Dimension reduction for integrative survival analysis

Abstract

We propose a constrained maximum partial likelihood estimator for dimension reduction in integrative (e.g., pan-cancer) survival analysis with high-dimensional covariates. We assume that for each population in the study, the hazard function follows a distinct Cox proportional hazards model. To borrow information across populations, we assume that all of the hazard functions depend only on a small number of linear combinations of the predictors. We estimate these linear combinations using an algorithm based on "distance-to-set" penalties. This allows us to impose both low-rankness and sparsity. We derive asymptotic results which reveal that our estimator of the regression coefficients is more efficient than fitting a separate proportional hazards model for each population. Numerical experiments suggest that our method outperforms related competitors under various data generating models. We use our method to perform a pan-cancer survival analysis relating protein expression to survival across 18 distinct cancer types. Our approach identifies six linear combinations, depending on only 20 proteins, which explain survival across the cancer types. Finally, we validate our fitted model on four external datasets and show that our estimated coefficients can lead to better prediction than popular competitors.

Binned multinomial logistic regression for integrative cell type annotation

“…From a methodological perspective, there is a growing interest in developing methods for jointly analyzing datasets from heterogeneous sources. Most often, these methods assume distinct data generating models for each source and aim improve efficiency by exploiting similarities across sources (Zhao et al, 2015;Huang et al, 2017;Ventz et al, 2021;Molstad and Patra, 2021). For example, Huang et al (2017) assumed a similar sparsity pattern for regression coefficients corresponding to separate populations.…”