Augmenting beta regression for periodontal proportion data via the SAS NLMIXED procedure

Area of Science:

• Biostatistics
• Dental Research
• Periodontology

Background:

• Clinical attachment level (CAL) is crucial for assessing periodontal disease (PD).
• Tooth-level PD quantification often involves proportions of diseased sites, which can include zero or one, making standard beta regression inapplicable.
• Existing methods may require ad hoc data transformations, potentially compromising results.

Purpose of the Study:

• To introduce and evaluate an augmented beta regression (BR) framework for analyzing clustered proportion data in dental research, specifically addressing the challenge of zero and one values.
• To provide a statistically robust alternative to traditional methods that require data transformation.

Main Methods:

• Developed an augmented BR framework incorporating non-zero masses at zero and one to handle complete proportions.
• Utilized maximum likelihood estimation via SAS® Proc NLMIXED for parameter estimation.
• Validated the methodology through simulation studies and application to a real cross-sectional periodontal disease dataset.

Main Results:

• The augmented BR model demonstrated a superior fit to clustered periodontal proportion data compared to the standard beta model.
• The framework successfully accounted for clustering and the presence of zero/one proportions without data transformation.
• Simulation studies and real-data application confirmed the model's effectiveness in parameter estimation and risk quantification.

Conclusions:

• The augmented BR model is a recommended parametric alternative for fitting clustered proportion data in dental research, particularly when dealing with zeros and ones.
• This approach avoids the need for ad hoc data transformations, offering more reliable insights into periodontal disease risk.
• The methodology is implementable using standard SAS software.