# Fusion learning algorithm to combine partially heterogeneous Cox models

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## Abstract

We propose a fusion learning procedure to perform regression coefficients clustering in the Cox proportional hazards model when parameters are partially heterogeneous across certain predefined subgroups, such as age groups. One major issue pertains to the fact that the same covariate may have different influence on the survival time across different subgroups. Learning differences in covariate effects is of critical importance to understand the model heterogeneity resulted from the between-group heterogeneity, especially when the number of subgroups is large. We establish a computationally efficient procedure to learn the heterogeneous patterns of regression coefficients across the subgroups in Cox proportional hazards model. Utilizing a fusion learning algorithm coupled with the estimated parameter ordering, the proposed method mitigates greatly computational burden with little loss of statistical power. Extensive simulation studies are conducted to evaluate the performance of our method. Finally with a comparison to some popular conventional methods, we illustrate the proposed method by a vehicle leasing contract renewal analysis.

## Keywords

Fused lasso Regression coefficient clustering Extended BIC Cox proportional hazards model## Notes

### Acknowledgements

We are grateful to three anonymous reviewers for their valuable comments that have led to an improvement of this paper. This research is partially supported by the National Science Foundation DMS 1513595 and the National Institutes of Health R01 ES024732.

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