Joint modelling of time to event and repeated measurement of eucalyptus tree species in Kenya

Abstract

The characterization of the relationship between a longitudinal response process and a time-to-event has been a pressing challenge in biostatistical research. This has emerged as an important issue especially in genetic studies when one attempts to detect the common genes that govern both a longitudinal response and a developmental event. We considered the analysis of an ongoing study on Eucalyptus tree species by Kenya Forestry Research Institute (KEFRI) grown in five different sites. These species include four local landraces and six hybrid clones introduced from South Africa. The study was designed to compare height and diameter at breast height (DBH) measurements across the species and sites. The available data include information on time to reaching 15 metres in height (50% to pole height) and the repeated measurement of DBH fo the 10 species. In this study we d~scribe a joint modelwhich accommodates incomplete repeated measures and right-censored event times. Such an. approach allows us to account for possible association between the time-to-event and the repeated measurements, and permits the use of the repeated measures to increase the efficiency of the estimate of the event-time process, We also compare the different species and sites using multivariate analysis of variance (MANOVA) for repeated measurements. The species parameter estimates for the time-to-event components of the joint model in general decreased in absolute order of magnitudes as compared with the models assuming independence between the processes. Thus, the adjustment for the evolution of DBH measurements resulted in less separation between the clones and the local landraces. Joint modeling also allows other characteristics of the repeated measurements pattern, such as the rate of change (slope), to influence the risk of the event, the hazard ratios approach one. This indicates that the distinction between the species decreases if the random slope is added to the joint model. On the other hand, adjustment for the event rates widened the differences between the DBH measurements for GC642 and other species.