Estimation of extended mixed models using latent classes and latent processes: the R package lcmm

The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme), curvilinear and ordinal univariate longitudinal outcomes (lcmm) and curvilinear multivariate outcomes (multlcmm), as well as joint latent class mixed models (Jointlcmm) for a (Gaussian or curvilinear) longitudinal outcome and a time-to-event that can be possibly left-truncated right-censored and defined in a competing setting. Maximum likelihood esimators are obtained using a modified Marquardt algorithm with strict convergence criteria based on the parameters and likelihood stability, and on the negativity of the second derivatives. The package also provides various post-fit functions including goodness-of-fit analyses, classification, plots, predicted trajectories, individual dynamic prediction of the event and predictive accuracy assessment. This paper constitutes a companion paper to the package by introducing each family of models, the estimation technique, some implementation details and giving examples through a dataset on cognitive aging

Estimation of the Piecewise Exponential Model by Bayesian P-Splines via Gibbs Sampling: Robustness and Reliability of Posterior Estimates

In the investigation of disease dynamics, the effect of covariates on the hazard function is a major topic. Some recent smoothed estimation methods have been proposed, both frequentist and Bayesian, based on the relationship between penalized splines and mixed models theory. These approaches are also motivated by the possibility of using automatic procedures for determining the optimal amount of smoothing. However, estimation algorithms involve an analytically intractable hazard function, and thus require ad-hoc software routines. We propose a more user-friendly alternative, consisting in regularized estimation of piecewise exponential models by Bayesian P-splines. A further facilitation is that widespread Bayesian software, such as WinBUGS, can be used. The aim is assessing the robustness of this approach with respect to different prior functions and penalties. A large dataset from breast cancer patients, where results from validated clinical studies are available, is used as a benchmark to evaluate the reliability of the estimates. A second dataset from a small case series of sarcoma patients is used for evaluating the performances of the PE model as a tool for exploratory analysis. Concerning breast cancer data, the estimates are robust with respect to priors and penalties, and consistent with clinical knowledge. Concerning soft tissue sarcoma data, the estimates of the hazard function are sensitive with respect to the prior for the smoothing parameter, whereas the estimates of regression coefficients are robust. In conclusion, Gibbs sampling results an efficient computational strategy. The issue of the sensitivity with respect to the priors concerns only the estimates of the hazard function, and seems more likely to occur when non-large case series are investigated, calling for tailored solutions

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)

Variational Inference of Joint Models using Multivariate Gaussian Convolution Processes

We present a non-parametric prognostic framework for individualized event prediction based on joint modeling of both longitudinal and time-to-event data. Our approach exploits a multivariate Gaussian convolution process (MGCP) to model the evolution of longitudinal signals and a Cox model to map time-to-event data with longitudinal data modeled through the MGCP. Taking advantage of the unique structure imposed by convolved processes, we provide a variational inference framework to simultaneously estimate parameters in the joint MGCP-Cox model. This significantly reduces computational complexity and safeguards against model overfitting. Experiments on synthetic and real world data show that the proposed framework outperforms state-of-the art approaches built on two-stage inference and strong parametric assumptions

ADVANCES IN SYSTEM RELIABILITY-BASED DESIGN AND PROGNOSTICS AND HEALTH MANAGEMENT (PHM) FOR SYSTEM RESILIENCE ANALYSIS AND DESIGN

