## 3 Results
### 6-Month Relospitalization and MPV Relationship  
As shown by the statistical results regarding the relationship between MPV and 3-month rehospitalization, significant results were also found regarding the relationship between the MPV value and 6-month rehospitalization, revealing the fact that patients with HF who were rehospitalized at 6 months had a higher MPV value compared to those who were not rehospitalized at 6 months. These results are better illustrated graphically in the figure below (Figure 12), in which it can be observed in all three graphs that patients with HF rehospitalized at 6 months (1) had a higher MPV value (over 9 fl) compared to those who were not rehospitalized at 6 months (0) and who had MPV values below 9 fl.  
The explanations of the above phenomena are better argued by applying the logistic regression model, the estimated coefficients for which are shown in Table 6, a model by which we were able to predict the probability that a patient with HF will be rehospitalized at 6 months based on MPV value.  
Figure 11: Probability of HF patients being rehospitalized at 3 months based on the MPV value by applying the logistic regression model.  
The model applied in this case is the following: score (event occurrence = 6-month rehospitalization) = \(-11.3908\) + \(1.1836\)\(\times\) MPV. Starting from this model, let us assume that we have a patient with an MPV value of 10 fl. From here, applying the above-mentioned mathematical formula, it turns out that the score for this patient is 0.44. Applying the following equation: \(\mathbf{p}=\frac{\mathbf{1}}{\mathbf{1}+\mathbf{e}^{-\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\bm}}}}}}}}}}}}}}\), we obtain that the probability of the patient with an MPV of 10 fl is 0.61, representing a 61% chance to be rehospitalized at 6 months.  
The above mathematical model applied to HF patients rehospitalized at 6 months is statistically significant because the \(p\)-value associated with the coefficient for MPV (1.1836) is 0.000. The results obtained following the application of the above-mentioned mathematical formula are illustrated graphically in the figure below (Figure 13), in which it can be seen that, as the MPV value increases, the probability that a patient with HF will be rehospitalized at 6 months also increases.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Dep.** & **Re\_Hosp\_6** & **No.** & **260** & \\
**Variable:** & **mo** & **Observations:** & & \\ \hline Model: & Logit & Df Residuals: & 258 & & \\ Method: & MLE & Df Model: & 1 & & \\  & & Pseudo R-squ.: & 0.1125 & & \\ Converged: & TRUE & LL-Null: & \(-165.03\) & & \\ \hline  & **coef** & std err & Z & \(p>1\) z \(|\) & [0.025 & 0.975] \\ \hline Intercept & \(-11.3908\) & 1.959 & \(-5.813\) & 0 & \(-15.231\) & \(-7.55\) \\ MPV & **1.1836** & 0.215 & 5.51 & **0** & 0.763 & 1.605 \\ \hline \end{tabular}
\end{table}
Table 6: The relationship between MPV and the probability of 6-month rehospitalization, explained by the logistic regression model in patients with HF.  
Figure 12: MPV value in HF patients who were rehospitalized at 6 months (1) versus HF patients who were not rehospitalized at 6 months (0).  
Thus, starting from the arguments above, it can be said that, depending on the MPV value, we can predict the probability that a patient with HF will be rehospitalized at 6 months, and that patients with a higher MPV value have a greater probability of being rehospitalized at 6 months compared to patients with a lower MPV value.