exposure times, $t_{i}$, are simulated from the following PEH models (using inverse sampling): $$\lambda_{ij}=\exp\left(\beta_{j,0}+\mathbf{x}_{i}^{\prime}\boldsymbol{\beta}_{j}\right),\,\,j=1,\ldots,J$$ $$\boldsymbol{\beta}_{j}=\boldsymbol{\beta}_{j-1}+\boldsymbol{\epsilon}_{j},\,\,\boldsymbol{\epsilon}_{j}\sim N_{P}\left(0,\,0.25I_{P}\right)$$ $$\beta_{j,0}=-11+\log\left(j\right),\,\,\boldsymbol{\beta}_{0}=0,\,x_{i}\sim N\left(0,I_{P}\right),$$ where $\boldsymbol{\beta}_{j}=(\beta_{j,1},\ldots,\beta_{j,p})^{\prime}$ and $I_{p}$ is a $P\times P$ diagonal matrix.

The above data generating process (DGP) allows the flexibility of varying the number of parameters $P$, the sample size $n$, the proportion of the censored observations $p_{c}$ and the number of intervals $J$ partitioning the study period. In all simulations, the intervals are equidistant and have length equals to $20$ units of time.

The performance of the inference methodology is measured by the expected discrimination measure (EDM) between the density for the DGP, $f(t|\mathbf{x})$, and the predictive density $\hat{f}(t|\mathbf{x})$ of a given fitted model, $$EDM\left(f,\hat{f}\right)=\int\left[\int_{0}^{t}\frac{f\left(u|\mathbf{x}\right)}{F\left(t|\mathbf{x}\right)}\log\left(\frac{\nicefrac{f(u|\mathbf{x})}{F(t|\mathbf{x})}}{\nicefrac{\hat{f}(u|\mathbf{x})}{\hat{F}(u|\mathbf{x})}}\right)du\right]p\left(\mathbf{x}\right)d\mathbf{x},$$ where $F(t|\mathbf{x})$ and $\hat{F}(t|\mathbf{x})$ are the cumulative distribution functions (computed at time $t$) for the DGP and the fitted model respectively, and $p(\mathbf{x})$ is the marginal distribution of the covariates. For PEH models $F(t|\mathbf{x})=1-S(t|\mathbf{x})$ where $S(t|\mathbf{x})$ is the survival function. The expression in the inner integral was proposed by @di2004measure, and is referred to as the measure of discrimination between two past-life distributions. To compute EDM, the inner intregral is evaluated numerically using the trapezoidal rule and the outer integral is approximated by taking the average over 