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A network-constrain Weibull AFT model for biomarkers discovery

Claudia Angelini, Daniela De Canditiis, Italia De Feis, Antonella Iuliano

TL;DR

This work proposes AFTNet, a novel network‐constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation and establishes the theoretical consistency for the AFTNet estimator.

Abstract

We propose AFTNet, a novel network-constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation. When using the log-linear representation, the inference problem becomes a structured sparse regression problem for which we explicitly incorporate the correlation patterns among predictors using a double penalty that promotes both sparsity and grouping effect. Moreover, we establish the theoretical consistency for the AFTNet estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Finally, we evaluate AFTNet performance both on synthetic and real data examples.

A network-constrain Weibull AFT model for biomarkers discovery

TL;DR

This work proposes AFTNet, a novel network‐constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation and establishes the theoretical consistency for the AFTNet estimator.

Abstract

We propose AFTNet, a novel network-constraint survival analysis method based on the Weibull accelerated failure time (AFT) model solved by a penalized likelihood approach for variable selection and estimation. When using the log-linear representation, the inference problem becomes a structured sparse regression problem for which we explicitly incorporate the correlation patterns among predictors using a double penalty that promotes both sparsity and grouping effect. Moreover, we establish the theoretical consistency for the AFTNet estimator and present an efficient iterative computational algorithm based on the proximal gradient descent method. Finally, we evaluate AFTNet performance both on synthetic and real data examples.
Paper Structure (11 sections, 4 theorems, 81 equations, 6 figures, 6 tables, 1 algorithm)

This paper contains 11 sections, 4 theorems, 81 equations, 6 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical background
  3. The log-linear AFT model
  4. The Weibull AFT model
  5. Inference
  6. Theoretical properties
  7. Numerical implementation
  8. $\lambda$ parameter selection
  9. Simulation results
  10. Real case studies
  11. Conclusions

Key Result

Theorem 1

Under Assumptions assump1,assump2 and assump3 for all $\hat{\boldsymbol{\theta}}$ local minimizers, i.e. that satisfy the first order condition it holds with high probability.

Figures (6)

  • Figure 1: Not-overlapping case. Box-plots of the performance metrics results between AFTNet and penAFT with $n_T=110$, $n_D=55$, $p=220$ (weak effect) and $\alpha=0.5$ for $\sigma=0.5, 1, 1.5$ (from the left-side to the right-side), respectively, averaged over 20 independent replications.
  • Figure 2: Not-overlapping case. Box-plots of the performance metrics results between AFTNet and penAFT with $n_T=275$, $n_D=138$, $p=1100$ (strong effect) and $\alpha=0.5$ for $\sigma=0.5, 1, 1.5$ (from the left-side to the right-side), respectively, averaged over 20 independent replications.
  • Figure 3: Not-overlapping case. ROC curve for $\sigma=1$ with a weak effect (on the left-side) and a strong effect (on the right-side).
  • Figure 4: Overlapping case. Box-plots of the performance metrics results between AFTNet and penAFT with $n_T=110$, $n_D=55$, $p=220$ (weak effect) and $\alpha=0.5$ for $\sigma=0.5, 1, 1.5$ (from the left-side to the right-side), respectively, averaged over 20 independent replications.
  • Figure 5: Overlapping case. Box-plots of the performance metrics results between AFTNet and penAFT with $n_T=275$, $n_D=138$, $p=1100$ (strong effect) and $\alpha=0.5$ for $\sigma=0.5, 1, 1.5$ (from the left-side to the right-side), respectively, averaged over 20 independent replications.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • Proof 1
  • Proposition 1: cfr. Prop 2.5 pag. 24 in book_martin