Efficient Estimation of the Maximal Association between Multiple Predictors and a Survival Outcome

TL;DR

This paper introduces a scalable, reliable method for testing the maximal association between high-dimensional predictors and survival outcomes, addressing bias and computational challenges in post-selection inference.

Contribution

It develops semi-parametrically efficient estimators and a stabilization technique for valid, scalable inference on predictor-survival associations in high-dimensional settings.

Findings

Method provides valid tests even with superpolynomial predictor growth

Simulation results support asymptotic theory at moderate sample sizes

Applied to viral gene expression data to identify relevant patterns

Abstract

This paper develops a new approach to post-selection inference for screening high-dimensional predictors of survival outcomes. Post-selection inference for right-censored outcome data has been investigated in the literature, but much remains to be done to make the methods both reliable and computationally-scalable in high-dimensions. Machine learning tools are commonly used to provide {\it predictions} of survival outcomes, but the estimated effect of a selected predictor suffers from confirmation bias unless the selection is taken into account. The new approach involves construction of semi-parametrically efficient estimators of the linear association between the predictors and the survival outcome, which are used to build a test statistic for detecting the presence of an association between any of the predictors and the outcome. Further, a stabilization technique reminiscent of bagging allows a normal calibration for the resulting test statistic, which enables the construction of confidence intervals for the maximal association between predictors and the outcome and also greatly reduces computational cost. Theoretical results show that this testing procedure is valid even when the number of predictors grows superpolynomially with sample size, and our simulations support that this asymptotic guarantee is indicative the performance of the test at moderate sample sizes. The new approach is applied to the problem of identifying patterns in viral gene expression associated with the potency of an antiviral drug.