A Bayesian Weibull survival model for time to infection data measured with delay

Area of Science:

• Veterinary epidemiology
• Biostatistics
• Infectious disease modeling

Background:

• Survival analysis is crucial for identifying infection-related factors.
• Delayed detection of infection, common in chronic diseases, can bias survival time estimates.
• Accurate modeling is needed to account for latent infection periods.

Purpose of the Study:

• To assess the impact of ignoring delayed infection detection on survival time estimations.
• To propose and validate a Bayesian Weibull regression model that adjusts for delayed detection.
• To apply the model to estimate the age of natural infection with Mycobacterium avium subsp. paratuberculosis (MAP) in dairy cattle.

Main Methods:

• Simulations were used to evaluate bias caused by non-differential and differential detection delays.
• A Bayesian Weibull regression model was developed to correct for delayed infection detection.
• The model was applied to time-to-seropositivity data for MAP in Danish dairy cattle.

Main Results:

• Ignoring detection delay significantly biased hazard function estimates and regression coefficients.
• The proposed Bayesian model provided corrected estimates across various simulation scenarios.
• The model revealed that susceptibility to MAP infection decreases with age, while seroconversion probability increases.

Conclusions:

• Delayed infection detection can severely distort survival estimates, particularly for chronic infections.
• The proposed Bayesian Weibull model effectively corrects for detection delays, offering more accurate survival analyses.
• Understanding infection timing in cattle is vital for herd management and disease control.