Marginal false discovery rate for a penalized transformation survival model

Abstract

Survival analysis that involves moderate/high dimensional covariates has become common. Most of the existing analyses have been focused on estimation and variable selection, using penalization and other regularization techniques. To draw more definitive conclusions, a handful of studies have also conducted inference. The recently developed mFDR (marginal false discovery rate) technique provides an alternative inference perspective and can be advantageous in multiple aspects. The existing inference studies for regularized estimation of survival data with moderate/high dimensional covariates assume the Cox and other specific models, which may not be sufficiently flexible. To tackle this problem, the analysis scope is expanded to the transformation model, which is robust and has been shown to be desirable for practical data analysis. Statistical validity is rigorously established. Two data analyses are conducted. Overall, an alternative inference approach has been developed for survival analysis with moderate/high dimensional data.

Keywords: Marginal false discovery rate; Survival analysis; Transformation model.

Fig. 1.

Scheme of different associations with survival.

Fig. 2.

Simulation 1: estimated and actual mFDR values with various sample sizes (left), signal levels (middle), and dimensions (right).

Fig. 3.

Simulations 2 (left) and 3 (right): estimated mFDR values with various correlation coefficients.

Fig. 4.

Simulations 2 (left) and 3 (right): numbers of false and true positives with various correlation coefficients

Fig. 5.

Analysis of Loan data (left) and SKCM data (right) using the proposed approach: estimated mFDR and number of covariates selected as a function of tuning.