Explained Variation in a Fully Specified Model for Data-Grouped Survival Data

An additive hazards model may be used to quantify the effect of genetic and environmental predictors on flowering of sugar beet plants recorded as data-grouped time-to-event data. Estimated predictor effects have an intuitive interpretation rooted in the underlying time dynamics of the flowering process. However, agricultural experiments are often designed using several plots containing a large number of plants that are subsequently being monitored. In this article, we consider an additive hazards model with an additional plot structure induced by latent shared frailty variables. This approach enables us to derive a method to assess the quality of predictors in terms of how much plot variation they explain. We apply the method to a large data set exploring flowering of sugar beet and conclude that the genetic predictor biotype, which has a strong effect, also explains a substantial amount of the plot variation. The method is also applied to a data set from medical research concerning days to virus positivity of serum samples in AIDS patients.