# Variable Selection via Fused Sparse‐Group Lasso Penalized Multi‐state Models Incorporating Molecular Data

## TL;DR

This paper introduces a new statistical method for analyzing complex disease progression data by combining molecular information with advanced regularization techniques.

## Contribution

The novel fused sparse-group lasso method enables joint variable selection and effect estimation in multi-state models with high-dimensional molecular data.

## Key findings

- The proposed FSGL method effectively selects relevant covariates while enforcing similar effects across disease transitions.
- Simulation studies and AML data analysis demonstrate improved performance over global lasso regularization in sparse model selection.
- The ADMM optimization algorithm successfully adapts to transition-specific hazards regression in multi-state frameworks.

## Abstract

In multi‐state models based on high‐dimensional data, effective modeling strategies are required to determine an optimal, ideally parsimonious model. In particular, linking covariate effects across transitions is needed to conduct joint variable selection. A useful technique to reduce model complexity is to address homogeneous covariate effects for distinct transitions. We integrate this approach to data‐driven variable selection by extended regularization methods within multi‐state model building. We propose the fused sparse‐group lasso (FSGL) penalized Cox‐type regression in the framework of multi‐state models combining the penalization concepts of pairwise differences of covariate effects along with transition‐wise grouping. For optimization, we adapt the alternating direction method of multipliers (ADMM) algorithm to transition‐specific hazards regression in the multi‐state setting. In a simulation study and application to acute myeloid leukemia (AML) data, we evaluate the algorithm's ability to select a sparse model incorporating relevant transition‐specific effects and similar cross‐transition effects. We investigate settings in which the combined penalty is beneficial compared to global lasso regularization.

Clinical Trial Registration: The AMLSG 09‐09 trial is registered with ClinicalTrials.gov (NCT00893399) and has been completed.