Conference Agenda

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Session Overview
Session
Joint / longitudinal modelling
Time:
Monday, 25/Aug/2025:
2:00pm - 3:30pm

Location: ETH E21

D-BSSE, ETH, 54 seats

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Presentations
12-joint-modeling: 1

Assessing surrogacy from joint modelling and mediation analysis when surrogates are either censored event times or longitudinal biomarker: cancer application

Virginie RONDEAU1, Quentin LECOENT2, Catherine LEGRAND3

1Department of Biostatistics, Bordeaux Population Health Research Center, INSERM U1219, Université de Bordeaux, Bordeaux, France; 2Department of Public Health Sciences, University of Chicago, Chicago, IL, USA; 3ISBA/LIDAM, UCLouvain, Louvain-la-Neuve, Belgium

Background

Before a candidate surrogate endpoint can be used in a clinical trial, it must be statistically validated. Joint modelling is a powerful approach to better understand the treatment effect when time-to-event and longitudinal endpoints commonly co-occur.

The aim of our approach is to decompose the total treatment effect on the final endpoint into a direct treatment effect and an indirect treatment effect mediated through a carefully constructed mediation path with a longitudinal mediator or a time to event mediator.

Methods

We focus on the cases where the final endpoint is a time-to event endpoint (such as time-to-death) and the surrogate is either a time-to-event or a longitudinal biomarker. Two new joint models were proposed depending on the nature of the surrogate. A mediation analysis is proposed to decompose the total effect of the treatment on the final endpoint as a direct effect and an indirect effect through the surrogate. The ratio of the indirect effect over the total effect of the treatment on the final endpoint can be computed from the parameters of the model and used as a measure of surrogacy. Inference is based on maximization of the penalized partial likelihood approach in the framework of the proposed joint models and has been evaluated via a large scale simulation study.

Results

We present the application to survival mediation analysis using real datasets in oncology with or without a meta-analytic nature of the data in order to quantify the proportion of treatment effect through the surrogate. The proposed mediation analyses study the time-to-relapse as a surrogate of overall survival in gastric cancer and the tumor size as a surrogate biomarker of overall survival in colorectal cancer.

The R-package frailtypack available on https://CRAN.R-project.org/package=frailtypack provides a user-friendly implementation of the above estimation and inference procedure.

Conclusion

We proposed a valuable tool to inform decision-making and advance our understanding of different treatment effects in mediation analysis with either a longitudinal mediator or a time-to-event mediator for a final survival endpoint.

  • Q. Lecoent, C. Legrand, and V. Rondeau. Time-to-event surrogate endpoint validation using mediation and meta-analytic data. Biostatistics, 2022.
  • Q. Lecoent, C. Legrand, and V. Rondeau. Validation of longitudinal marker as a surrogate using mediation analysis and joint modeling: evolution of PSA as a surrogate for DFS. Biometrical Journal, 2024.
  • Q. Lecoent, C. Legrand, and V. Rondeau. Tutorial for Surrogate Endpoint Validation Using Joint Modeling and Mediation Analysis. https://doi.org/10.48550/arXiv.2502.08443


12-joint-modeling: 2

Joint Modelling Using Semiparametric Accelerated Failure Time Approaches: Application to Health-Related Quality of Life Analysis

Ding Ma1, Patrick Maher1, Andrew Martin1,2

1ULTRA Team, Centre for Clinical Research, The University of Queensland, Australia; 2Australasian Gastro-Intestinal Trials Group (AGITG)

Background: Joint models (JMs) are well established for incorporating longitudinal biomarkers in time-to-event outcome prediction, but may be overlooked for predicting longitudinal health-related quality of life (HRQoL) outcomes in favour of linear mixed models (LMMs). LMMs rest on a missing-at-random assumption that may be uncertain in oncology trials where HRQoL assessments cease at progression. JMs may provide an advantage here, however popular software restricts the time-to-event component to proportional hazards (PH) models or simple parametric models, limiting their applicability to trials like AGITG INTEGRATE IIa (I2a). We have previously investigated a JM (R package JSM) with a semiparametric proportional odds (sPO) sub-model which yielded promising results. We now propose two flexible JM approaches that incorporate semiparametric accelerated failure time (sAFT) sub-models.

Methods: The first approach1 used Bernstein polynomials to approximate the baseline hazard function, employing rescaling strategies to enhance computational stability. The second approach2 adopted Gaussian basis functions to approximate the baseline hazard, and incorporated a roughness penalty with an automatic smoothing parameter selection procedure. We fitted the two JM models via a Bayesian method using uninformative priors for most parameters, except for those involved in the roughness penalty in the second approach. We applied both approaches to I2a.

Results: We obtained stable estimates for I2a using the first approach that aligned with the original I2a results. Estimates from the second approach exhibited instability, indicating areas that require further refinement.

Conclusion: The two approaches of sAFT sub-models represent novel alternatives to the proportional hazards models or simple parametric models for use in JMs with HRQoL, however challenges remain fitting the second approach. The dynamic range of the accelerated failure time term required intensive computation via posterior draws. Along with this, the MCMC computation involved many parameters with dispersed initial estimates (due to uninformative priors) thereby reducing stability. We are working to address the instabilities and will present our ongoing efforts.

References
[1] Panaro RV. spsurv: An R package for semi-parametric survival analysis. arXiv preprint arXiv:2003.10548.2020.
[2] Ma D, Ma J, Graham PL. On semiparametric accelerated failure time models with time-varying covariates: A maximum penalised likelihood estimation. Stat Med. 2023;42(30):5577–5595.



