MOUSSA FORMULA IOL Calculator & Research Suite

1. Download Template

• ⬇ Download Prediction Template (.xlsx)

2. Upload Data

3. Calculate

Run Prediction

1. Prepare Data

Upload an Excel file containing Prediction Errors (Predicted Rx - Actual Rx).
Each column should represent a formula (e.g., "Moussa", "Barrett", "Kane", "Cooke").
Optional: Include a column named "AXL" if you want subgroup analysis.

• ⬇ Download Stats Template (.xlsx)

2. Upload Prediction Errors

3. Run Analysis

Run Advanced Stats

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. If omitted, the Corneal Refractive Index defaults to 1.3375.

1. Constant Optimisation (Data Preparation)

Prediction Error (PE) is calculated universally as: Actual Postoperative Refraction − Predicted Refraction.

• 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.

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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.

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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:

• Optimised Constants Summary (optimised_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. Subgroups are automatically generated if an AXL column is present.
• 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 & Cluster Testing)

To ensure robust statistical validity, especially given the non-normal distribution of absolute errors and the tracking of bilateral eye datasets, the Research Suite employs a uniform cluster-robust distribution framework regardless of the final FWER method selected. Instead of treating correlated eyes as independent data collections, the engine handles variance inflation via Cluster Bootstrapping (n=2000 iterations) sampled at the patient hierarchy level.

To activate this protection: Ensure your dataset contains a patient identifier column (accepted variations include id, hosp_id, hospid, ptid, or pt_id, which are not case sensitive). Crucially, bilateral eyes must share the exact same ID string. (e.g., Do not append "-1" and "-2" to differentiate eyes, as the algorithm will treat them as unique, independent patients). If detected, the algorithm automatically clusters matching IDs. If absent, the system simply assigns each eye its own unique cluster ID (a cluster size of 1), meaning the math naturally resolves to standard independent statistics without changing the core cluster-robust pipeline.

• Morgan-Pitman Test for Precision (SD): Evaluates the equality of variances to monitor whether a targeted formula is significantly more stable (lower variance) than an alternative. To optimise computational efficiency, if all eyes in the dataset belong to independent patients (no bilateral clusters detected) and a standard FWER correction (e.g., Hommel, Holm, or Bonferroni) is selected, the system runs an asymptotic Morgan-Pitman test with HC4 robust extensions. However, if bilateral dependent eyes are detected OR if the Romano-Wolf step-down FWER correction is active, the engine automatically upgrades to a computationally intensive Morgan-Pitman test paired with Wild Cluster Bootstrapping (WCB) and CR0 standard errors to guarantee rigorous cluster-robust protection and accurate joint null distributions.
• Yang's Modified Obuchowski Test (Accuracy/McNemar): A cluster-robust McNemar evaluation with adjustments for cluster-level tracking and continuity corrections, ensuring clear categorical checks within configurable refractive goal parameters. Note: As an asymptotic evaluation, this test does not generate a bootstrapped joint-null distribution. Therefore, if the Romano-Wolf FWER correction is selected globally, this specific accuracy test will intelligently fall back to a Hommel adjustment.
• Absolute Error Trimming (Invalid Threshold): Performs mean-difference monitoring while automatically excluding invalid values based on the configured Invalid TGT (default |PE| ≥ 4.0D). This minimises statistical distortion caused by gross surgical outliers without modifying your original clinical files.
• Family-Wise Error Rate (FWER) Controls: Multiple comparison checks are stringently managed to minimise Type I error accumulation. Users can dynamically configure corrections using Romano-Wolf Step-Down adjustments (which capture actual joint distribution patterns during bootstrap resamples), Hommel matrix configurations, Holm updates, or standard Bonferroni boundaries.