Estimation in the High Dimensional Additive Hazard Model with l0 Type of Penalty

High-dimensional data is commonly observed in survival data analysis. Penalized regression is widely applied for parameter selection given this type of data. The LASSO, SCAD and MCP methods are basic penalties developed in recent years in order to achieve more accurate selection of parameters. The l0 penalty, which selects the best subset of parameters and provides unbiased estimation, is relatively difficult to handle due to its NP-hard complexity resulted from the non-smooth and non-convex objective function. For the additive hazard model, most methods developed so far focus on providing a smoothed version of l0-norm. Instead of mimicking these methods, two augmented Lagrangian based algorithms, namely the ADMM-l0 method and the APM-l0 method, are proposed to approximate the optimal solution generated by the l0 penalty. The ADMM-l0 algorithm can achieve unbiased parameter estimation, while the two-step APM-l0 method is computationally more efficient. The convergence of ADMM-l0 can be proved under strict assumptions. Under moderate sample sizes, both methods perform well in selecting the best subset of parameters, especially in terms of controlling the false positive rate. Finally, both methods are applied to two real datasets.