## 4 Results  
### Analysis of Selected Covariates  
Table 1 shows the results obtained for all the significant models, in terms of (i) log-likelihood, computed using importance sampling Monte-Carlo methods with a size of 10,000 samples, (ii) Bayesian information criterion (BIC) index, (iii) standard error (SE), and (iv) significance of the covariate influence on the model parameters, evaluated in terms of \(p\)-value.  
In what follows, we focus our attention on model 2 of Table 1, which, besides exhibiting a good compromise of log-likelihood, BIC and SE, has been deemed of particular interest from the clinical standpoint; indeed, dyslipidemia is a known clinical cofactor in the incidence of AMI and, therefore, it is interesting to investigate its influence on the cTnT release curve.  
The influence of dyslipidemia on parameter \(b\) was explicitly introduced in the model as follows:  
\[log(b)=log(b_{pop})+\beta_{b_{\textit{Dyslipidemia}_{1}}}*[\textit{Dyslipidemia}=1]+\omega_{b} \tag{7}\]  
where \(\beta_{b_{\textit{Dyslipidemia}_{1}}}\) represents a part of the fixed effect, specific for the dyslipidemia class, and \(\omega_{b}\) is the random effect specific to each individual. Since it is not possible to constrain the parameter values through the definition of specific bounds, whose values must be positive, we chose a log-normal distribution for the parameters, as shown in Equation (7).  
Figure 4 shows the cTnT acquisitions of the 27 STEMI patients grouped according to the dyslipidemia covariate: the mean, the standard deviation, and the median values for the distribution of the experimental data are reported, for both dyslipidemic and non-dyslipidemic patients, in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**M** & **Cov\({}_{1}\)** & **Cov\({}_{2}\)** & **Cov\({}_{3}\)** & \(-\)**2 LL** & **BIC** & **SE** & **PM(Cov: \(p_{\text{val}}\))** \\ \hline
1 & & & & \(-\)1613.80 & \(-\)1576.76 & 0.655 & \\ \hline
2 & D & & & \(-\)1651.87 & \(-\)1569.93 & 0.427 & \(b\) (D: \(p=2.46\times 10^{-5}\)) \\ \hline
3 & D & AI & & \(-\)1655.09 & \(-\)1604.58 & 1.575 & \(b\)(D: \(p=1.65\times 10^{-7}\)), T\({}_{d}\)(AI: \(p=1.65\times 10^{-9}\)) \\ \hline
4 & D & A & & \(-\)1560.24 & \(-\)1507.51 & 0.142 & \(b\)(D,A: \(p_{D}=5.5\times 10^{-10}\), \(p_{A}=0.015\)), T\({}_{d}\)(A: \(p=3.3\times 10^{-15}\)), C\({}_{50}\)(A: \(p=3.3\times 10^{-15}\)) \\ \hline
5 & A & AI & & \(-\)1586.06 & \(-\)1536.63 & 0.42 & \(b\)(A,AI: \(p_{A}=8.55\times 10^{-10}\), \(p_{AI}=8.85\times 10^{-5}\)), T\({}_{d}\)(A: \(p=3.3\times 10^{-15}\)), C\({}_{50}\)(A: \((p=3.3\times 10^{-15}\))) \\ \hline
6 & A & AI & D & \(-\)1574.81 & \(-\)1505.38 & 0.183 & \(b\)(D: \(p_{D}=4.2\times 10^{-10}\), \(T_{d}\)(A,AI: \(p=0.015\)) \\ \hline \end{tabular}
\end{table}
Table 1: Effects of the covariates on the parameters of model (6). M: model, PM: parameters of model (6) significantly influenced (the specific covariate is reported in square bracket), A: age, D: dyslipidemia, AI: aortic insufficiency. For each model, it is reported the effect of each covariate (in square brackets) on the parameters, and the associated \(p\) value computed via Wald’s test, and corrected for multiple tests using the Bonferroni.