MOUSSA FORMULA - UPDATE IN PROGRESS

1. Download Template

• ⬇ Download Prediction Template (.xlsx)

2. Upload Data

3. Calculate

Run Prediction

Instructions for Use

To use the Research Suite, ensure your data is formatted correctly using the provided templates. Note: Throughout the entire platform (Calculator, Optimisation, Prediction), the Age parameter is mandatory unless all extended biometry values (Lens Thickness, Central Corneal Thickness, and HCD/WTW) are provided.

1. Constant Optimisation (Data Preparation)

• Required: Lens_Model, AXL, K1, K2, ACDepth, Gender, IOL_Implanted, Postoperative_Refraction.
• Conditional: Age (Mandatory if LensThickness, CCT, and HCD are not provided).
• Optional: Pt_ID, LensThickness, CCT, HCD, Biometer, TK.

---

2. Bulk Prediction (Data Preparation)

For predicting outcomes on a new dataset using a specific A-constant:

• Required: a_constant, AXL, K1, K2, ACDepth, Gender, IOL_Implanted.
• Conditional: Age (Mandatory if LensThickness, CCT, and HCD are not provided).
• Optional: Pt_ID, Lens_Model, LensThickness, CCT, HCD (WTW), Biometer (Defaults to 'Other'), TK (Defaults to 'N').

Note: Ideally, use the optimised Moussa A-constant obtained from the Optimisation tab for best results.

---

3. Methodology & Generated Outputs

The Research Suite employs a rigorous statistical framework to ensure high-quality analysis. The system automatically handles the following:

A. Constant Optimisation

For automatically calculated formulas (Moussa, SRK/T, Hoffer Q, Holladay 1, Haigis), the system iteratively solves for the lens constant that minimises the Mean Absolute Error (MAE). This ensures the Mean Prediction Error (MPE) is zero for the specific Lens Model dataset, adhering to modern IOL constant optimisation standards.

B. Comprehensive Data Analysis

The system generates three primary Excel spreadsheets containing detailed breakdowns:

• Optimized Constants Summary (optimized_constants_summary.xlsx): Lists the final optimised constants for each formula.
• Summary Performance Metrics (summary_performance_metrics_by_group.xlsx): Metrics including MAE, MedAE, SD, Min/Max errors, and % within bounds.
• Detailed Predictions (detailed_predictions_and_errors.xlsx): Raw dataset enriched with prediction errors.

C. Visual Analysis (Generated Graphs)

A suite of high-resolution figures is generated for publication-quality reporting.

D. Advanced Statistical Analysis (Dependence Tests)

To ensure robust statistical validity, especially given the non-normal distribution of absolute errors in biometry, the Research Suite employs the Wilcox-Holladay-Wang-Koch (WHWK) methodology. Instead of relying on parametric assumptions, the system uses Bootstrapping (n=2000 iterations) for all pairwise comparisons:

• Morgan-Pitman Test (Precision/SD): A bootstrapped test comparing the Standard Deviations (SD) of prediction errors. This assesses whether one formula is significantly more precise (lower variance) than another.
• McNemar’s Test (Accuracy): A bootstrapped test comparing the proportion of eyes with prediction errors within ±0.50 D. This assesses categorical accuracy.
• Yuen’s Test (Robust Central Tendency): A bootstrapped test comparing 20% Trimmed Means. This is performed on both Absolute Errors (MAE) and Squared Errors (MSE) to compare performance while statistically mitigating the impact of gross outliers (e.g., >4.0D surprises) without requiring manual data exclusion.
• Bootstrapped MAE & RMSE: Direct comparison of Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) using bootstrap resamples to generate two-tailed P-values and 95% Confidence Intervals for the difference between formulas.
• Holm-Bonferroni Correction: All pairwise P-values are adjusted using the Holm method to strictly control the Family-Wise Error Rate (FWER) across multiple comparisons.