## 4 Results
### Assessment of the Model against Experimental Data  
A visual predictive check analysis (VPC) was performed setting the number of the bins equal to 8: in this way, we achieved a good compromise between the approximation and estimation of the data. Furthermore, the least-squares criterion was chosen as the data-grouping method. Figure 7 shows the results of the VPC for the model of interest: the blue areas delimit the predicted percentiles for 10-90% while the red area represents 50% of the simulated dataset--here, we generate a dataset of 10,000 simulated time series.  
Figure 6: Model results for some of the 27 STEMI patients. For each subject, the population model (red light line), obtained by the fixed effects estimated from all the patients, and the individual fit (colorful line), obtained by taking into account the random effects, are reported. The experimental acquisitions are denoted by dots.  
Figure 7: Visual predictive check analysis computed on the whole population, and obtained by simulating, through the Monte-Carlo method; 10,000 time series.  
The three blue lines indicate the empirical percentiles, while the red area and the red dots identify the areas outside the predicted intervals, and the outliers, as points located outside the closest percentile, respectively. From Figure 7, we can observe that the blue area for the 90 empirical percentile is very large, compared to the other ones: probably, this is due to the high variability in the observed data (blue dots). Furthermore, from Figure 7, it is possible to note that in the final part of the plot, the three quantiles appear closer than the model suggests. This means that in this part of the curve, the model could suggest incorrect results. A careful inspection of the results shown in Figure 7 reveals the presence of two outliers, distributed at the beginning and at the end of the curve: in particular, a small red area is localized in correspondence with the first outlier, probably due to the inconsistency in the first measurements, which is different for all the patients. Finally, to further assess the structural model, the relationship between observations and predictions was reported in Figure 8, where all the data are distributed among the line represented by the equation \(y=x\). This suggests that the model is capable of correctly explaining all the experimental data. Note that the data outside the 90% prediction interval are associated with the first acquisition, as confirmation of the presence of the outlier and of the red area at the beginning of the curve in Figure 7.  
However, no particular misspecification can be detected, confirming the suitability of the model. Figure 9 shows the results obtained from the convergence analysis of the MCMC method for five trajectories of the population parameters. This analysis consists of running the estimation task several times, starting from different randomly generated initial values of the fixed parameters. This type of test allows us to understand if MCMC has explored a parameter space large enough to reach the true posterior distribution of the parameters, and if the estimated values belong to that distribution [41].  
Figure 8: Observations vs individual predictions for the model taking into account the dyslipidemia covariate (i.e., model 2 in Table 1).  
As we can see from Figure 9, the results are in agreement in all five trajectories and, in particular, converge to roughly the same value of \(-2\)LL (i.e., the difference between two log likelihoods), as shown in Figure 10.