Dose-time-response modeling using negative binomial distribution.

Area of Science:

• Biostatistics
• Epidemiology
• Pharmacometrics

Background:

• Determining safe and effective drug dosage is critical for treating diseases.
• Epidemiological studies often involve observing cure rates across different drug dose levels.
• Overdispersed count data in such studies can be modeled using the negative binomial distribution.

Purpose of the Study:

• To investigate the combined effect of drug dosage and time on treatment response.
• To develop a statistical model that accounts for both dose and time in epidemiological studies.
• To provide methods for estimating effective dose and time parameters.

Main Methods:

• Proposed a novel dose-time-response model incorporating the negative binomial distribution.
• Formulated closed-form point estimation and confidence bands for key parameters like ED(100p)(t) and LT(100p)(d).
• Utilized numerical illustrations to evaluate the model's performance.

Main Results:

• The developed model effectively integrates dose and time effects on drug response.
• Closed-form solutions for estimation and confidence bands were successfully derived.
• Numerical analyses confirmed the model's applicability and performance.

Conclusions:

• The proposed dose-time-response model offers a robust framework for analyzing drug efficacy in epidemiological contexts.
• The model provides valuable tools for estimating effective drug doses and treatment durations.
• This approach enhances the understanding of drug-disease interactions over time and varying dosages.