Joint Models Resist Missing Biomarker Data but Falter Under High Measurement Error

Simulation findings demonstrate that joint models for longitudinal data and survival outcomes remain robust in the presence of truncated or intermittently missing markers, although elevated measurement error on biomarker values increases analytical uncertainty and can produce moderate-to-large bias.

Tracking dynamic health information over time is critical for monitoring and predicting patient health status, where biomarkers serve as longitudinal endogenous variables. In clinical research, the Time-Dependent Cox Model has been widely applied to analyze associations between biomarker measurements and time-to-event outcomes.

A primary analytical complication arises when terminal events truncate the observation of a biomarker’s full trajectory, creating longitudinal data that are Missing Not At Random. Joint models are designed to accommodate this specific form of missingness by explicitly modeling the missing process caused by the terminating event.

Within this joint framework, researchers integrate a longitudinal sub-model for the biomarker trajectory using a mixed-effects approach alongside a time-to-event sub-model for the terminating event. Nevertheless, methodological difficulties persist whenever biomarker measurements are subject to additional sources of Missing Not At Random data beyond the terminating event itself.

To evaluate these approaches, researchers Matteo Petrosino, Laura Antolini, Stefania Galimberti, and Paola Rebora conducted a simulation study reported in BMC Medical Research Methodology, assessing the robustness of joint models across diverse missing data mechanisms and comparing their performance to the Time-Dependent Cox Model when estimating hazard-based associations between biomarker values and terminal event risks. The authors also applied the joint model in an intensive care setting characterized by multiple missing sources.

The comparative analyses revealed that the Time-Dependent Cox Model remains effective when measurement error is minimal, but joint modeling is preferable when error is abundant, especially under conditions involving Missing Not At Random longitudinal data. Consequently, the authors conclude that the correct modeling of the biomarker trajectory within the joint model framework is essential for conducting a robust analysis.

In evaluating the methodological performance of these analytical frameworks, the simulation investigation specifically focused on how accurately models estimate the hazard-based association connecting endogenous biomarker measurements to terminal event occurrences. A central challenge highlighted in the investigation involves the nature of endogenous longitudinal variables, whose complete trajectories are cut short when patients experience a terminal event. Because this event-driven truncation prevents further data collection, it inherently generates a Missing Not At Random mechanism in the longitudinal series. While Joint Models directly account for this terminating event process by linking a mixed-effects trajectory sub-model with a survival sub-model, the research highlights that practical difficulties remain whenever biomarker data encounter other simultaneous sources of Missing Not At Random missingness.

The comparative simulation experiments further detailed the delicate balance between biomarker measurement error and model choice when evaluating hazard risks. Although Joint Models demonstrate resilience when faced with markers that are intermittently missing or truncated by terminal events, the presence of substantial measurement error in the biomarker values introduces considerable analytical uncertainty and can generate moderate-to-large bias. When biomarker values are subject to minimal measurement error, the standard Time-Dependent Cox Model remains an effective tool for hazard estimation. However, when measurement error is abundant, joint modeling proves superior, particularly in scenarios characterized by Missing Not At Random mechanisms in the longitudinal records.

Beyond synthetic simulations, the study demonstrated the real-world relevance of these methodological principles by examining an Intensive Care setting characterized by multiple coexisting sources of missing data. In critical care environments where dynamic longitudinal markers are gathered to monitor and predict health status changes, observations are frequently compromised by both intermittent omissions and event truncation. Under these multifaceted conditions, the authors emphasize that properly characterizing and specifying the longitudinal biomarker trajectory within the joint model framework remains indispensable for ensuring valid, robust statistical inference.

Subject of Research: Robustness of joint models for longitudinal biomarker data and survival outcomes

Article Title: Joint modeling of longitudinal data and survival outcomes with multiple missing sources: a simulation study

Article References: Petrosino, M., Antolini, L., Galimberti, S., & Rebora, P. (2026). Joint modeling of longitudinal data and survival outcomes with multiple missing sources: a simulation study. BMC Medical Research Methodology. https://doi.org/10.1186/s12874-026-02988-w

Image Credits: AI Generated

DOI: 10.1186/s12874-026-02988-w

Keywords: joint models, time-dependent Cox model, longitudinal data, survival outcomes, biomarkers, missing not at random, measurement error, simulation study, Joint, modeling, longitudinal, data