## 3 Results
### Indirect Signs of ACL Graft Insufficiency
#### 3.2.1 Overall Graft State  
To model overall graft state, Bayesian multilevel logistic regression with varying intercepts across patients was used. Model coefficients are presented in Table 4 and selected predicted posterior proportions are presented in Figure 7. Since the injured state was coded as the event, the posterior predicted probabilities in Figure 2 should be interpreted as predicted proportions of patients assessed with injured grafts.  
We observed that the model that incorporated SNQ and rSD at the sagittal plane predicted the proportions of injured grafts better than the model measuring the axial plane (BF = 1.922). Thus, we focused on the results from the better model. The proportion of injured grafts changed non-linearly over the course of the study, with the highest value at 36 weeks. Statistically credible relations were observed for both SNQ and rSD, which demonstrated increase in these indices was associated with an increase in the proportion of injured grafts. The association was much stronger for the SNQ index. Finally, a high difference between men and women was observed in regard to change in proportions over the weeks. The proportions steadily increased over the course of the study in female patients, while the proportions increased rapidly up to week 24 and then rapidly decreased in male patients. At week 96, the proportions came close to the level observed at week 2 in male patients. The effects of weight-bearing and age were not statistically credible.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{6}{c}{**Overall Graft State**} \\  & \multicolumn{3}{c}{**Sagittal**} & \multicolumn{3}{c}{**Axial**} \\ \cline{3-8}  & **Me** & **Li** & **UI** & **Me** & **Li** & **UI** \\ \hline \multirow{9}{*}{\(\beta\)} & Intercept & \(-0.92\) & \(-1.82\) & \(-0.05\) & \(-0.8\) & \(-1.69\) & \(0.1\) \\  & Week [L] & \(\mathbf{1.3}\) & \(\mathbf{0.17}\) & \(\mathbf{2.39}\) & \(\mathbf{0.89}\) & \(\mathbf{-0.27}\) & \(\mathbf{2.07}\) \\  & Week [Q] & \(\mathbf{-1.51}\) & \(\mathbf{-2.58}\) & \(\mathbf{-0.43}\) & \(\mathbf{-1.46}\) & \(\mathbf{-2.51}\) & \(\mathbf{-0.42}\) \\  & SNQ & \(\mathbf{1.61}\) & \(\mathbf{1.04}\) & \(\mathbf{2.26}\) & \(\mathbf{1.84}\) & \(\mathbf{1.2}\) & \(\mathbf{2.48}\) \\  & SD & \(\mathbf{0.64}\) & \(\mathbf{0.19}\) & \(\mathbf{1.13}\) & \(0.22\) & \(-0.24\) & \(0.66\) \\  & Sex & \(-0.3\) & \(-1.08\) & \(0.48\) & \(-0.49\) & \(-1.27\) & \(0.26\) \\  & Age & \(0.27\) & \(-0.51\) & \(1.04\) & \(0.2\) & \(-0.57\) & \(0.97\) \\  & Weight bearing & \(0.06\) & \(-0.8\) & \(0.95\) & \(0.18\) & \(-0.71\) & \(1.05\) \\  & Week [L] : Sex & \(0.53\) & \(-0.42\) & \(1.59\) & \(0.13\) & \(-0.89\) & \(1.12\) \\  & Week [Q] : Sex & \(\mathbf{1.06}\) & \(\mathbf{0.05}\) & \(\mathbf{2.1}\) & \(0.96\) & \(-0.08\) & \(1.95\) \\  & Week [L] : Age & \(0.01\) & \(-0.97\) & \(1.01\) & \(-0.02\) & \(-0.99\) & \(0.97\) \\  & Week [Q] : Age & \(-0.53\) & \(-1.54\) & \(0.4\) & \(-0.79\) & \(-1.8\) & \(0.15\) \\  & Week [L] : Weight bearing & \(0.44\) & \(-0.68\) & \(1.54\) & \(0.59\) & \(-0.49\) & \(1.72\) \\  & Week [Q] : Weight bearing & \(0.38\) & \(-0.69\) & \(1.39\) & \(0.19\) & \(-0.87\) & \(1.24\) \\ \hline \hline \(\tau\) & \(\beta\) Intercept & \(2.41\) & \(1.61\) & \(3.4\) & \(2.45\) & \(1.7\) & \(3.44\) \\ \hline \multicolumn{9}{c}{Model accuracy} & \multicolumn{3}{c}{\(0.91\)} & \multicolumn{3}{c}{\(0.9\)} \\ \hline \hline \end{tabular} Note: Me is median of posterior, and LI and UI are lower and user bounds of 95% credible interval. [L] and [Q]—linear and quadratic trends. The ’\(\cdot\)’ symbol indicates interaction term. \(\beta\)—regression weight; \(\tau\)—patient random effect. The coefficients are on the logit scale. Statistically credible effects are bolded.  
\end{table}
Table 4: Results of Bayesian multilevel logistic regressions with graft state as the dependent variable.