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The most powerful and comprehensive approach of study in modern biology is to understand the whole process of development and all events of importance to development which occur in the process. As a consequence, joint modeling of developmental processes and events has become one of the most demanding tasks in statistical research. Here, we propose a joint modeling framework for functional mapping of specific quantitative trait loci (QTLs) which controls developmental processes and the timing of development and their causal correlation over time. The joint model contains two submodels, one for a developmental process, known as a longitudinal trait, and the other for a developmental event, known as the time to event, which are connected through a QTL mapping framework. A nonparametric approach is used to model the mean and covariance function of the longitudinal trait while the traditional Cox proportional hazard (PH) model is used to model the event time. The joint model is applied to map QTLs that control whole-plant vegetative biomass growth and time to first flower in soybeans. Results show that this model should be broadly useful for detecting genes controlling physiological and pathological processes and other events of interest in biomedicine.

A Bayesian Framework for Functional Mapping through Joint Modeling of Longitudinal and Time-to-Event Data