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Landmarking with Latent Class Mixed Models for Dynamic Prediction of Time-to-event Data with Heterogeneous Biomarker Trajectories

This paper proposes a computationally efficient landmarking approach integrated with latent class mixed models, implemented in the R package `landmaRk`, to improve dynamic time-to-event prediction for large-scale EHR data by accounting for heterogeneous biomarker trajectories that traditional methods fail to capture.

Original authors: Víctor Velasco-Pardo, Nathan Constantine-Cooke, Charlie W. Lees, Catalina A. Vallejos

Published 2026-06-24

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Víctor Velasco-Pardo, Nathan Constantine-Cooke, Charlie W. Lees, Catalina A. Vallejos

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Predicting the Future from a Messy Past

Imagine you are trying to predict who will win a long-distance race. You have a massive list of runners (patients), and you have been tracking their speed (biomarkers) every time they pass a checkpoint.

In the medical world, doctors have access to huge digital records (Electronic Health Records) containing these speed checks for thousands of people. The goal is to use this history to predict who might drop out of the race (experience a health event) in the future.

However, there is a problem: Not all runners are the same.
Some runners start fast and slow down. Others start slow and sprint at the end. Some have hidden injuries we can't see. Traditional prediction tools often assume everyone is running on the same track with the same style, just adjusting for things we can see (like age or gender). But in reality, there are hidden "sub-groups" of runners with completely different patterns.

This paper introduces a new way to predict race outcomes that accounts for these hidden groups, and it does so without getting bogged down in heavy math that crashes computers.

The Old Ways: The "Last Seen" and the "Super-Computer"

Before this paper, there were two main ways to make these predictions:

The "Last Seen" Method (LOCF):
Imagine a coach looking at a runner and saying, "Okay, the last time I saw you, you were running at 5 mph. I'll assume you keep running at 5 mph until the next checkpoint."
- The Flaw: This ignores the fact that the runner might have tripped, sped up, or slowed down between checks. It's a rough guess that ignores measurement errors.
The "Super-Computer" Method (Joint Models):
This method tries to build a perfect, complex 3D map of every single runner's path and their chance of dropping out all at once.
- The Flaw: It is incredibly heavy. If you have data on 100,000 people, this method is like trying to solve a puzzle with a million pieces using a calculator. It takes too long and often fails on large datasets.

There was also a method called Joint Latent Class Models that tried to find hidden groups (like "sprinters" vs. "marathoners"), but it was just as heavy and slow as the Super-Computer method.

The New Solution: The "Smart Landmark"

The authors propose a new strategy called Landmarking with Latent Class Mixed Models (LCMM). Think of this as a modular, smart checkpoint system.

1. The Landmark Concept (The Checkpoints)

Instead of trying to predict the whole race at once, you pick specific moments in time (landmarks), like "Month 6" or "Year 2."

At Month 6, you only look at the people who are still in the race.
You look at their history up to that point.
You make a prediction for the next few months.
Then you move to Month 7, and repeat.

This is flexible. It handles the fact that people join and leave the study at different times, which is common in real-world hospital data.

2. The Secret Sauce: Finding Hidden Groups (LCMM)

This is where the paper shines. When looking at the history up to a checkpoint, the new method asks: "Is this runner part of a hidden group?"

Imagine the runners are actually three different species of animals:

Group A: Starts high, dips low, then spikes up.
Group B: Stays steady in the middle.
Group C: Starts high and slowly declines.

Old methods might just average everyone out. The new method uses Latent Class Mixed Models (LCMM) to say, "Ah, this runner looks like a Group A animal." It then uses the specific pattern of Group A to make the prediction.

Crucially, the paper found that knowing the group label is more important than the exact math of the path. Even if the math predicting the exact speed is similar to old methods, knowing which group the person belongs to gives a huge boost in accuracy.

3. The Tool: `landmaRk`

The authors didn't just write a theory; they built a Swiss Army Knife for this. They created a free software package called landmaRk.

