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

Table 2 Summary of input parameters and assumptions in the Monte Carlo simulation of the SCDS results adjusted for outcome misclassification, selection bias and confounding

Input Parameters	Distribution	Source (reference)
*Outcome misclassification (information bias)*
Observed exposure: mercury concentration in maternal hair (mg/g)	Mean_x = 6.9, SD_x = 4.5	Myers et al., 2003 (7)
Observed outcome: Score on Boston naming test	Mean_y = 26.5, SD_y = 4.8	Myers et al., 2003 (7)
Observed b₁	N (-0.012, 0.046)	Myers et al., 2003 (7)
Observed b₀	= 26.5 - 6.9 × 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 (0.0,1.95)	Hypothetical (no data available), limits chosen as to allow BNT score vary between 0 and 60
a2: relative adjustment in outcome for proportion p2 of subjects	U (0.0,1.95)

*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	643	Myers et al. 2003 (7)
Number of eligible subjects	1480	Calculated as 740 × 2 (740 are ~50% of eligible population (7)
Number of subjects excluded from the analysis	837	Calculated as 1480 - 643
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)