The Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD) statement was used as a reporting guideline [17].
Source Of Data
From January 2010, patients undergoing ARCR in a Swiss tertiary orthopedic clinic were prospectively documented in a register [14]. Patient follow-up at 6 months post-surgery comprised various objective and subjective patient-reported outcomes including the Constant-Murley Score (CS), Oxford Shoulder Score (OSS) and Subjective Shoulder Value (SSV). An additional 2- to 4-year post-operative evaluation of patient-reported outcomes and level of satisfaction was made by postal questionnaire. All parameters were collected in clinical report forms after the baseline clinical examination or immediately after surgery. Quality checks and data management were done using a Research Electronic Data Capture (REDCap) database [18].
Participants
Adult patients were included if (1) they had a partial or complete rotator cuff tear that was assessed by magnetic resonance imaging (MRI) and confirmed intra-operatively, and (2) underwent ARCR between October 2013 and June 2021. Revision surgeries were excluded as well as contralateral ARCRs in patients with bilateral injuries.
Treatment And Rehabilitation
Shoulder arthroscopy was performed according to internationally standardized procedures with patients in a beach-chair position under general anesthesia [19]. All patients followed a standard 3-phase post-operative physical therapy protocol involving: (1) 6 weeks of passive mobilization with an abduction brace (DonJoy UltraSling ER; ORMED GmbH, Freiburg, Germany); (2) 4 to 6 weeks of active-assisted mobilization and coordination training; and (3) specific progressive resistance exercises for the operated shoulder.
Outcome
For prediction modeling of 6-month outcome, we focused on the OSS, which is a 12-item patient-reported outcome assessing daily functional activities in relation to use of the shoulder [20]. The OSS is a condition-specific questionnaire developed for patients with a degenerative or inflammatory shoulder condition including rotator cuff injuries. The twelve items or questions are answered by the patient independently and address the degree of pain and possible handicaps experienced during activities of daily living within the last 4 post-operative weeks. There are five response categories for each question corresponding to a score ranging from 0 to 4. All scores are then combined to produce a final score ranging from 0 (worst outcome) to 48 (best outcome).
Prognostic Factors
A list of 35 prognostic factors was generated by the primary and senior authors (TS, LA) based on previous systematic reviews [6–12]. Three experienced orthopedic shoulder surgeons (AM, MF, MS) were asked to independently assess the importance of each prognostic factor using a scale ranging from 0 (not important) to 5 (very important) for the prediction of the 6-month OSS.
All 35 factors were documented and available in the local register. However, we excluded eight potential prognostic factors (i.e., pre-operative medication, pre-operative physiotherapy, overall baseline CS, baseline abduction, flexion and external rotation, baseline muscle strength and fatty infiltration of rotator cuff muscles) with more than 20% missing values. Five additional potential prognostic factors highly associated with other assessed prognostic factors (i.e., baseline pain-related question from the CS, general health status, rotator cuff tear pattern, the extent of the rotator cuff tear and the baseline pain-related question from a VAS scale) were also excluded.
Twenty-two potential prognostic factors were finally retained for development of the prediction model as well as seven patient-related parameters including age at surgery, sex, body mass index, American Society of Anesthesiologists (ASA) physical status classification, smoking status at surgery, level of depression and anxiety using the European Quality of Life 5 Dimensions 5 Level (EQ-5D-5L) scale [21] and baseline OSS. Eight disease-related parameters were also assessed: dominance of the affected side, traumatic onset, supraspinatus tear, subscapularis tear, infraspinatus tear, tear severity, tendon degeneration and tendon delamination. Lastly, nine procedure-related parameters (including pre-operative management details) were assessed: pre-operative steroid infiltrations, symptom duration, operation duration, number of anchors, number of threads, acromioclavicular joint resection, acromioplasty, capsulotomy, and biceps tendon status and treatment.
Post-hoc Sample Size Calculation
An R package developed by Riley et al. [22] was used to estimate the necessary sample size for the development of a multivariable prediction model for continuous outcomes (pmsampsize package). The estimation required an expected R squared value for the future prediction model of 0.2, the number of parameters to be assessed during the multivariable prediction model development of 36, and an average outcome value in the population of interest (i.e., intercept) of 40 with its standard deviation (SD) of 8. The necessary sample size was estimated at 1,361.
Missing Data
For reasons of practicality and comprehension, we performed a complete-case analysis. Therefore, all patients with any missing values for candidate prognostic factors were excluded from the present analysis.
Statistical Analyses
All analyses were performed using R [23].
Types of models used
Classic linear regression models were fitted using ordinary least square estimation and the identity link glm() function. Tobit regression models are a specific class of regression models particularly relevant for censored outcomes such as the OSS, which is subject to floor and ceiling effects [24]. Tobit regression models were specified using the crch package and associated crch() function [25].
Univariable regression analyses
Univariable regressions using both linear and Tobit approaches were performed between all candidate prognostic factors and the outcome. Regression coefficients and their 95% confidence intervals (CIs) were estimated as well as the associated R squared.
Prognostic factor handling
Following the ten principles to strengthen prognosis research[26], continuous prognostic factors were kept continuous as far as possible. For categorical variables, an attempt was made to avoid sparse categories. Based on univariable regression models, a second-order polynomial transformation of continuous predictors such as age at surgery or baseline body mass index was tested to account for the non-linear association with post-operative OSS.
Model building procedures
Three different sets of factors were compared. “Set 1” comprised ten factors with the highest R squared values in the univariable analysis (plus the baseline OSS value). “Set 2” regrouped the ten factors estimated by surgeons as having the best predictive ability (plus the baseline OSS value). “Set 3” regrouped the variables retained after a stepwise backward regression procedure.
Internal validation
To estimate the apparent and internally validated performance of our models, a split-sample validation was performed using 70% of the data for the training set and 30% for the test set. To assess the impact of random variation among our dataset, a bootstrap validation using 500 repetitions was performed for coefficient estimation and model performance metrics.
Model performance
The six models were compared in terms of overall performance (using Akaike’s Information Criterion (AIC) and model bias, which represents the systematic error observed in a prediction model) and discriminative ability (using R squared and Root Mean Squared Error (RMSE)). Regression coefficients (β) were presented in the main text for the model presenting the best predictive ability.
Patient And Public Involvement In Research Statement
No patient or member of the public was involved in the design of this study. Patients directly filled out the Oxford Shoulder Score based on their own experience after the surgery.