Mathematics
The model is simple to state. Fitting it to real people, measured a few times over decades, is where the open problems are.
A person's state x is a vector of biomarkers. The hazard surface U is the log mortality hazard relative to a reference. It is estimated non-linearly, with interactions, and allowed to vary with age and sex. The map on the home page is one two-dimensional slice of U.
Each person drifts through the terrain with age a, plus fluctuation. The hypothesis is that μ and Σ are shared across people, and that a low-dimensional personal parameter θi (position, rate, sensitivity, resilience) captures the differences between them.
Cohorts measure blood every two to four years. What can be identified about θi from so few points, and how should shrinkage toward the population be designed so it is honest about what one person's data can say?
Cross-sectional age gradients mix true within-person change with birth-cohort differences and the selective survival of healthier people. Of 123 markers, 110 drift with age cross-sectionally. How much is real movement?
Clinical labs are dense but ordered when something is wrong. Joint models of measurement timing and value are needed before routine health-system data can be used.
Complex-systems theory predicts rising variance and autocorrelation as a regulated system loses stability. Which estimators survive sparse, noisy, irregular observation?
Which test, at which age, most reduces uncertainty about a person's future? Expected information gain per dollar turns the landscape into a decision tool.