Covariate dimension reduction for survival data via the Gaussian process latent variable model

TL;DR

This paper introduces a novel probabilistic method combining Gaussian Process Latent Variable Models with Weibull Proportional Hazards to reduce covariate dimensions in survival data, improving robustness and predictive accuracy.

Contribution

It presents a new integrated model for non-linear dimensionality reduction in survival analysis, enhancing overfitting prevention and enabling multi-source data integration.

Findings

Reduced overfitting in high-dimensional survival data

Improved predictive performance over traditional methods

Successfully distinguished risk groups using gene expression data

Abstract

The analysis of high dimensional survival data is challenging, primarily due to the problem of overfitting which occurs when spurious relationships are inferred from data that subsequently fail to exist in test data. Here we propose a novel method of extracting a low dimensional representation of covariates in survival data by combining the popular Gaussian Process Latent Variable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). The combined model offers a flexible non-linear probabilistic method of detecting and extracting any intrinsic low dimensional structure from high dimensional data. By reducing the covariate dimension we aim to diminish the risk of overfitting and increase the robustness and accuracy with which we infer relationships between covariates and survival outcomes. In addition, we can simultaneously combine information from multiple data sources by expressing multiple datasets in terms of the same low dimensional space. We present results from several simulation studies that illustrate a reduction in overfitting and an increase in predictive performance, as well as successful detection of intrinsic dimensionality. We provide evidence that it is advantageous to combine dimensionality reduction with survival outcomes rather than performing unsupervised dimensionality reduction on its own. Finally, we use our model to analyse experimental gene expression data and detect and extract a low dimensional representation that allows us to distinguish high and low risk groups with superior accuracy compared to doing regression on the original high dimensional data.