A Location‐Scale Joint Model for Studying the Link Between the Time‐Dependent Subject‐Specific Variability of Blood Pressure and Competing Events

Given the high incidence of cardio and cerebrovascular diseases (CVD), and their association with morbidity and mortality, their prevention is a major public health issue. A high level of blood pressure is a well-known risk factor for these events, and an increasing number of studies suggest that blood pressure variability may also be an independent risk factor. However, these studies suffer from significant methodological weaknesses. In this work, we propose a new location-scale joint model for the repeated measures of a marker and competing events. This joint model combines a mixed model including a subject-specific and time-dependent residual variance modeled through random effects, and cause-specific proportional intensity models for the competing events. The risk of events may depend simultaneously on the current value of the variance, as well as, the current value and the current slope of the marker trajectory. The model is estimated by maximizing the likelihood function using the Marquardt-Levenberg algorithm. The estimation procedure is implemented in an R-package and is validated through a simulation study. This model is applied to study the association between blood pressure variability and the risk of CVD and death from other causes. Using data from a large clinical trial on the secondary prevention of stroke, we find that the current individual variability of blood pressure is associated with the risk of CVD and death. Moreover, the comparison with a model without heterogeneous variance shows the importance of taking into account this variability in the goodness-of-fit and for dynamic predictions.