in this paper can effectively address the data issue as it is designed for.

In this paper, we consider the discharge time $T$, with the time-dependent covariate, the logarithm of the cumulative charge $Z_1$, and the stationary covariates consisting of the categorical variables, $Z_2,\dots,Z_{25}$, associated with 25 Major Diagnosis Code (MDC) and the degree ($1\sim 4$) of the Severity of Illness, $Z_{26}$. Our analysis is conducted on a subsample of the entire SPARCS 2013 database with sample size $400$. The summary statistics of our subsample are presented in Table \[table: 3.1\].

The penalized maximum likelihood estimators $\hat{b}_{AL}$ are reported in Table \[table: real\]. The non-parametric estimator $\int_0^t\hat{\lambda}^{s}_{n}(s)ds$ for the cumulative baseline hazard are plotted in Figure \[fig: real data study\].

In Table \[table: real\], the significant negative coefficients for log-charge indicates the strong positive correlation between the total charge and los. In addition, it seems that there does not exist robust connection between the los and the severity/mortality of illness.

By Figure \[fig: real data study\], the day 5 seems to be relatively special because the variation of the slope of the cumulative hazard turns from increasing to decreasing around this time, which implies that for patients who have already 