P3LS: Point Process Partial Least Squares

TL;DR

This paper introduces P3LS, a novel partial least squares method tailored for analyzing point process data, specifically for medical imaging applications like kidney function diagnosis, combining dimension reduction with point process analysis.

Contribution

The paper develops P3LS, a new PLS methodology that incorporates point process predictors and leverages log-Gaussian Cox processes for analyzing time-varying intensities.

Findings

P3LS effectively analyzes inhomogeneous point processes.

Simulation studies demonstrate the method's empirical properties.

Application to kidney data aids in diagnosing renal disease.

Abstract

Many studies collect data that can be considered as a realization of a point process. Included are medical imaging data where photon counts are recorded by a gamma camera from patients being injected with a gamma emitting tracer. It is of interest to develop analytic methods that can help with diagnosis as well as in the training of inexpert radiologists. Partial least squares (PLS) is a popular analytic approach that combines features from linear modeling as well as dimension reduction to provide parsimonious prediction and classification. However, existing PLS methodologies do not include the analysis of point process predictors. In this article, we introduce point process PLS (P3LS) for analyzing latent time-varying intensity functions from collections of inhomogeneous point processes. A novel estimation procedure for $P^3LS$ is developed that utilizes the properties of log-Gaussian Cox processes, and its empirical properties are examined in simulation studies. The method is used to analyze kidney functionality in patients with renal disease in order to aid in the diagnosis of kidney obstruction.