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A Location-Scale Joint Model for Studying the Link Between the Time-Dependent Subject-Specific Variability of Blood
Léonie Courcoul1, Christophe Tzourio1, Mark Woodward2,3
1Univ. Bordeaux, INSERM, Bordeaux Population Health, U1219, France.
Insights
Blood pressure variability is a significant risk factor for cardiovascular and cerebrovascular diseases (CVD). Our new statistical model confirms this link, improving risk prediction for CVD and death.
Area of Science:
- Biostatistics
- Epidemiology
- Cardiovascular Research
Background:
- Cardio and cerebrovascular diseases (CVD) pose a major public health challenge due to high morbidity and mortality.
- Elevated blood pressure is a known risk factor, and emerging evidence suggests blood pressure variability may also be an independent predictor.
- Existing studies on blood pressure variability often have methodological limitations.
Purpose of the Study:
- To propose and validate a novel joint statistical model for analyzing repeated measures of a marker and competing events.
- To investigate the association between blood pressure variability and the risk of CVD and all-cause mortality.
- To demonstrate the importance of accounting for heterogeneous variance in risk prediction models.
Main Methods:
- Development of a joint location-scale model incorporating a mixed model with subject-specific, time-dependent residual variance and cause-specific proportional intensity models for competing events.
- The model allows event risk to depend on the current value and slope of the marker trajectory, and its variance.
- Estimation via maximum likelihood using the Marquardt-Levenberg algorithm, implemented in an R-package and validated by simulation.
Main Results:
- Application to a large clinical trial on stroke secondary prevention reveals that individual blood pressure variability is associated with the risk of CVD and death.
- The proposed model demonstrates improved goodness-of-fit and predictive accuracy compared to models that do not account for heterogeneous variance.
- The findings highlight the clinical relevance of incorporating blood pressure variability into risk assessment.
Conclusions:
- The developed joint model effectively captures the complex relationship between marker variability and competing risks.
- Blood pressure variability is confirmed as a significant independent risk factor for CVD and mortality.
- Accounting for heterogeneous variance is crucial for accurate risk prediction and clinical decision-making in cardiovascular health.
Abstract:
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.
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Special considerations while measuring blood pressure
Monitoring Both Arms:
Monitoring BP in both arms during the initial assessment is advisable, as the systolic value may differ by five to ten mm Hg between arms. For subsequent BP assessments, use the arm with the higher reading.

