Association of longitudinal pet ownership with wheezing in 3-year-old children using the distributed lag model: the Japan Environment and Children’s Study

Table 1 Simulation experiment results: bias

time	γ=0			γ=0.975			γ=0.9999
time	Single	Multi	DLM	Single	Multi	DLM	Single	Multi	DLM
Scenario 1
6	0.0	0.1	0.0	93.2	-0.2	0.1	131.7	1.4	-0.8
12	-0.3	-0.2	-0.1	97.3	0.5	-0.1	131.9	-3.1	-0.5
18	-0.5	-0.4	-0.1	100.1	-0.4	-0.1	132.1	0.2	-0.2
24	0.1	0.2	-0.1	101.9	0.0	-0.1	132.3	-0.1	0.1
30	-0.3	-0.2	-0.1	102.8	0.2	-0.1	132.3	2.1	0.3
36	-0.2	-0.1	-0.1	102.7	-1.6	-0.1	132.3	0.0	0.4
42	-0.3	-0.3	-0.1	102.2	1.1	0.0	132.3	0.6	0.3
48	-0.1	0.0	-0.1	100.3	-0.1	0.1	132.1	-1.7	0.2
54	-0.1	-0.1	-0.1	97.6	1.1	0.2	131.9	0.0	0.0
60	-0.3	-0.2	-0.1	93.4	-0.5	0.3	131.7	0.0	-0.4
Scenario 2
6	0.4	0.3	0.1	98.9	-0.2	-0.1	139.4	-1.2	-0.1
12	-0.3	-0.2	-0.2	99.1	0.1	-0.1	134.8	3.4	-0.2
18	-0.4	-0.3	-0.2	99.7	-0.1	0.0	131.3	-0.6	-0.2
24	-0.3	-0.2	-0.2	100.3	0.4	0.1	129.0	0.5	-0.1
30	-0.3	-0.2	-0.1	100.6	-0.1	0.2	127.7	-3.1	-0.1
36	0.0	0.1	0.0	100.7	1.1	0.2	127.6	-2.5	0.0
42	-0.3	-0.2	0.0	100.1	-0.8	0.1	128.7	3.0	0.0
48	-0.2	-0.1	0.0	99.4	-0.3	0.0	130.8	2.3	0.1
54	-0.5	-0.4	0.0	98.7	-0.3	-0.2	134.1	-3.2	0.2
60	-0.1	0.0	0.0	98.3	-0.4	-0.4	138.6	1.1	0.3
Scenario 3
6	0.3	0.3	0.9	33.6	0.5	-0.1	49.4	0.9	-3.4
12	0.4	0.4	-4.2	35.1	0.5	-4.1	49.5	0.3	-3.2
18	-0.3	-0.3	-0.9	36.6	-0.9	-0.6	49.6	-1.6	0.9
24	-0.1	-0.1	4.5	38.7	-0.1	4.6	49.8	-0.7	5.6
30	-0.1	-0.1	9.4	41.3	0.4	9.4	50.0	2.3	9.4
36	-6.5	-6.5	-12.3	20.8	-5.9	-12.4	25.2	-5.8	-13.2
42	-0.4	-0.4	-11.4	21.9	-0.6	-11.6	25.2	-7.5	-12.8
48	6.5	6.6	11.5	43.1	6.3	11.4	50.1	9.2	10.5
54	0.2	0.2	6.2	39.9	0.1	6.3	49.9	3.4	6.5
60	-0.5	-0.5	-2.6	37.7	0.3	-2.1	49.7	-0.3	-0.1

Bias rounded to the fourth decimal place and multiplied by \({10}^{2}\)
Single, the exposure at each time point is used in a separate regression model; Multi, the exposures at each time point are simultaneously entered into a single regression model; DLM, the Distributed Lag Model
γ represents the correlation used to generate data between exposures
Scenario 1: Exposure effects are constant regardless of time point. Scenario 2: Exposure effects’ magnitude is an upward convex quadratic curve. Scenario 3: Exposure effects exist only from \(t = 36 \text{ to } 47\)

ISSN: 1476-069X