Failures of engineered systems can lead to significant economic and societal losses. Despite tremendous efforts (e.g., $200 billion annually) denoted to reliability and maintenance, unexpected catastrophic failures still occurs. To minimize the losses, reliability of engineered systems must be ensured throughout their life-cycle amidst uncertain operational condition and manufacturing variability. In most engineered systems, the required system reliability level under adverse events is achieved by adding system redundancies and/or conducting system reliability-based design optimization (RBDO). However, a high level of system redundancy increases a system's life-cycle cost (LCC) and system RBDO cannot ensure the system reliability when unexpected loading/environmental conditions are applied and unexpected system failures are developed. In contrast, a new design paradigm, referred to as resilience-driven system design, can ensure highly reliable system designs under any loading/environmental conditions and system failures while considerably reducing systems' LCC. In order to facilitate the development of formal methodologies for this design paradigm, this research aims at advancing two essential and co-related research areas: Research Thrust 1 - system RBDO and Research Thrust 2 - system prognostics and health management (PHM). In Research Thrust 1, reliability analyses under uncertainty will be carried out in both component and system levels against critical failure mechanisms. In Research Thrust 2, highly accurate and robust PHM systems will be designed for engineered systems with a single or multiple time-scale(s). To demonstrate the effectiveness of the proposed system RBDO and PHM techniques, multiple engineering case studies will be presented and discussed. Following the development of Research Thrusts 1 and 2, Research Thrust 3 - resilience-driven system design will establish a theoretical basis and design framework of engineering resilience in a mathematical and statistical context, where engineering resilience will be formulated in terms of system reliability and restoration and the proposed design framework will be demonstrated with a simplified aircraft control actuator design problem

A scalable formulation of joint modelling for longitudinal and time to event data and its application on large electronic health record data of diabetes complications

INTRODUCTION: Clinical decision-making in the management of diabetes and other chronic diseases depends upon individualised risk predictions of progression of the disease or complica- tions of disease. With sequential measurements of biomarkers, it should be possible to make dynamic predictions that are updated as new data arrive. Since the 1990s, methods have been developed to jointly model longitudinal measurements of biomarkers and time-to-event data, aiming to facilitate predictions in various fields. These methods offer a comprehensive approach to analyse both the longitudinal changes in biomarkers, and the occurrence of events, allowing for a more integrated understanding of the underlying processes and improved predictive capabilities. The aim of this thesis is to investigate whether established methods for joint modelling are able to scale to large-scale electronic health record datasets with multiple biomarkers measured asynchronously, and evaluates the performance of a novel approach that overcomes the limitations of existing methods. METHODS: The epidemiological study design utilised in this research is a retrospective observa- tional study. The data used for these analyses were obtained from a registry encompassing all individuals with type 1 diabetes in Scotland, which is delivered by the Scottish Care Information - Diabetes Collaboration platform. The two outcomes studied were time to cardiovascular disease (CVD) and time to end-stage renal disease (ESRD) from T1D diag- nosis. The longitudinal biomarkers examined in the study were glycosylated haemoglobin (HbA1c) and estimated glomerular filtration rate (eGFR). These biomarkers and endpoints were selected based on their prevalence in the T1D population and the established association between these biomarkers and the outcomes. As a state-of-the-art method for joint modelling, Brilleman’s stan_jm() function was evaluated. This is an implementation of a shared parameter joint model for longitudinal and time-to- event data in Stan contributed to the rstanarm package. This was compared with a novel approach based on sequential Bayesian updating of a continuous-time state-space model for the biomarkers, with predictions generated by a Kalman filter algorithm using the ctsem package fed into a Poisson time-splitting regression model for the events. In contrast to the standard joint modelling approach that can only fit a linear mixed model to the biomarkers, the ctsem package is able to fit a broader family of models that include terms for autoregressive drift and diffusion. As a baseline for comparison, a last-observation-carried-forward model was evaluated to predict time-to-event. RESULTS: The analyses were conducted using renal replacement therapy outcome data regarding 29764 individuals and cardiovascular disease outcome data on 29479 individuals in Scotland (as per the 2019 national registry extract). The CVD dataset was reduced to 24779 individuals with both HbA1c and eGFR data measured on the same date; a limitation of the modelling function itself. The datasets include 799 events of renal replacement therapy (RRT) or death due to renal failure (6.71 years average follow-up) and 2274 CVD events (7.54 years average follow-up) respectively. The standard approach to joint modelling using quadrature to integrate over the trajectories of the latent biomarker states, implemented in rstanarm, was found to be too slow to use even with moderate-sized datasets, e.g. 17.5 hours for a subset of 2633 subjects, 35.9 hours for 5265 subjects, and more than 68 hours for 10532 subjects. The sequential Bayesian updating approach was much faster, as it was able to analyse a dataset of 29121 individuals over 225598.3 person-years in 19 hours. Comparison of the fit of different longitudinal biomarker submodels showed that the fit of models that also included a drift and diffusion term was much better (AIC 51139 deviance units lower) than models that included only a linear mixed model slope term. Despite this, the improvement in predictive performance was slight for CVD (C-statistic 0.680 to 0.696 for 2112 individuals) and only moderate for end-stage renal disease (C-statistic 0.88 to 0.91 for 2000 individuals) by adding terms for diffusion and drift. The predictive performance of joint modelling in these datasets was only slightly better than using last-observation-carried-forward in the Poisson regression model (C-statistic 0.819 over 8625 person-years). CONCLUSIONS: I have demonstrated that unlike the standard approach to joint modelling, implemented in rstanarm, the time-splitting joint modelling approach based on sequential Bayesian updating can scale to a large dataset and allows biomarker trajectories to be modelled with a wider family of models that have better fit than simple linear mixed models. However, in this application, where the only biomarkers were HbA1c and eGFR, and the outcomes were time-to-CVD and end-stage renal disease, the increment in the predictive performance of joint modelling compared with last-observation-carried forward was slight. For other outcomes, where the ability to predict time-to-event depends upon modelling latent biomarker trajectories rather than just using the last-observation-carried-forward, the advantages of joint modelling may be greater. This thesis proceeds as follows. The first two chapters serve as an introduction to the joint modelling of longitudinal and time-to-event data and its relation to other methods for clinical risk prediction. Briefly, this part explores the rationale for utilising such an approach to manage chronic diseases, such as T1D, better. The methodological chapters of this thesis describe the mathematical formulation of a multivariate shared-parameter joint model and introduce its application and performance on a subset of individuals with T1D and data pertaining to CVD and ESRD outcomes. Additionally, the mathematical formulation of an alternative time-splitting approach is demonstrated and compared to a conventional method for estimating longitudinal trajectories of clinical biomarkers used in risk prediction. Also, the key features of the pipeline required to implement this approach are outlined. The final chapters of the thesis present an applied example that demonstrates the estimation and evaluation of the alternative modelling approach and explores the types of inferences that can be obtained for a subset of individuals with T1D that might progress to ESRD. Finally, this thesis highlights the strengths and weaknesses of applying and scaling up more complex modelling approaches to facilitate dynamic risk prediction for precision medicine

