# Adaptive Sparsening and Smoothing of the Treatment Model for Longitudinal Causal Inference Using Outcome‐Adaptive LASSO and Marginal Fused LASSO

## TL;DR

This paper introduces a new method for selecting important variables in longitudinal studies to better estimate causal effects over time.

## Contribution

The novel two-step procedure combines adaptive LASSO methods to improve causal effect estimation in time-varying treatment settings.

## Key findings

- The proposed LOAL method adaptively selects covariates to reduce estimator variance in longitudinal causal inference.
- The adaptive fused LASSO improves model efficiency and reduces bias compared to pooled logistic regression models.
- Simulation studies and real data application demonstrate the practical usefulness of the proposed approach.

## Abstract

Causal variable selection in time‐varying treatment settings is challenging due to evolving confounding effects. Existing methods mainly focus on time‐fixed exposures and are not directly applicable to time‐varying scenarios. We propose a novel two‐step procedure for variable selection when modeling the treatment probability at each time point. We first introduce a novel approach to longitudinal confounder selection using a Longitudinal Outcome Adaptive LASSO (LOAL) that will data‐adaptively select covariates with theoretical justification of variance reduction of the estimator of the causal effect. We then propose an adaptive fused LASSO that can collapse treatment model parameters over time points with the goal of simplifying the models in order to improve the efficiency of the estimator while minimizing model misspecification bias compared with naive pooled logistic regression models. Our simulation studies highlight the need for and usefulness of the proposed approach in practice. We implemented our method on data from the Nicotine Dependence in Teens study to estimate the effect of the timing of alcohol initiation during adolescence on depressive symptoms in early adulthood.