jmstate, a Flexible Python Package for Multi-State Joint Modeling

Classical joint modeling approaches often rely on competing risks or recurrent event formulations to account for complex real-world processes involving evolving longitudinal markers and discrete event occurrences. However, these frameworks typically capture only limited aspects of the underlying event dynamics. Multi-state joint models offer a more flexible alternative by representing full event histories through a network of possible transitions, including recurrent cycles and terminal absorptions, all potentially influenced by longitudinal covariates. In this paper, we propose a general framework that unifies longitudinal biomarker modeling with multi-state event processes defined on arbitrary directed graphs. Our approach accommodates both Markovian and semi-Markovian transition structures, and extends classical joint models by coupling nonlinear mixed-effects longitudinal submodels with multi-state survival processes via shared latent structures. We derive the full likelihood and develop scalable inference procedures based on stochastic gradient descent. Furthermore, we introduce a dynamic prediction framework, enabling individualized risk assessments along complex state-transition trajectories. To facilitate reproducibility and dissemination, we provide an open-source Python library \texttt{jmstate} implementing the proposed methodology, available on \href{https://pypi.org/project/jmstate/}{PyPI}. Simulation experiments and a biomedical case study demonstrate the flexibility and performance of the framework in representing complex longitudinal and multi-state event dynamics. The full Python notebooks used to reproduce the experiments as well as the source code of this paper are available on \href{https://gitlab.com/felixlaplante0/jmstate-paper/}{GitLab}.

Properties of the Stochastic Approximation EM Algorithm with Mini-batch Sampling

To speed up convergence a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation Maximization (MCMC-SAEM) algorithm for general latent variable models is proposed. For exponential models the algorithm is shown to be convergent under classical conditions as the number of iterations increases. Numerical experiments illustrate the performance of the mini-batch algorithm in various models. In particular, we highlight that an appropriate choice of the mini-batch size results in a tremendous speed-up of the convergence of the sequence of estimators generated by the algorithm. Moreover, insights on the effect of the mini-batch size on the limit distribution are presented.