Modular: You can swap out parts. Want to use a simple "Last Seen" method? Fine. Want to use the new "Hidden Group" method? Fine. Want to try a different survival calculator? You can plug it in.
Fast: It is designed to run on massive datasets (like hospital records) without crashing, unlike the heavy "Super-Computer" methods.

What Did They Test?

They tested this in two ways:

The Simulation (The Practice Race):
They created fake data where they knew the "truth" (there were exactly 3 hidden groups).
- Result: The new method (Landmarking + Hidden Groups) was much better at predicting the outcome than the old "Last Seen" method or the heavy "Super-Computer" methods. It was also faster.
- Key Finding: The biggest win came from telling the model which group the person belongs to, not just the math of their speed.
The Real Data (The AIDS Dataset):
They used real historical data from a clinical trial about HIV/AIDS patients, tracking their CD4 counts (a measure of immune health) to predict death.
- Result: The new method again outperformed the old ones. It found hidden patterns in how patients' immune systems were changing that the old methods missed.
- Note: The "Super-Computer" methods (Joint Models) were slower and actually less accurate at calibration (getting the probabilities right) than the new modular approach.

The Bottom Line

The paper claims that by combining Landmarking (checking the race at specific times) with Latent Class Models (finding hidden groups of similar runners), we can predict health outcomes much better and faster than before.

They also gave the medical community a free, flexible tool (landmaRk) to do this easily, allowing researchers to mix and match different math strategies without needing to be coding wizards.

In short: They found a way to spot hidden patterns in messy medical data to make better predictions, and they built a user-friendly toolkit to make it happen without slowing down the computer.

Technical Summary: Landmarking with Latent Class Mixed Models for Dynamic Prediction

Problem Statement
The increasing accessibility of electronic health records (EHR) offers opportunities for dynamic risk prediction of time-to-event outcomes using repeated measurements of time-varying covariates, such as biomarkers. However, existing dynamic prediction methods face significant limitations when applied to real-world biomedical data.

Homogeneity Assumption: Traditional landmarking and joint models for longitudinal and survival data (JMLS) typically assume that longitudinal trajectories are homogeneous across individuals, with heterogeneity captured only by observed covariates or thin-tailed random effects (e.g., normal distributions). This assumption fails when latent population structures exist—subgroups of individuals sharing distinct trajectory patterns and risk profiles that cannot be explained by observed covariates.
Computational Scalability: While Joint Latent Class Models (JLCM) can account for such latent heterogeneity, they are computationally intensive and often fail to scale to large EHR datasets. Furthermore, JLCMs and JMLS often require a common baseline time ( $t=0$ ) for all individuals, which is incompatible with the varying follow-up periods and in/outflow of patients typical in EHR settings.
Software Limitations: Existing software for landmarking analysis is often rigid, typically restricting users to "Last Observation Carried Forward" (LOCF) or Linear Mixed Effects (LME) models for summarizing trajectories, and Cox Proportional Hazards models for survival. This limits the ability to implement more flexible, heterogeneity-aware strategies.

Methodology
The authors propose a novel heterogeneity-aware landmarking approach that integrates Latent Class Mixed Models (LCMM) into the landmarking framework. The methodology operates as follows:

