An Overview and Recent Developments in the Analysis of Multistate Processes

Abstract Joint models for longitudinal and survival data have gained a lot of attention in recent years, with the development of myriad extensions to the basic model, including those which allow for multivariate longitudinal data, competing risks and recurrent events. Several software packages are now also available for their implementation. Although mathematically straightforward, the inclusion of multiple longitudinal outcomes in the joint model remains computationally difficult due to the large number of random effects required, which hampers the practical application of this extension. We present a novel approach that enables the fitting of such models with more realistic computational times. The idea behind the approach is to split the estimation of the joint model in two steps: estimating a multivariate mixed model for the longitudinal outcomes and then using the output from this model to fit the survival submodel. So-called two-stage approaches have previously been proposed and …

Piecewise exponential additive mixed models (PAMMs) provide a flexible framework for analyzing censored and truncated time-to-event data, bridging classical hazard-based modeling with modern regression techniques. They enable the estimation of complex covariate effects, including non-linear and time-varying (cumulative) effects, and naturally incorporate time-varying covariates. Moreover, PAMMs are applicable across a wide range of survival settings, including non-proportional hazards, recurrent events, competing risks, and multi-state analyses. This article introduces the pammtools package, which facilitates data transformation, estimation, and interpretation for PAMMs within a unified workflow. The package provides a comprehensive, user-friendly, and extensible interface covering the full modeling pipeline, from data transformation to estimation and visualization. In addition, simulation-based inference allows the calculation of confidence intervals for arbitrary quantities of intere …

Semi-competing risks refer to the time-to-event analysis setting, where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical contexts, including studies of preeclampsia, a condition that may arise during pregnancy and for which delivery is a terminal event. Models that acknowledge semi-competing risks enable investigation of relationships between covariates and the joint timing of the outcomes, but methods for model selection and prediction of semi-competing risks in high dimensions are lacking. Moreover, in such settings researchers commonly analyze only a single or composite outcome, losing valuable information and limiting clinical utility-in the obstetric setting, this means ignoring valuable insight into timing of delivery after preeclampsia has onset. To address this gap, we propose a novel penalized estimation framework for frailty-based illness-death multi-state mo …

Most existing time-to-event methods focus on either single-event or competing-risks settings, leaving multi-event scenarios relatively underexplored. In many healthcare applications, for example, a patient may experience multiple clinical events, that can be non-exclusive and semi-competing. A common workaround is to train independent single-event models for such multi-event problems, but this approach fails to exploit dependencies and shared structures across events. To overcome these limitations, we propose MENSA (Multi-Event Network for Survival Analysis), a deep learning model that jointly learns flexible time-to-event distributions for multiple events, whether competing or co-occurring. In addition, we introduce a novel trajectory-based likelihood term that captures the temporal ordering between events. Across four multi-event datasets, MENSA improves predictive performance over many state-of-the-art baselines. Source code is available at https://github.com/thecml/mensa.

In our case, the entire data-generating distribution is parameterized by intensities, and we can carry out targeting according to the log-likelihood loss function and least favorable submodel presented by Rytgaard et al. (2022, Section 5.2) . A similar procedure was applied for competing risks settings in Rytgaard et al. (2021) . We will assume for now that we have (initial) estimators for all clever weights and covariates from Theorem 1 . Estimating the clever covariates poses an additional challenge in recurrent events settings as compared to the competing risks setting, and we return to this specifically in Section 6 .