Table 3.

Simulation experiment results: mean squared error

	γ=0			γ=0.975			γ=0.9999
time	Single	Multi	DLM	Single	Multi	DLM	Single	Multi	DLM
Scenario 1
6	0.5	0.5	0.4	87.3	1.6	0.7	173.8	26.7	3.3
12	0.5	0.5	0.2	95.1	2.3	0.2	174.4	37.7	1.5
18	0.5	0.5	0.2	100.5	2.4	0.2	174.9	38.8	0.8
24	0.6	0.6	0.1	104.3	2.2	0.1	175.3	37.8	0.6
30	0.5	0.5	0.1	106.1	2.2	0.1	175.5	36.1	0.7
36	0.5	0.5	0.1	105.8	2.2	0.2	175.5	40.4	0.9
42	0.5	0.5	0.1	104.7	2.4	0.2	175.3	40.1	0.8
48	0.5	0.5	0.1	100.9	2.3	0.1	174.9	35.3	0.7
54	0.5	0.5	0.1	95.7	2.4	0.1	174.5	39.2	1.0
60	0.5	0.5	0.3	87.6	1.5	0.5	173.8	26.9	3.1
Scenario 2
6	0.5	0.5	0.5	98.2	1.6	0.7	194.8	26.3	3.0
12	0.5	0.5	0.2	98.7	2.1	0.2	182.2	38.3	1.4
18	0.5	0.5	0.2	99.8	2.2	0.2	172.8	37.2	0.8
24	0.5	0.5	0.1	101.1	2.4	0.1	166.7	38.9	0.6
30	0.5	0.5	0.1	101.7	2.3	0.1	163.5	38.1	0.7
36	0.5	0.5	0.1	101.8	2.3	0.1	163.3	42.1	0.9
42	0.5	0.5	0.1	100.5	2.3	0.1	166.0	38.0	0.9
48	0.5	0.5	0.1	99.2	2.2	0.1	171.6	40.0	0.7
54	0.6	0.6	0.2	97.9	2.3	0.1	180.2	39.1	1.0
60	0.5	0.6	0.4	97.1	1.6	0.5	192.3	25.7	3.0
Scenario 3
6	0.7	0.7	0.6	11.8	2.1	1.0	25.0	32.4	4.7
12	0.6	0.6	0.4	12.9	2.8	0.4	25.1	46.1	2.2
18	0.7	0.7	0.2	13.9	3.0	0.3	25.2	45.1	1.2
24	0.6	0.6	0.4	15.5	3.0	0.4	25.3	48.2	1.2
30	0.6	0.6	1.0	17.6	3.1	1.1	25.5	47.5	2.0
36	1.0	1.0	1.7	4.8	3.4	1.8	6.9	47.0	3.1
42	0.6	0.6	1.5	5.3	3.1	1.6	6.9	46.6	2.9
48	1.1	1.1	1.5	19.1	3.5	1.4	25.6	46.6	2.1
54	0.6	0.6	0.6	16.5	2.8	0.5	25.5	45.6	2.0
60	0.7	0.7	0.5	14.8	2.1	0.8	25.3	31.9	4.9

MSE 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 $t=36\text{to}47$