Landmarking Framework: The approach fits survival models sequentially at pre-specified landmark times ( $s$ ). At each $s$ , the risk set ( $R_s$ ) is identified (individuals event-free up to $s$ ).
Longitudinal Summarization via LCMM: Instead of using LOCF or standard LME, the method employs LCMMs to model the longitudinal trajectory $Y_i(s)$ $Y_{i} (s)$ observed up to time $s$ $s$ for individuals in $R_s$ $R_{s}$ .
- The LCMM assumes the population consists of $G$ latent classes, each with distinct trajectory patterns.
- Cluster membership is modeled via multinomial logistic regression.
- For each individual, the method calculates posterior probabilities of cluster membership ( $\hat{\pi}_{ig}$ ) based on observed data.
- Trajectory Summary ( $\hat{y}_i(s)$ ): To account for uncertainty in cluster allocation, the method averages cluster-specific trajectory predictions weighted by the posterior probabilities: $\hat{y}_i(s) = \sum \hat{\pi}_{ig} \hat{y}_i(s | c_i=g)$ .
- Cluster Label Input: The method also considers including the predicted cluster label ( $\hat{c}_i$ ) as a covariate in the survival model, providing a parsimonious summary of trajectory shape.
Survival Modeling: A landmark-specific survival model (e.g., Cox PH) is fitted using the summarized trajectory $\hat{y}_i(s)$ and optionally the predicted cluster label $\hat{c}_i$ to estimate the conditional probability of being event-free at $s+w$ .
Implementation (landmaRk): The authors developed landmaRk, a modular R package available on CRAN. It implements a pipeline for:
1. Defining risk sets and landmark times.
2. Fitting longitudinal submodels (supporting LOCF, LME, and LCMM).
3. Fitting survival submodels.
4. Evaluating predictive performance (using time-dependent AUC and Brier scores) via cross-validation.
  The modularity allows users to swap components and define custom longitudinal or survival models.

Key Results
The performance of the proposed method was evaluated through simulation studies and a case study using the AIDS dataset.

Simulation Studies:
- Data were generated under Joint Latent Class Model specifications with varying sample sizes, error distributions (normal vs. heavy-tailed), and Weibull shape parameters.
- Performance: LCMM-based landmarking models that included the predicted cluster labels (e.g., LCMM2cl) consistently outperformed traditional landmarking (LOCF, LME) and standard JLCMs in terms of discrimination (tdAUC) and calibration (Brier score).
- Cluster Labels vs. Trajectory Reconstruction: The improvement in prediction was primarily driven by the inclusion of the predicted cluster labels rather than the reconstruction of the trajectory itself. The predicted values $\hat{y}_i(s)$ from LCMM were often similar to those from LME, but the cluster labels captured additional prognostic information regarding the trajectory shape.
- Robustness: Fitting landmark-specific LCMMs (re-estimating clusters at each $s$ ) proved more robust to over-specification of the number of clusters ( $G$ ) compared to fitting a single global model.
- Efficiency: The proposed approach was computationally more efficient than JLCMs, making it suitable for larger datasets.
Case Study (AIDS Dataset):
- Using CD4 count trajectories to predict time to death, the heterogeneity-aware landmarking approach (specifically LCMM2cl at earlier landmarks) generally achieved higher discrimination than LOCF and LME.
- Joint models (JLCM) showed inferior discrimination and substantially worse calibration compared to the landmarking approaches.
- Performance varied by landmark time and horizon, with no single model being uniformly best, but the heterogeneity-aware approach consistently improved upon static-only and LOCF baselines.

Significance and Claims
The paper claims two primary contributions:

Methodological Innovation: It introduces a computationally efficient, heterogeneity-aware dynamic risk prediction strategy that leverages LCMMs within the landmarking paradigm. This addresses the unmet need for scalable methods that account for latent population structure in EHR data, overcoming the computational bottlenecks of JLCMs and the homogeneity assumptions of traditional landmarking.
Software Development: The landmaRk package provides a standardized, modular framework for landmarking analysis. By formalizing landmarking as a pipeline of interchangeable components, it facilitates the comparison of different model specifications (e.g., LME vs. LCMM) and accelerates the development and reproducibility of dynamic risk prediction strategies.

The authors emphasize that their approach is particularly valuable for EHR settings where data heterogeneity is high and computational scalability is critical. They note that while the number of clusters ( $G$ ) must be specified, the method demonstrates robustness to slight misspecification, and the inclusion of predicted cluster labels serves as a key mechanism for capturing trajectory shape information that improves prognostic accuracy.