Table 1.

Empirical squared bias and empirical relative efficiency (measured with respect to the mean squared error of UDLIM estimate) of marginal lagged effects across five different two-dimensional distributed lag interaction models based on 1000 simulation datasets. The lagged effects of the both exposures are generated from the same cubic DL function.

Interaction Structure	Metric	UDLIM	CDLIM	TDLIM	BTDLIM	BCDLIM
(1) No Interaction	Squared Bias	0.02	0.00	0.19	0.13	0.00
	Relative Efficiency	1.00	6.82	19.24	8.09	6.27
(2) Tukey’s Structure	Squared Bias	0.01	0.00	0.01	0.01	0.00
	Relative Efficiency	1.00	6.14	18.66	6.71	5.76
(3) Kronecker Product	Squared Bias	0.02	0.00	1.05	0.90	0.00
	Relative Efficiency	1.00	6.68	3.45	2.77	6.17
(4) Sparse	Squared Bias	0.00	66.22	67.14	1.43	0.08
	Relative Efficiency	1.00	0.07	0.07	1.71	2.80
(5) Unstructured	Squared Bias	0.00	93.08	93.98	1.08	0.09
	Relative Efficiency	1.00	0.05	0.05	1.88	2.70