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

Table 2 Bias, standard deviation, nominal coverage of 95% confidence interval for the overall cumulative association between distributed lags of PM₁₀ (lag0–730) and all-cause mortality estimated by a model with different adjustment methods for seasonality and long-term time-trend over 10,000 samples of different simulation settings based on time-series data for Seoul, 2002–2013

Concurvity^a	Adjustment^b	Observable Lag Pattern 1^a			Observable Lag Pattern 2^a
Concurvity^a	Adjustment^b	Bias (%)	SD^c	Coverage^d(%)	Bias (%)	SD^c	Coverage^d(%)
Low	Not adjusted	−50.1	0.004	0	− 509.2	0.004	0
	NCS(t,4df/year)	885.2	1.457	89.6	9259.9	1.459	88.9
	NCS(t,10df/year)	− 2239.6	19.994	94.3	−21,974.9	19.651	94.7
	10,5,5	−0.5	0.047	95.0	−2.6	0.047	94.9
High	Not adjusted	−54.1	0.003	0	− 549.4	0.003	0
	NCS(t,4df/year)	1346.0	1.828	88.7	14,086.5	1.825	87.9
	NCS(t,10df/year)	− 496.0	24.822	94.9	− 2649.2	24.971	94.6
	10,5,5	−0.4	0.056	94.8	2.9	0.055	95.0

Abbreviations: df degrees of freedom, NCS natural cubic spline, NCS(t,pdf/year) NCS of time throughout the study period with pdf per year, PM₁₀ particulate matter with aerodynamic diameter ≤10 μm, SD standard deviation
^aSimulation settings: Low concurvity & Observable lag pattern 1, Low concurvity & Observable lag pattern 2, High concurvity & Observable lag pattern 1, and High concurvity & Observable lag pattern 2; Observable lag patterns 1–2 are provided in Fig. 2
^bNCS(doy,10df)+I(year)+NCS(week,5df)+NCS(month,5df) is described as 10,5,5; NCS(doy,10df) is NCS of day of the year with 10df; I(year) is an indicator function of year throughout the study period; NCS(week,5df) is NCS of the order of week throughout the study period with 5df; NCS(month,5df) is NCS of the order of month throughout the study period with 5df
^cSD of estimates of the overall cumulative coefficient (as 10 μg/m³ increase of PM₁₀)
^dNominal coverage of 95% confidence intervals

ISSN: 1471-2288