Efficient sparse estimation on interval-censored data with approximated L0 norm: Application to child mortality

A novel penalty for the proportional hazards model under the interval-censored failure time data structure is discussed, with which the subject of variable selection is rarely studied. The penalty comes from an idea to approximate some information criterion, e.g., the BIC or AIC, and the core process is to smooth the ℓ(0) norm. Compared with usual regularization methods, the proposed approach is free of heavily time-consuming hyperparameter tuning. The efficiency is further improved by fitting the model and selecting variables in one step. To achieve this, sieve likelihood is introduced, which simultaneously estimates the coefficients and baseline cumulative hazards function. Furthermore, it is shown that the three desired properties for penalties, i.e., continuity, sparsity, and unbiasedness, are all guaranteed. Numerical results show that the proposed sparse estimation method is of great accuracy and efficiency. Finally, the method is used on data of Nigerian children and the key factors that have effects on child mortality are found.