Identification of influential observations in high-dimensional cancer survival data through the rank product test

Survival analysis is a statistical technique widely used in many fields of science, in particular in the medical area, and which studies the time until an event of interest occurs. Outlier detection in this context has gained great importance due to the fact that the identification of long or short-term survivors may lead to the detection of new prognostic factors. However, the results obtained using different outlier detection methods and residuals are seldom the same and are strongly dependent of the specific Cox proportional hazards model selected. In particular, when the inherent data have a high number of covariates, dimensionality reduction becomes a key challenge, usually addressed through regularized optimization, e.g. using Lasso, Ridge or Elastic Net regression. In the case of transcriptomics studies, this is an ubiquitous problem, since each observation has a very high number of associated covariates (genes).

In order to solve this issue, we propose to use the Rank Product test, a non-parametric technique, as a method to identify discrepant observations independently of the selection method and deviance considered. An example based on the The Cancer Genome Atlas (TCGA) ovarian cancer dataset is presented, where the covariates are patients' gene expressions. Three sub-models were considered, and, for each one, different outliers were obtained. Additionally, a resampling strategy was conducted to demonstrate the methods' consistency and robustness. The Rank Product worked as a consensus method to identify observations that can be influential under survival models, thus potential outliers in the high-dimensional space.

The proposed technique allows us to combine the different results obtained by each sub-model and find which observations are systematically ranked as putative outliers to be explored further from a clinical point of view.