An S-Plus function to calculate relative risks and adjusted means for regression models using natural splines.

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Generalized linear models (GLMs) are widely used for analyzing various data types.
• Modeling complex relationships between predictors and outcomes often requires flexible approaches like splines.
• Existing methods may lack integrated tools for calculating and visualizing specific risk and change metrics.

Purpose of the Study:

• To develop an S-Plus function for calculating key statistical measures in GLMs with natural cubic splines.
• To provide tools for estimating relative risks (RR), log relative risks (logRR), mean percent change (MPC), and adjusted mean differences (MD).
• To enable publication-quality graphical representation of these measures against a reference value.

Main Methods:

• Implementation of an S-Plus function utilizing natural cubic spline basis functions.
• Direct use of estimated coefficients and the fitted correlation matrix for calculations.
• Accommodating various degrees of freedom for the natural splines.
• Generation of plots with confidence limits for estimated quantities.

Main Results:

• The function successfully calculates RR, logRR, MPC (logarithmic link), and MD (identity link).
• Graphical outputs display these statistics relative to a user-defined reference.
• The method accommodates flexible modeling of predictor effects using splines.
• Specific values can be computed for comparison across different independent variable values.

Conclusions:

• The developed S-Plus function offers a comprehensive tool for analyzing GLMs with natural cubic splines.
• It facilitates the interpretation of model results through key statistical metrics and visualizations.
• This tool enhances the ability to assess risk and change in statistical modeling contexts.