Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis

Area of Science:

• Statistics
• Biostatistics
• Computational Statistics

Background:

• Monotone nonparametric regression is crucial for modeling monotonic relationships in data.
• Bayesian frameworks offer flexibility in incorporating prior knowledge.
• Traditional dose-response models often assume specific functional forms.

Purpose of the Study:

• To develop a flexible Bayesian method for monotone nonparametric regression.
• To investigate the suitability of different parametric distribution functions for modeling monotone curves.
• To provide a framework for eliciting informative priors in dose-response analysis.

Main Methods:

• Modeling monotone functions as mixtures of shifted and scaled parametric probability distribution functions.
• Utilizing a general random probability measure as a prior for the mixing distribution.
• Investigating the two-sided power distribution function for its computational and mathematical properties.

Main Results:

• The two-sided power distribution function is identified as a well-suited choice for the underlying parametric distribution.
• The proposed Bayesian model allows for informative prior elicitation on dose-response curves.
• The method demonstrates competitive performance compared to existing approaches in simulation studies.

Conclusions:

• The proposed Bayesian approach provides a robust and flexible method for monotone nonparametric regression.
• The two-sided power distribution offers practical advantages in this modeling context.
• The method is effective for analyzing dose-response data and allows for informed prior specification.