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The analysis of high dimensional survival data is challenging, primarily dueto the problem of overfitting which occurs when spurious relationships areinferred from data that subsequently fail to exist in test data. Here wepropose a novel method of extracting a low dimensional representation ofcovariates in survival data by combining the popular Gaussian Process LatentVariable Model (GPLVM) with a Weibull Proportional Hazards Model (WPHM). Thecombined model offers a flexible non-linear probabilistic method of detectingand extracting any intrinsic low dimensional structure from high dimensionaldata. By reducing the covariate dimension we aim to diminish the risk ofoverfitting and increase the robustness and accuracy with which we inferrelationships between covariates and survival outcomes. In addition, we cansimultaneously combine information from multiple data sources by expressingmultiple datasets in terms of the same low dimensional space. We presentresults from several simulation studies that illustrate a reduction inoverfitting and an increase in predictive performance, as well as successfuldetection of intrinsic dimensionality. We provide evidence that it isadvantageous to combine dimensionality reduction with survival outcomes ratherthan performing unsupervised dimensionality reduction on its own. Finally, weuse our model to analyse experimental gene expression data and detect andextract a low dimensional representation that allows us to distinguish high andlow risk groups with superior accuracy compared to doing regression on theoriginal high dimensional data.

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