Estimating uncertainty in observational studies of associations between continuous variables: example of methylmercury and neuropsychological testing in children

Table 1 Summary of input parameters and assumptions in the Monte Carlo simulation of the FIS results adjusted for outcome misclassification, selection bias and confounding

Input Parameters	Distribution	Source (reference)
*Outcome misclassification (information bias)*
Observed exposure: mercury concentration in cord blood (mg/L),	Mean_x = 31.99, SD_x = 25.53	Budtz-Jorgensen et al. 2005; based on median and 99^th percentile in a log-normal distribution (39)
Observed outcome: Score on Boston naming test	Mean_y = 25, SD_y = 5.3	Mean: Grandjean et al. 1997 (4), SD from Budtz-Jorgensen et al. 2004
Observed b₁	N (-0.019, 0.0063)	Budtz-Jorgensen et al. 2005 (39)
Observed b₀	= 25 - 31.99 × Observed b₁	Derived using standard linear regression formula (b₀ = -b₁ )
P1: proportion of exposed with a1 (negative) adjustment	U (0.1,0.3)	Hypothetical (no data available)
P2: proportion of exposed with a2 (positive) adjustment	U (0.1,0.3)
a1: relative adjustment in outcome for proportion p1 of subjects	U (0.0,0.31)	Hypothetical (no data available), limits chosen to allow BNT score vary between 0 and 60
a2: relative adjustment in outcome for proportion p2 of subjects	U (0.0,0.48)

*Selection bias*
Observed exposure: mercury concentration in cord blood (mg/L),	See above
10,000 vectors (Mean_y, Sd_y, b₀, b₁) adjusted for information bias	Output of Information Bias module
Number of subjects included in the analysis	866	Grandjean et al. 1997; N in Boston Naming Test "no cues" (4)
Number of eligible subjects	1362	Calculated as 1022/0.75 (1022 are ~75% of all births (44)
Number of subjects excluded from the analysis	496	Derived as 1362-866
Relative difference between mean exposure of subjects not included and mean exposure of included subjects	U (-5%,5%)	Hypothetical (no data available)
Relative difference between mean outcome of subjects not included and mean outcome of included subjects	U (-10%,10%)	Hypothetical (no data available)
Slope multiplier (to get to slope of non-included subjects)	U (0,2)	Hypothetical (no data available)

*Confounding*
10,000 vectors (Mean_x, SD_x, Mean_y, SD_y, b₀, b₁) adjusted for information and selection bias	Output of Selection Bias Module
Pearson correlation between confounder (WAIS) and exposure	U (-0.5, 0.5)	Hypothetical (no data available)
Pearson correlation between confounder (WAIS) and outcome	U (0.2, 0.8)	Hypothetical (no data available)