In this study, we applied the time-stratified case-crossover (ts-CCO) design, regarded as a self-matched case-control study, which compares the exposure in the case period when events occurred with exposures in nearby referent periods, to examine the differences in exposure which may contribute to the differences in the daily count of cases [18 (link)]. Therefore, a time-stratified case-crossover design was adopted to regulate potential confounders (e.g., age, gender, etc) using self-control and exclude long-term impact of air pollutants (e.g., secular trend, seasonality, etc.) by stratification of time. We used the calendar month as the time stratum, to control the effects of long-term trend, seasonality, and day of the week [17 (link)]. We conducted a quasi-Poisson regression, controlling over-dispersion problem, combined with distributed lag non-linear model (DLNM) to estimate the non-linear and delayed influence of air pollution on IS onset. DLNM is based on the definition of “cross-basis”, a bi-dimensional space of functions to reflect the non-linear exposure-responses and lag structure of the association [19 (link), 20 (link)]. In this study, consequently, the combination of DLNM with the ts-CCO design was employed, which allows estimating the short-term, non-linear and delayed effect of air pollutant using cross-basis functions for depicting the relationship between air pollutant and IS onset along the dimensions of exposure and lag simultaneously based on removing control confounders and long-term trend by ts-CCO design.
A quasi-Poisson regression model combined with time-stratified case-crossover design and DLNM was built as follows:
where t is the day of observation; Yt is the count of IS cases on t; μt is the expectation of Yt; Populationye is the year-end population size; α is an intercept; Pollutanti, t, Tempt, and RHt are the ith pollutant concentration, temperature and relative humidity on t, respectively; cb() represents the cross-basis function with three pre-specified parameters of maximal lag maxlagi, degree of freedom for lag-response natural spline df2i − 1, and degree of freedom for exposure-response natural spline df2i for pollutant, temperature or relative humidity; Holiday is used to control the effect of public holidays; Stratum is the time stratum in the time-stratified case-crossover design. We defined natural cubic spline function with 3 df for air pollution and meteorological factors to mimic the exposure-response pattern of air pollution-IS onset associations, as well as lag spaces with 3 df to estimate the lag effects. To capture the complete lag-response curve, the maximal lag of air pollutants was set to 14 days; for the sake of simplification and without loss of generalization, meanwhile, this maximal lag was assigned to the length of the case and control periods. In addition, a 3-day duration was specified to be the maximal lag of meteorological factors. The df and maximum lag days for air pollution determination referred to the Akaike information criterion for quasi-Poisson (Q-AIC), which could produce the relatively superior model.
We initially conducted single-pollutant model to evaluate the association between air pollution and IS onset, and then the significant air pollutants were included in multi-pollutant model. Spearman’s correlation tests were used to estimate the associations between air pollution and meteorological factors, and pollutants with correlation coefficient r > 0.60 were not included in multi-pollutant model simultaneously to address the collinearity between air pollutants. In order to identify the high-risk or low-risk air pollution condition, the influence of extreme air pollution was evaluated and presented as relative risk (RR) by comparing the 99th above or 1st below percentiles of air pollution to the median values. We calculated the single day lag influence and the cumulative lag influence (lag0–1, lag0–6, lag0–8, lag0–10, lag0–12, lag0–13, and lag0–14) to effectively depict the characteristics of the association between air pollution and IS onset. In addition, we conducted stratified analysis to investigate the impact of air pollution on subgroups according to gender (male and female) and age groups (adult: 18–64 years; the elderly: ≥ 65 years).
All analyses were conducted using R version 3.5.1 with the dlnm package for fitting the DLNM, the gnm package for conditional quasi-Poisson regression.
Sensitivity analyses were performed to test the robustness of the selected model, which were as following: df [2 (link)–6 (link)] for air pollution, and df [2 (link)–6 (link)] for lag space were changed; the maximum lag days (12–21 days) for air pollution were extended.
A quasi-Poisson regression model combined with time-stratified case-crossover design and DLNM was built as follows:
where t is the day of observation; Yt is the count of IS cases on t; μt is the expectation of Yt; Populationye is the year-end population size; α is an intercept; Pollutanti, t, Tempt, and RHt are the ith pollutant concentration, temperature and relative humidity on t, respectively; cb() represents the cross-basis function with three pre-specified parameters of maximal lag maxlagi, degree of freedom for lag-response natural spline df2i − 1, and degree of freedom for exposure-response natural spline df2i for pollutant, temperature or relative humidity; Holiday is used to control the effect of public holidays; Stratum is the time stratum in the time-stratified case-crossover design. We defined natural cubic spline function with 3 df for air pollution and meteorological factors to mimic the exposure-response pattern of air pollution-IS onset associations, as well as lag spaces with 3 df to estimate the lag effects. To capture the complete lag-response curve, the maximal lag of air pollutants was set to 14 days; for the sake of simplification and without loss of generalization, meanwhile, this maximal lag was assigned to the length of the case and control periods. In addition, a 3-day duration was specified to be the maximal lag of meteorological factors. The df and maximum lag days for air pollution determination referred to the Akaike information criterion for quasi-Poisson (Q-AIC), which could produce the relatively superior model.
We initially conducted single-pollutant model to evaluate the association between air pollution and IS onset, and then the significant air pollutants were included in multi-pollutant model. Spearman’s correlation tests were used to estimate the associations between air pollution and meteorological factors, and pollutants with correlation coefficient r > 0.60 were not included in multi-pollutant model simultaneously to address the collinearity between air pollutants. In order to identify the high-risk or low-risk air pollution condition, the influence of extreme air pollution was evaluated and presented as relative risk (RR) by comparing the 99th above or 1st below percentiles of air pollution to the median values. We calculated the single day lag influence and the cumulative lag influence (lag0–1, lag0–6, lag0–8, lag0–10, lag0–12, lag0–13, and lag0–14) to effectively depict the characteristics of the association between air pollution and IS onset. In addition, we conducted stratified analysis to investigate the impact of air pollution on subgroups according to gender (male and female) and age groups (adult: 18–64 years; the elderly: ≥ 65 years).
All analyses were conducted using R version 3.5.1 with the dlnm package for fitting the DLNM, the gnm package for conditional quasi-Poisson regression.
Sensitivity analyses were performed to test the robustness of the selected model, which were as following: df [2 (link)–6 (link)] for air pollution, and df [2 (link)–6 (link)] for lag space were changed; the maximum lag days (12–21 days) for air pollution were extended.
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