Table 2. Penalized Regression Estimates of Main Prenatal Substance Exposure and Exposure Interactions Associated With Childhood Risk of Attention-Deficit/Hyperactivity Disorder.

Prenatal exposure	Log HRa
Main substanceb
Tobacco	0.40
Alcohol	−0.05
Cannabis	0.14
Opioids	0.70
Interaction between substances
2-Way
Tobacco and cannabis	Removed
Tobacco and alcohol	Removed
Tobacco and opioids	−0.51
Opioids and cannabis	0.23
Opioids and alcohol	0.17
Alcohol and cannabis	Removed
3-Way
Tobacco, opioids, and cannabis	0.20
Tobacco, opioids, and alcohol	−0.07
Tobacco, alcohol, and cannabis	Removed
Opioids, alcohol, and cannabis	Removed
4-Way	Removed
Tobacco, opioids, alcohol, and cannabis	Removed

Abbreviation: HR, hazard ratio.

^a Hazard ratios from Cox proportional hazards regression analysis using an elastic net model. Some variables were removed from the model during the penalized regression estimation. These variables were not statistically significant, and their estimated effect was essentially null. P values were not generated for penalized regression methods because of the bias-variance tradeoff and, given that the model removed uninformative variables, inclusion in the model was considered suggestive of an informative association.³² In this analysis, 95% CIs were not calculated because penalized estimates artificially reduce variance in estimations by penalizing and shrinking the coefficients, resulting in 95% CIs that are artificially small and giving the impression of high precision when those estimates instead reflect high levels of bias.

^b Main substance effects were accounted for by selecting the option to force them into the model.