A blended link approach to relative risk regression

Area of Science:

• Biostatistics
• Statistical modeling
• Health outcomes research

Background:

• Traditional binary regression often uses logit link functions, yielding odds ratios that are complex to interpret.
• Log-link functions offer a more intuitive relative risk interpretation but present practical and conceptual challenges, particularly with probability constraints.

Purpose of the Study:

• To propose and evaluate a novel smooth link function for binary regression that combines the interpretability of relative risks with practical implementation advantages.
• To address the limitations of existing log-link and logit-link functions in binary regression analysis.

Main Methods:

• Development of a new smooth link function that transitions from a log link to a scaled logit link above a specified cutoff.
• Comparison of the proposed smooth link function with traditional logit and log-link models using a simulation study.
• Application of the proposed method to a real-world dataset concerning diabetic retinopathy.

Main Results:

• The proposed smooth link function retains the relative risk interpretation for most individuals, offering a more accessible analysis.
• The new approach demonstrates conceptual clarity, ease of implementation, and generally reduced bias compared to existing methods.
• The smooth link function proved effective when applied to the diabetic retinopathy dataset.

Conclusions:

• The novel smooth link function provides a practical and conceptually clear alternative for binary regression, enhancing the interpretability of relative risks.
• This method simplifies the application of log-link-like interpretations in health outcomes research, particularly for non-extreme probabilities.
• The proposed function offers a valuable tool for researchers seeking more intuitive and less biased statistical models for binary data.