregation.

Abstract

Background: A new method for time series analysis was recently formulated and implemented that uses temporally aggregated outcome data to generate unbiased estimates of the underlying association between temporally disaggregated outcome and covariate data. However, the performance of the method was only tested in the context of the delayed nonlinear relation between temperature and mortality, and only in the case of the aggregation of sets of consecutive days.

Methods: We conduct a simulation analysis to test the performance of the method using (i) mortality and hospital admissions as health outcomes, (ii) temperature and nitrogen dioxide as exposures, and (iii) the three aggregation schemes most widely used in open access health data, including aggregations of sets of non-consecutive days.

Results: With sufficient data for analysis, the method can recover the underlying association for all combinations of outcomes, exposures, and aggregation schemes. The bias and variability of the estimates increase with the degree of aggregation of the outcome data, and they decrease with increasing sample size (length of dataset, number of cases). Remarkably, estimates are also unbiased even in extreme cases with weekly outcome data in an association confounded by the day of the week, such as those of air pollution models.

Conclusions: With sufficient data, the method is able to flexibly generate unbiased estimates, generalizing previous results to other outcomes, exposures and types and degrees of aggregation. Such results can boost the use of available temporally aggregated health data for research, translation, and policymaking, especially in low-resource and rural areas.