Correlated time to event data: Modeling repeated clinical mastitis data from dairy cattle in New York State

Mastitis is the most prevalent production disease in dairy herds worldwide and is considered to be the most economically important disease of dairy cattle. Modeling the risk of cows contracting mastitis is therefore of great interest for both targeting prevention programs and evaluating treatment protocols. Clinical mastitis (CM) is a disease of recurrent nature, thus correlation between the subsequent events within one cow may be present. This would violate the assumption behind most statistical time-to-event models. In the case of time to event models, the semi-parametric Cox regression models have become the default tool in modeling the time to an event. Limited methods are currently available to evaluate marginal and random (frailty) effects to account for multiple correlation sources. The objective of this study was to explore the implications of using several Cox or related semi-parametric or parametric models to estimate the hazard for CM in the presence of correlation between events. We evaluated the Andersen-Gill model which uses robust standard errors to account for the correlation, the Conditional Anderson-Gill model that uses stratification to account for event dependence, the Frailty model that introduces a random term to account for unobserved (cow level) heterogeneity, and a related generalized linear mixed model that uses Poisson regression to allow multi-level modeling of time-to-event data. We analyzed data on the occurrence of CM from five dairy farms in New York State. Data were from 8206 cows with 721, 275, 119, and 57 first, second, third, and fourth occurrences of CM, respectively, in the same lactation. The analysis of our sample dataset demonstrated that both cow- and farm-level correlation are present in the case of CM. The Conditional Frailty model was able to model one source of correlation in a random effect and one in a fixed effect. Poisson modeling allowed for simultaneous estimation of within cow correlation and within herd correlation.