Predictive Model for 1-Year Pain and Function Outcomes After Thumb Joint Surgery in Osteoarthritic Patients

This study aims to develop and validate predictive models for assessing pain and hand function outcomes one year after trapeziometacarpal joint (TMJ) arthroplasty using the Touch® prosthesis. The study leverages a single-center prospective registry from a specialized orthopedic hospital in Zurich, Switzerland.

Analytical methods:

The investigators will use the following modeling approach to determine the best predictive value for the 1-year outcome of pain. The model chosen is:

- Extreme Gradient Boosting (XGBoost): A non-parametric, ensemble-based approach that combines decision trees through boosting to capture complex feature interactions and model non-linearity effectively. XGBoost also includes L1 and L2 regularization, allowing it to manage overfitting while providing strong predictive performance. XGBoost is known for its superior performance in capturing intricate relationships, providing robust predictions across various data contexts, as well as obtaining the first prize in many AI datathons.

Missing data:

The investigators anticipate missing data for patient-reported, clinical, radiological and supplementary variables. To address this, the investigators will

1. Assess the extent and patterns of missingness for each variable using descriptive statistics and graphical methods.
2. Investigate reasons for missing values and potential differences between individuals with and without incomplete data.
3. Handle missing data using XGBoost's native capability to manage missing values directly by learning optimal splits for missing data, thereby eliminating the need for external imputation approaches for this model.

Model development:

Extreme Gradient Boosting (XGBoost):

• The data will be split into a training (70%) and testing (30%) set. The XGBoost model will be trained using hyperparameter tuning through grid search combined with repeated 5-fold cross-validation (repeated 5 times) on the training set. This repeated cross-validation serves as internal validation to ensure robust and unbiased estimation of model performance during training. The grid space search will explore a reasonable range of values for key hyperparameters, such as:

  • Number of boosting rounds (nrounds): (e.g., 50, 100, 200)
  • Learning rate (eta): (e.g., 0,05, 0.1, 0.3)
  • Maximum depth of trees (max_depth): (e.g., 2, 4, 6)
  • Minimum sum of instances in each node (min_child_weight): (e.g., 1, 2, 4)
• The grid space will be kept moderate in size to balance comprehensiveness with computational feasibility, ensuring a thorough exploration of important hyperparameters while avoiding an overly exhaustive search.
• In developing our model, the investigators will aim to enhance the performance and reduce overfitting by employing feature selection to address collinearity. The investigators will also investigate a minimal feature set using feature importance scores from an initial XGBoost model as well as expert knowledge to prioritize clinically relevant predictors. Lastly, the investigators will explore feature engineering (e.g., polynomial transformations) to enhance the predictive power of our model.

Model evaluation:

• Held-Out Test Set: After internal validation and hyperparameter tuning, the final model will be evaluated on the 30% held-out test set to assess its performance on unseen data, providing an unbiased estimate of generalizability.

• Performance Metrics:

  • R² (Coefficient of Determination): To evaluate the proportion of variance explained by the model.
  • Mean Absolute Error (MAE): To quantify the average magnitude of prediction errors and assess model accuracy for continuous outcomes, offering a clinician-friendly interpretation of error.
  • Calibration and Validation Plots: To assess the agreement between observed and predicted outcomes, evaluating how well the predicted values align with the true values in the study population.
• Learning Curve: Learning curves will be employed to evaluate the model performance across different training set sizes. By plotting training and validation errors against the number of training sample sizes (subsets of whole dataset), the investigators can assess the model fit, observe the learning behavior, and determine whether our model performance would benefit from additional training data.
• Prediction Uncertainty: The investigators will use bootstrap aggregation (bagging), following methods from Hastie et al., to obtain prediction intervals, which quantify uncertainty in individual XGBoost predictions by analyzing the variance in prediction errors across bootstrap samples. Unlike confidence intervals, these intervals account for both model misspecification and outcome uncertainty.

Model output:

The investigators will use the final model to develop a web-based outcome calculator for pain and function 1-year after surgery. This tool is intended primarily for use by the clinicians, aiming to facilitate shared decision-making with the patients. By providing clear visualizations and easy-to-understand classifications, the calculator will help clinicians explain potential outcomes to patients and support patient engagement in their treatment planning. The model output will include either the predicted pain score on a 0-10 Numeric Rating Scale (NRS) or the bMHQ hand function score, which ranges from 0-100.

Based on the outcome, the exact predicted values will be visually highlighted followingly:

• Green: NRS 0-3, bMHQ 67-100 (indicative of positive outcomes)
• Orange: NRS 4-7, bMHQ 34-66 (indicative of moderate outcomes)
• Red: NRS 8-10, bMHQ 0-33 (indicative of poor outcomes) This classification aims to provide a quick, visual representation of the predicted outcomes, making it easier for clinicians and patients to interpret the results and understand the level of risk or expected recovery potential. The classification thresholds may be subject to change based on further validation to ensure accuracy and clinical relevance.