Longitudinal biomarker studies for cancer screening seek markers that are informative for both early detection and long-term risk prediction. Early detection markers typically show acute associations, with trajectories that change sharply just before diagnosis. Long-term risk predictors are often reflected by sustained changes in slopes or levels over time. This work compares three statistical strategies for detecting associations between longitudinal biomarkers and survival outcomes: the Cox model with time-varying covariates, joint models for simultaneous longitudinal and survival processes, and conditional models that model longitudinal data conditional on terminal events.
The three approaches use different modeling frameworks for the joint density of repeated biomarker measurements and survival time, which leads to distinct advantages and disadvantages for detecting acute versus long-term associations.
The Cox model with time-varying covariates treats biomarker measurements as covariates that change over time in a proportional hazards framework. Its likelihood is convex, providing computational stability and typically fast convergence.
Joint models simultaneously model the longitudinal biomarker trajectory and time-to-event process within a unified likelihood. They can capture complex dependency structures between the longitudinal process and the hazard but depend on correct specification of the longitudinal and survival submodels.
Conditional models model longitudinal trajectories conditional on a terminal event (for example, diagnosis) and have been proposed to separate trajectory behavior before the terminal event. They offer a framework that can disentangle short-term (acute) versus long-term effects of biomarkers on event risk.
The comparison used simulation studies with regular yearly visits and moderate measurement error to reflect commonly encountered longitudinal screening data. Simulations evaluated power and Type I error rates across different data-generating mechanisms to examine robustness to assumption violations and to quantify the power advantage, if any, of tests that match the underlying association structure (acute versus long-term).
Across the scenarios considered, the Cox model controlled Type I error rates and maintained high power for detecting associations. In contrast, both conditional and joint models demonstrated inflated Type I error when the longitudinal model was misspecified. The conditional and joint approaches outperformed the Cox model in power only when their model specification matched the data-generating mechanism precisely. Thus, while joint and conditional tests can be more powerful under correct specification, they are less robust to misspecification than the Cox approach.
Model misspecification emerged as a critical vulnerability for joint and conditional frameworks; inflated Type I errors indicate a risk of false-positive associations if the longitudinal model is not correctly specified. By design, only the conditional model can effectively disentangle acute short-term changes from long-term trajectory effects, which is an important interpretive advantage when the timing of biomarker change relative to diagnosis is of interest. The Cox model benefits from a convex likelihood, which provides faster convergence and greater computational stability across the scenarios evaluated.
The three approaches were applied to an analysis of CA-125 and ovarian cancer within the National Cancer Institute Prostate, Lung, Colorectal, and Ovarian (PLCO) Cancer Screening Trial. The empirical findings from the PLCO application followed patterns observed in the simulations: the Cox model retained controlled Type I error and competitive power, while conditional and joint models showed advantages only when model assumptions aligned with the observed biomarker–event association structure.
Choosing an approach for longitudinal biomarker analysis requires weighing robustness, interpretability, and statistical power. The Cox model with time-varying covariates provides a robust, computationally stable choice that controlled Type I error and retained strong power across simulated settings with yearly sampling and moderate measurement error. Joint and conditional models offer potentially greater power and the ability to parse timing-specific effects, but this comes at the cost of sensitivity to longitudinal model specification and potential Type I error inflation when that specification is incorrect. The conditional model uniquely supports separation of acute versus long-term effects, which is valuable for early detection research focused on prediagnostic trajectory changes.
The comparisons and conclusions are based on simulations with regular annual visits and moderate measurement error, and on a single empirical application (CA-125 in PLCO). Results indicate that the Cox model is a robust default for many longitudinal biomarker screening settings, while joint and conditional frameworks can be advantageous when there is confidence in model specification or when distinguishing acute from long-term effects is essential. Specific implementation details, additional data scenarios, and broader empirical validation were not reported in the source and therefore are not described here.