# Latent class profile model with time-dependent covariates: a study on symptom patterning of patients for head and neck cancer

## TL;DR

This paper introduces a new statistical model to identify symptom patterns in head and neck cancer patients, incorporating time-dependent factors.

## Contribution

The novel contribution is extending the latent class profile model to include time-specific structures and time-dependent covariates.

## Key findings

- The proposed model allows for simultaneous estimation of latent class parameters using the EM algorithm.
- Numerical studies validate the model's effectiveness in capturing associations between symptom patterns and covariates.
- Application to head and neck cancer data demonstrates the model's practical utility.

## Abstract

The latent class profile model (LCPM) is a widely used technique for identifying distinct subgroups within a sample based on observations' longitudinal responses to categorical items. This paper proposes an expanded version of LCPM by embedding time-specific structures. Such development allows analysts to investigate associations between latent class memberships and time-dependent predictors at specific time points. We suggest a simultaneous estimation of latent class measurement parameters via the expectation-maximization (EM) algorithm, which yields valid point and interval estimators of associations between latent class memberships and covariates. We illustrate the validity of our estimation strategy via numerical studies. In addition, we demonstrate the novelty of the proposed model by analyzing the head and neck cancer data set.