Abstract
Population modeling aims to mathematically represent and predict how individual variability shapes broader population dynamics. In this context, population modeling often deals with time-series data from multiple subjects who share the same model structure, but whose individual parameters arc assumed to be samples from a probability distribution. In pharmacometrics, this takes the form of nonlinear mixed-effects (NLME) models, which capture both fixed population-level effects and random individual deviations amid complex nonlinearities and noisy data. The estimation of NLME parameters can be viewed as a form of bilevel optimization, where both population and individual-level objectives are intertwined. A widely used method for this is the Stochastic Approximation Expectation-Maximization (SAEM) algorithm, which iteratively combines stochastic simulation of latent variables with deterministic maximization steps, enabling efficient navigation of complex likelihood surfaces where direct optimization is intractable.
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