Faster Monte Carlo estimation of joint models for time-to-event and multivariate longitudinal data

Fast and flexible inference for joint models of multivariate longitudinal and survival data using integrated nested Laplace approximations

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events, and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the integrated nested Laplace approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared with alternative estimation strategies. We further apply the methodology to analyze five longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research.

Dynamic risk score modeling for multiple longitudinal risk factors and survival

Modeling disease risk and survival using longitudinal risk factor trajectories is of interest in various clinical scenarios. The capacity to build a prognostic model using the trajectories of multiple longitudinal risk factors, in the presence of potential dependent censoring, would enable more informed, personalized decision making. A dynamic risk score modeling framework is proposed for multiple longitudinal risk factors and survival in the presence of dependent censoring, where both events depend on participants' post-baseline clinical progression and form a competing risks structure. The model requires relatively few random effects regardless of the number of longitudinal risk factors and can therefore accommodate multiple longitudinal risk factors in a parsimonious manner. The proposed method performed satisfactorily in extensive simulation studies. It is further applied to the motivating registry study on pediatric acute liver failure to model death using the trajectories of multiple clinical and biochemical markers. Once established, the model yields an easily calculable longitudinal risk score that can be used for disease monitoring among future patients.

A two‐level copula joint model for joint analysis of longitudinal and competing risks data

In this article, we propose a two-level copula joint model to analyze clinical data with multiple disparate continuous longitudinal outcomes and multiple event-times in the presence of competing risks. At the first level, we use a copula to model the dependence between competing latent event-times, in the process constructing the submodel for the observed event-time, and employ the Gaussian copula to construct the submodel for the longitudinal outcomes that accounts for their conditional dependence; these submodels are glued together at the second level via the Gaussian copula to construct a joint model that incorporates conditional dependence between the observed event-time and the longitudinal outcomes. To have the flexibility to accommodate skewed data and examine possibly different covariate effects on quantiles of a non-Gaussian outcome, we propose linear quantile mixed models for the continuous longitudinal data. We adopt a Bayesian framework for model estimation and inference via Markov Chain Monte Carlo sampling. We examine the performance of the copula joint model through a simulation study and show that our proposed method outperforms the conventional approach assuming conditional independence with smaller biases and better coverage probabilities of the Bayesian credible intervals. Finally, we carry out an analysis of clinical data on renal transplantation for illustration.

Full Blood Count Trends for Colorectal Cancer Detection in Primary Care: Development and Validation of a Dynamic Prediction Model

Colorectal cancer has low survival rates when late-stage, so earlier detection is important. The full blood count (FBC) is a common blood test performed in primary care. Relevant trends in repeated FBCs are related to colorectal cancer presence. We developed and internally validated dynamic prediction models utilising trends for early detection. We performed a cohort study. Sex-stratified multivariate joint models included age at baseline (most recent FBC) and simultaneous trends over historical haemoglobin, mean corpuscular volume (MCV), and platelet measurements up to baseline FBC for two-year risk of diagnosis. Performance measures included the c-statistic and calibration slope. We analysed 250,716 males and 246,695 females in the development cohort and 312,444 males and 462,900 females in the validation cohort, with 0.4% of males and 0.3% of females diagnosed two years after baseline FBC. Compared to average population trends, patient-level declines in haemoglobin and MCV and rise in platelets up to baseline FBC increased risk of diagnosis in two years. C-statistic: 0.751 (males) and 0.763 (females). Calibration slope: 1.06 (males) and 1.05 (females). Our models perform well, with low miscalibration. Utilising trends could bring forward diagnoses to earlier stages and improve survival rates. External validation is now required.

Dynamic Risk Prediction via a Joint Frailty-Copula Model and IPD Meta-Analysis: Building Web Applications

Clinical risk prediction formulas for cancer patients can be improved by dynamically updating the formulas by intermediate events, such as tumor progression. The increased accessibility of individual patient data (IPD) from multiple studies has motivated the development of dynamic prediction formulas accounting for between-study heterogeneity. A joint frailty-copula model for overall survival and time to tumor progression has the potential to develop a dynamic prediction formula of death from heterogenous studies. However, the process of developing, validating, and publishing the prediction formula is complex, which has not been sufficiently described in the literature. In this article, we provide a tutorial in order to build a web-based application for dynamic risk prediction for cancer patients on the basis of the R packages joint.Cox and Shiny. We demonstrate the proposed methods using a dataset of breast cancer patients from multiple clinical studies. Following this tutorial, we demonstrate how one can publish web applications available online, which can be manipulated by any user through a smartphone or personal computer. After learning this tutorial, developers acquire the ability to build an online web application using their own datasets.

Modeling repeated self-reported outcome data: a continuous-time longitudinal Item Response Theory model

Item Response Theory (IRT) models have received growing interest in health science for analyzing latent constructs such as depression, anxiety, quality of life or cognitive functioning from the information provided by each individual's items responses. However, in the presence of repeated item measures, IRT methods usually assume that the measurement occasions are made at the exact same time for all patients. In this paper, we show how the IRT methodology can be combined with the mixed model theory to provide a longitudinal IRT model which exploits the information of a measurement scale provided at the item level while simultaneously handling observation times that may vary across individuals and items. The latent construct is a latent process defined in continuous time that is linked to the observed item responses through a measurement model at each individual- and occasion-specific observation time; we focus here on a Graded Response Model for binary and ordinal items. The Maximum Likelihood Estimation procedure of the model is available in the R package lcmm. The proposed approach is contextualized in a clinical example in end-stage renal disease, the PREDIALA study. The objective is to study the trajectories of depressive symptomatology (as measured by 7 items of the Hospital Anxiety and Depression scale) according to the time from registration on the renal transplant waiting list and the renal replacement therapy. We also illustrate how the method can be used to assess Differential Item Functioning and lack of measurement invariance over time.