A Single Index Model for Longitudinal Outcomes to Optimize Individual Treatment Decision Rules

TL;DR

This paper proposes a novel single index model that uses baseline covariates to distinguish longitudinal treatment outcomes, enhancing personalized treatment decisions especially when mean responses are similar across treatments.

Contribution

It introduces a method to estimate biosignatures as linear combinations of baseline features that maximize divergence between treatment trajectories, improving precision medicine approaches.

Findings

Method effectively distinguishes treatment trajectories in simulations.

Outperforms traditional methods in handling missing data.

Demonstrated utility in a depression clinical trial.

Abstract

A pressing challenge in medical research is to identify optimal treatments for individual patients. This is particularly challenging in mental health settings where mean responses are often similar across multiple treatments. For example, the mean longitudinal trajectories for patients treated with an active drug and placebo may be very similar but different treatments may exhibit distinctly different individual trajectory shapes. Most precision medicine approaches using longitudinal data often ignore information from the longitudinal data structure. This paper investigates a powerful precision medicine approach by examining the impact of baseline covariates on longitudinal outcome trajectories to guide treatment decisions instead of traditional scalar outcome measures derived from longitudinal data, such as a change score. We introduce a method of estimating "biosignatures" defined as linear combinations of baseline characteristics (i.e., a single index) that optimally separate longitudinal trajectories among different treatment groups. The criterion used is to maximize the Kullback-Leibler Divergence between different treatment outcome distributions. The approach is illustrated via simulation studies and a depression clinical trial. The approach is also contrasted with more traditional methods and compares performance in the presence of missing data.