12-joint-modeling: 3

Using Joint Models to Assess Delayed Initiation of Salvage Therapy following Biochemical Recurrence for Prostate Cancer.

Jeremy M G Taylor1, Dimitris Rizopoulos2, Lukas Owens3

1University of Michigan, United States of America; 2Erasmus Medical Center, The Netherlands; 3Fred Hutchinson Cancer Center, United States of America

Prostate cancer patients who undergo prostatectomy are closely monitored for recurrence and metastasis using routine prostate-specific antigen (PSA) measurements. When PSA levels rise, this is called Biochemical Recurrence and at that point salvage therapies (ST) are considered to decrease the risk of metastasis. However, if the likelihood of metastases in the near future is thought to be low and due to the side effects of these therapies, patients may wish to delay the initiation of salvage therapy. A possible dynamic treatment strategy is that patients delay starting ST until their PSA values rises above a higher threshold. In this work, we use data from Memorial Sloan Kettering Cancer Center to estimate the risk of metastasis under such strategies. Due to the observational nature of this data, we face the challenge that PSA is simultaneously a time-varying confounder and an intermediate variable for salvage therapy. We specify a joint longitudinal survival model for the PSA trajectory, the hazard of metastases and the hazard of death from other causes. The model also incorporates a counterfactual framework. The model is estimated and the predictions for individual patients are made using a Bayesian approach, implemented via the R package JMbayes2.



12-joint-modeling: 4

Faster Estimation of Quasi-Monte Carlo Methods for Joint Models of Multivariate Longitudinal Data and Penalized Cox Regression

Adeboye Azeez, Colin Noel

University of Free State, South Africa

The estimation of joint models for time-to-event and multivariate longitudinal data presents significant computational challenges, particularly when utilizing Monte Carlo simulations. This study compares classical Vanilla Monte Carlo (MC) methods with two Quasi-Monte Carlo (QMC) techniques, Sobol and Halton sequences, in the context of joint models incorporating penalized Cox regression. The QMC integration framework extends the Monte Carlo Expectation Maximisation approaches that are commonly adopted. The motivation behind QMC sequences to improve convergence speed and computational efficiency by distributing nodes more uniformly. Simulations and a clinical dataset application demonstrate that QMC methods outperform Vanilla MC in terms of convergence speed, computational efficiency, and accuracy for all sample sizes, offer a distinct convergence speed advantage. By reducing variance and accelerating convergence, QMC methods provide a more efficient alternative for fitting complex joint models with penalized regression, especially in high-dimensional settings. The findings highlight the advantages of QMC methods in improving the practical application and computational feasibility of joint modelling approaches.



12-joint-modeling: 5

Regularization and Flexible Methods to Improve Complete Cancer Prevalence Predictions in the Prevalence Incidence Analysis Model

Fabrizio Di Mari1, Roberta De Angelis2, Therese ML Andersson3, Enoch Yi-Tung Chen3, Silvia Rossi2, Paul W Dickman3, Roberto Rocci1, Mark Clements3

1Sapienza University of Rome, Italy; 2Italian National Institute of Health, Italy; 3Karolinska Institutet, Sweden

Cancer prevalence is one of the primary measures used to assess the impact of the disease on a population. It helps the healthcare system quantify the burden of cancer and allocate resources to improve patient care. Prevalence is defined as the proportion of individuals with a current or past diagnosis of cancer within a population at a specific time. The Prevalence Incidence Analysis Model (PIAMOD) is commonly used to estimate the prevalence of an irreversible disease, such as cancer, in population-based studies. It primarily relies on modeling two key estimands, incidence and net survival, which are combined in a back-calculation method to estimate prevalence. Incidence rate is specified as an Age-Period-Cohort (APC) model using Poisson regression, while net survival is estimated within a relative survival framework. However, the APC model selection is based on a stepwise procedure that does not consider any measures of generalization performance. Additionally, net survival is estimated either non-parametrically, which results in high variability at the tails, or using a Weibull mixture cure model, which has been shown to lack sufficient flexibility to fit the observed data. These issues are significant concerns when the primary objective is to assess the future burden of a disease.
To address these drawbacks, we propose a Least Absolute Shrinkage and Selection Operator (LASSO)-driven model selection procedure for selecting the APC model. The strength of the penalization is chosen to minimize prediction error in the last observed years, left out during the training phase. For estimating net survival, we use flexible parametric survival cure models, which have been shown to adapt much better to the data than the Weibull mixture cure model and have less variability at the tails than the non-parametric estimator. We compared the novel and classical procedures using data from colon cancer patients diagnosed between 1958 and 2019 in Sweden. Furthermore, we compared the predicted incidence cases and cause-specific mortality cases with observed data up to 2023 using public sources. Our proposed method performed better than the classical approach across most of the validation measures considered.
Key References
Verdecchia, A., De Angelis, G., Capocaccia, R. (2002). Estimation and projections of cancer prevalence from cancer registry data. Statistics in Medicine, 21(22), 3511–3526.
Andersson, T. M. L., Dickman, P. W., Eloranta, S., & Lambert, P. C. (2011). Estimating and modelling cure in population-based cancer studies within the framework of flexible parametric survival models. BMC Medical Research Methodology, 11(1), 96.



 
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