Alternative adjustment for seasonality and long-term time-trend in time-series analysis for long-term environmental exposures and disease counts

Abstract

Background: Time-series analysis with case-only data is a prominent method for the effect of environmental determinants on disease events in environmental epidemiology. In this analysis, adjustment for seasonality and long-term time-trend is crucial to obtain valid findings. When applying this analysis for long-term exposure (e.g., months, years) of which effects are usually studied via survival analysis with individual-level longitudinal data, unlike its application for short-term exposure (e.g., days, weeks), a standard adjustment method for seasonality and long-term time-trend can extremely inflate standard error of coefficient estimates of the effects. Given that individual-level longitudinal data are difficult to construct and often available to limited populations, if this inflation of standard error can be solved, rich case-only data over regions and countries would be very useful to test a variety of research hypotheses considering unique local contexts.

Methods: We discuss adjustment methods for seasonality and time-trend used in time-series analysis in environmental epidemiology and explain why standard errors can be inflated. We suggest alternative methods to solve this problem. We conduct simulation analyses based on real data for Seoul, South Korea, 2002-2013, and time-series analysis using real data for seven major South Korean cities, 2006-2013 to identify whether the association between long-term exposure and health outcomes can be estimated via time-series analysis with alternative adjustment methods.

Results: Simulation analyses and real-data analysis confirmed that frequently used adjustment methods such as a spline function of a variable representing time extremely inflate standard errors of estimates for associations between long-term exposure and health outcomes. Instead, alternative methods such as a combination of functions of variables representing time can make sufficient adjustment with efficiency.

Conclusions: Our findings suggest that time-series analysis with case-only data can be applied for estimating long-term exposure effects. Rich case-only data such as death certificates and hospitalization records combined with repeated measurements of environmental determinants across countries would have high potentials for investigating the effects of long-term exposure on health outcomes allowing for unique contexts of local populations.

Keywords: Case-only data; Environmental exposure; Long-term exposure; Seasonality; Time-series analysis; Time-trend.

Fig. 1

Seasonality and time-trend in daily time-series in Seoul, 2002–2013. a PM₁₀ concentration (μg/m³). b all-cause mortality (number of deaths/day), estimated by different functions of variables representing time. Abbreviation: df, degrees of freedom; doy, day of the week; NCS, natural cubic spline; I(year), an indicator function of year throughout the study period; NCS(doy,10df), NCS of day of the year with 10df; NCS(month,5df), NCS of the order of month throughout the study period with 5df; NCS(t,pdf/year), NCS of time throughout the study period with pdf per year; NCS(week,5df), NCS of the order of week throughout the study period with 5df; PM₁₀, particulate matter with aerodynamic diameter ≤10 μm

Fig. 2

Two hypothetical observable lag patterns of the association between 1 μg/m³ increase of exposure to PM₁₀ and mortality, used to generate simulation samples. Abbreviation: PM₁₀, particulate matter with aerodynamic diameter ≤10 μm

Fig. 3

Estimated lag patterns of the association between PM₁₀ and all-cause mortality by different methods to adjust for seasonality and time-trend over 5000 samples of different simulation settings based on time-series data for Seoul, 2002–2013. a and b Low concurvity and Observable lag pattern 1. c and d Low concurvity and Observable lag pattern 2. e and f High concurvity and Observable lag pattern 1. g and h High concurvity and Observable lag pattern 2. Abbreviation: df, degrees of freedom; doy, day of the week; I(year), an indicator function of year throughout the study period; NCS, natural cubic spline; NCS(doy,10df), NCS of day of the year with 10df; NCS(month,5df), NCS of the order of month throughout the study period with 5df; NCS(t,10df/year), NCS of time throughout the study period with 10df per year; NCS(week,5df), NCS of the order of week throughout the study period with 5df; PM₁₀, particulate matter with aerodynamic diameter ≤10 μm

Fig. 4

Percentage increase of mortality risk per a 10 μg/m³ increase of PM₁₀ by exposure duration in seven major cities of South Korea, 2006–2013. a All-cause mortality. b Cardiovascular mortality. c Respiratory mortality

Fig. 5

Estimated lag patterns of the association between a 10 μg/m³ increase of PM₁₀ and mortality in seven major cities of South Korea, 2006–2013. a All-cause mortality. b Cardiovascular mortality. c Respiratory mortality