Transfer learning for accelerated failure time model with microarray data

Abstract

Background: In microarray prognostic studies, researchers aim to identify genes associated with disease progression. However, due to the rarity of certain diseases and the cost of sample collection, researchers often face the challenge of limited sample size, which may prevent accurate estimation and risk assessment. This challenge necessitates methods that can leverage information from external data (i.e., source cohorts) to improve gene selection and risk assessment based on the current sample (i.e., target cohort).

Method: We propose a transfer learning method for the accelerated failure time (AFT) model to enhance the fit on the target cohort by adaptively borrowing information from the source cohorts. We use a Leave-One-Out cross validation based procedure to evaluate the relative stability of selected genes and overall predictive power.

Conclusion: In simulation studies, the transfer learning method for the AFT model can correctly identify a small number of genes, its estimation error is smaller than the estimation error obtained without using the source cohorts. Furthermore, the proposed method demonstrates satisfactory accuracy and robustness in addressing heterogeneity across the cohorts compared to the method that directly combines the target and the source cohorts in the AFT model. We analyze the GSE88770 and GSE25055 data using the proposed method. The selected genes are relatively stable, and the proposed method can make an overall satisfactory risk prediction.

Keywords: Auxiliary studies; Gene expression data; Survival analysis; Transfer learning; Weighted least squares.

Algorithm 1

Process of Trans-AFT Algorithm

Fig. 1

Sum of absolute estimation errors of the Lasso-AFT, Pooled-AFT, Trans-AFT method with homogeneous designs under two configurations. The proportion of censoring is set to 20$\%$, 50$\%$, 70$\%$. The y axis corresponds to ${\Vert b-\beta \Vert }_1$ for some estimator b

Fig. 2

Sum of absolute estimation errors of the Lasso-AFT, Pooled-AFT, Trans-AFT method with heterogeneous designs under two configurations. The proportion of censoring is set to 20$\%$, 50$\%$, 70$\%$. The y axis corresponds to ${\Vert b-\beta \Vert }_1$ for some estimator b

Fig. 3

Flow diagram of date processing, analysis, and evaluation

Fig. 4

GSE88770 data: occurrence index of individual genes selected by proposed transfer learning method

Fig. 5

GSE88770 data: K-M survival curves of two hypothetical risk groups identified by proposed transfer learning method

Fig. 6

GSE25055 data: occurrence index of individual genes selected by proposed transfer learning method

Fig. 7

GSE25055 data: K-M survival curves of two hypothetical risk groups identified by proposed transfer learning methods

Fig. 8

GSE25065 data: K-M survival curves of two hypothetical risk groups identified by proposed transfer learning methods