Survival analysis (SA) is a well-known statistical technique for the study of temporal events. In SA, time-to-an-event data is modeled using a parametric probabilistic function of fully or partially observed covariates. All the existing technique for survival analysis assume that the covariates are statistically independent. To integrate the cause-effect relationship between covariates and the time-to-event outcome, we present to you DAGSurv which encodes the causal DAG structure into the analysis of temporal data and eventually leads to better results (higher Concordance Index).
This code requires the following key dependencies:
- Python 3.8
- torch==1.6.0
- pycox==0.2.1
To train the DAGSurv model, please run the main.py as python main.py
There are a number of hyper-parameters present in the script which can be easily changed.
We evaluated our approach on two real-world and two synthetic datasets; and used time-dependent Concordance Index(C-td) as our evaluation metric.
- METABRIC : The Molecular Taxonomy of Breast Cancer International Consor- tium (METABRIC) is a clinical dataset which consists of gene expressions used to determine different subgroups of breast cancer. We consider the data for 1,904 patients with each patient having 9 covariates. Furthermore, out of the total 1,904 patients, 801 (42.06%) are right-censored, and the rest are deceased (event).
- GBSG : Rotterdam and German Breast Cancer Study Group (GBSG) contains breast-cancer data from Rotterdam Tumor bank. The dataset consists of 2,232 patients out of which 965 (43.23%) are right-censored, remaining are deceased (event), and there were no missing values. In total, there were 7 features per patient.
We employ the time-dependent concordance index (CI) as our evaluation metric since it is robust to changes in the survival risk over time. Mathematically it is given as,
Here, we present our results on the two real-world datasets mentioned above -
| Model/Experiment | METABRIC | GBSG |
|---|---|---|
| DAGSurv | 0.7323 ± 0.0056 | 0.6892 ± 0.0023 |
| DeepHit | 0.7309 ± 0.0047 | 0.6602 ± 0.0026 |
| DeepSurv | 0.6575 ± 0.0021 | 0.6651 ± 0.0020 |
| CoxTime | 0.6679 ± 0.0020 | 0.6687 ± 0.0019 |
[1] Yue Yu, Jie Chen, Tian Gao, Mo Yu. "DAG-GNN: DAG Structure Learning with Graph Neural Networks."
[2] Changhee Lee, William R. Zame, Jinsung Yoon, Mihaela van der Schaar. "DeepHit: A Deep Learning Approach to Survival Analysis with Competing Risks."