Table 1.

True and observed values in the simulated population.

Values in the Population (Notation)	True Values	Observed Values	Measurement Error	Postulated True Association with Latent Measure of Outcome a	Cutoffs Range (Increments)
Environmental exposure 1 (X1)	X1 ~ N(0,1), correlated with X2 by Pearson correlation ρ = 0.7	W1 = X1 + ε1	ε1 ~ N(0, σ2), where σ2 ℘ {0.0625, 0.25, 1}	{0.15, 0.25, 0.5}	−3 to 3 (in increments of 0.1) See Figure 1 for cutoffs for 5 categories
Environmental exposure 2 (X2)	X2 ~ N(0,1), correlated with X1 by Pearson correlation ρ = 0.7	W2 = X2 + ε2	ε2~N(0, 0.25)	0	<1 vs. ≥1
Sex (Z)	Z~Binomial(0.5, 1)	Z	None	1
Gestational age (Xga)	Xga = (43 – γ), where γ ~ χ2(3) 1 week was subtracted from the above gestational age for 5% of males	Wga = R((Xga + εga); 23, 43), Where R(.) b is function that round expression to integers, and then truncated to 23 to 43 weeks.	${\text{ε}}_{\text{ga}}~\text{ N}(0,\frac{1}{7^2})$	0.1	<37 vs. ≥37
Autism endophenotype (latent, Y)	Linear model: YLinear = β1X1 + β2X2 + β3Z + β4Xga + εy “Threshold” (semi-linear) model: If x1 < meanx1-standard deviationx1 then YThreshold = β2X2 + β3Z + β4Xga + εy If x1 ≥ meanx1-standard deviationx1 then YThreshold = 1.5 × β1X1 + β2X2 + β3Z + β4Xga + εy “Saturation” (semi-linear) model: If x1 < meanx1-standard deviationx1 then YSaturation = 1.5 × β1X1 + β2X2 + β3Z + β4Xga + εy If x1 ≥ meanx1-standard deviationx1 then YSaturation = 0.5 × β1X1 + β2X2 + β3Z + β4Xga + εy, εy ~ N(0,1)	Y b = R(T(y); 0, 18), where T(.) is a function that is transformed to a Y log-normal distribution that matched the observed AOSI in EARLI	due to rounding by R(.) b	Not applicable	0–6, 7–18

^a coefficients of linear regression, see text and bottom of the table for details, β’s; ^b R(f(.); min, max) is the function that rounds values of function f(.) to integers and truncates values (retains only values) that fall within interval [min, max].