Logistic regression is not enough: The need for Bayesian nonparametric modelling for causal inference using observational data, exemplified by the 'gateway' effect
Introduction: Logistic regression (LR)-type model limitations for causal inference are explained theoretically and empirically through the lens of the purported gateway effect from e-cigarette use to smoking. Previous studies have reported that baseline e-cigarette use quadruples odds of follow-up smoking (binarized) in LR-type models of adolescent longitudinal cohorts (LCs), such that increased e-cigarette use would counteract smoking declines. However, US population-level trends show accelerated smoking declines to record-lows when e-cigarette use increased, presenting an apparent paradox. Methods: Population Assessment of Tobacco and Health (USA) Youth Waves 3 to 4 were analyzed with Bayesian Additive Regression Trees (BART) to model baseline e-cigarette use (treatment) and change in number of days smoking from baseline to follow-up (numerical response) among never- and ever-smoking respondents (group effects), adjusting for confounding risk factors (socio-demographic, intra-individual, behavioural, peer influence, and family background). Unlike LR-type models, BART provides nonlinear, nonparametric modelling with counterfactuals and provides causal effect estimates with principled uncertainty estimation. Results: The average effect of e-cigarette use on smoking was both clinically and statistically significant among ever-smoking adolescents (-2 days smoking [diversionary effect; opposite to gateway]) and was not clinically significant among never-smoking adolescents (<1-day absolute change in days smoking [null effect]). Conclusions: When LC data are analyzed with causal inference techniques, the gateway effect disappears, consistent with population-level trends. This likely explains why gateway effects predicted in previous LR-type studies have not materialized in a population-level reversal/unexpected slowing of the US adolescent smoking decline, resolving the paradox.