Estimation methods with ordered exposure subject to measurement error and missingness in semi-ecological design

Table 2 Application to respiratory symptoms and exposure to carbon black

G = 8, n_y = (245, 240, 129, 224, 157, 192, 174, 53), δ = 0.36
	$s_{b}^{2}$	$s_{η}^{2}$	Naive(se)	GBS(se^∗)	CGBS(se^∗)	CEM(se)
n _x= full	0.41	0.92	-0.0408(0.019)	-0.1593(0.059)	-0.1709(0.059)	-0.1589(0.014)
					^∗ inflated standard error due to GBS approach
				GBS	CGBS	CEM(se)
n _x= 50				-0.1501	-0.1725	-0.1456(0.023)
n _x= 20				-0.1270	-0.1637	-0.1371(0.025)
n _x= 10				-0.1004	-0.1600	-0.1338(0.025)

Grouping with job category: Estimate of β ₁(with standard error in parentheses) G: number of groups; n _x: number of exposures per group; s: estimate variance of the between group distribution of log-transformed exposures; $s_{b}^{2}$ : estimate variance of the between worker distribution of log-transformed exposures; GBS: group-based strategy; CGBS: constrained group-based; Monte Carlo EM (CEM).

ISSN: 1471-2288