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

Abstract

Survival analysis methods can be used to identify factors associated with the time to induction of infection. In the absence of a perfect test, detection of infection is generally delayed and depends on the duration of the latent infection period. We assess, via simulations, the impact of ignoring the delayed detection of infection on estimated survival times and propose a Bayesian Weibull regression model, which adjusts for the delayed detection of infection. The presence of non-differential detection delay seriously biased the baseline hazard and the shape of the hazard function. For differential detection delay, the associated regression coefficients were also biased. The extent of bias largely depended on the longevity of the delay. In all considered simulation scenarios our model led to corrected estimates. We utilized the proposed model in order to assess the age at natural infection with Mycobacterium avium subsp. paratuberculosis (MAP) in Danish dairy cattle from the analysis of available time to milk-seropositivity data that detected infection with delay. The proposed model captured the inverse relationship between the incidence rate of infection and that of seroconversion with time: susceptibility to infection decreases with time (shape parameter under the proposed model was ρ = 0.56 < 1), while older animals had a higher probability of sero-converting ( ρ = 2.67 > 1, under standard Weibull regression). Cows infected earlier in their lives were more likely to subsequently shed detectable levels of MAP and, hence, be a liability to herd-mates. Our approach can be particularly useful in the case of chronic infections with a long latent infection period, which, if ignored, severely affects survival estimates.