## 2 Materials and Methods
### Data Analysis  
Statistical Analyses  
We used R 4.0.2 [12] for performing statistical analyses. To analyze changes in SNQs and indirect signs of ACL graft insufficiency over postoperative timepoints and their relationships to rSDs, sex, age, and weight bearing, a series of Bayesian multilevel regression was conducted with intercepts allowed to vary by patient. Details of the models are provided with the results. All continuous variables were entered into the models after transformation to Z-scale and categorical predictors were coded with orthogonal sum to zero  
Figure 4: PCL appearance (marked with white arrow): (**a**) normal, (**b**) buckling.  
Figure 5: **Anterior tibia subluxation.** Axial and sagittal image are merged ((**a**) and the cortex adjacent to PCL in the femoral notch (**b**)). Measurement of anterior tibial subluxation was made in the sagittal plane (**b**) at a location midway between the cortex adjacent to PCL in the femoral notch and the most lateral slice containing the lateral femoral condyle (marked on axial plane, (**a**)). The degree of tibial subluxation was measured by the distance between those two lines in millimeters (between lines B and C, (**b**)).  
contrasts. Change over weeks (week predictor) was modelled with orthogonal quadratic polynomial, which allowed us to capture non-linear trend in change of the parameters. For all categorical predictors, an interaction with week predictor was also investigated to test whether the change over weeks depended on these predictors. Each model was estimated separately for measurement made in sagittal and axial planes.  
In Bayesian statistics, the inference is based on analyzing posterior probability distributions of model parameters (e.g., regression weight of week predictor), obtained by integrating likelihood with prior probability distributions of the model parameters. The model parameter is statistically credible when 95% of credible intervals (CI) of the posterior distribution exclude zero [13]. As a point estimate of the effect, medians of the posterior distributions are presented. As priors for all regression weights, non-informative, standard normal distributions were used (i.e., with M = 0 and SD = 1).  
To present expected values of clinical parameters, we provide posterior predicted marginal means for SNQs and PCL subluxation and probabilities for overall graft state and PCL anterior subluxation. These values were computed from model parameters and can be thought of as better summary statistics than simple descriptive statistics, since they incorporate all the uncertainty in the data and model.  
For models with continuous dependent variables, Bayesian R2 [14] was provided as a measure of model fit. Therefore, prediction accuracy was reported for models with categorical dependent variables. Both statistics are in the range zero to one, with one indicating perfect model fit.  
To approximate posterior distributions of the models, a Markov Chain Monte Carlo (MCMC) sampling procedure was conducted using the brms (Bayesian Regression Models using 'Stan') package [15]. For each reported model, six parallel MCMC chains were used. Each chain consisted of 6000 samples, with 3000 samples used as warmup period and every 10 th sample recorded, which resulted in a total of 1800 recorded samples. Efficient sampling procedures resulted in well-mixed and autocorrelation-free chains and unimodal posteriors.