Change point testing in logistic regression models with interaction term.

Area of Science:

• Biostatistics
• Immunology
• Epidemiology

Background:

• Threshold effects, where relationships change at specific predictor values, are common in biological systems.
• Understanding these effects is crucial for defining protective immune responses against infections like HIV-1.
• Existing statistical methods may lack the power to accurately detect these critical change points.

Purpose of the Study:

• To develop and evaluate new hypothesis testing methods for change point models in logistic regression.
• To compare proposed tests against existing methods for accuracy and power in detecting threshold effects.
• To apply these methods to analyze immune responses related to mother-to-child transmission of HIV-1.

Main Methods:

• Investigated hypothesis testing for change point models with the change point variable as a main effect and in interaction terms.
• Proposed a test based on the maximum of likelihood ratios test statistic, with reference distribution via Monte Carlo simulation.
• Developed a maximum of weighted scores test, potentially more powerful when interaction effect direction is known.

Main Results:

• Simulation studies demonstrated that the proposed tests maintain correct Type I error rates.
• The new tests exhibited higher statistical power compared to several existing methods.
• The methods were successfully applied to real-world data on HIV-1 immune responses.

Conclusions:

• The proposed change point model-based testing methods are statistically sound and powerful.
• These methods provide valuable tools for analyzing complex biological data with threshold effects.
• The findings contribute to a better understanding of immune response dynamics in HIV-1 transmission.