Book of Abstracts XVIII Congreso de Biometría CEBMADRID

Abstracts of the XVIII Congreso de Biometría CEBMADRID held from 25 to 27 May in MadridInteractive modelling and prediction of patient evolution via multistate models / Leire Garmendia Bergés, Jordi Cortés Martínez and Guadalupe Gómez Melis : This research was funded by the Ministerio de Ciencia e Innovación (Spain) [PID2019104830RBI00]; and the Generalitat de Catalunya (Spain) [2017SGR622 and 2020PANDE00148].Operating characteristics of a model-based approach to incorporate non-concurrent controls in platform trials / Pavla Krotka, Martin Posch, Marta Bofill Roig : EU-PEARL (EU Patient-cEntric clinicAl tRial pLatforms) project has received funding from the Innovative Medicines Initiative (IMI) 2 Joint Undertaking (JU) under grant agreement No 853966. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and EFPIA and Children’s Tumor Foundation, Global Alliance for TB Drug Development non-profit organisation, Spring works Therapeutics Inc.Modeling COPD hospitalizations using variable domain functional regression / Pavel Hernández Amaro, María Durbán Reguera, María del Carmen Aguilera Morillo, Cristobal Esteban Gonzalez, Inma Arostegui : This work is supported by the grant ID2019-104901RB-I00 from the Spanish Ministry of Science, Innovation and Universities MCIN/AEI/10.13039/501100011033.Spatio-temporal quantile autoregression for detecting changes in daily temperature in northeastern Spain / Jorge Castillo-Mateo, Alan E. Gelfand, Jesús Asín, Ana C. Cebrián / Spatio-temporal quantile autoregression for detecting changes in daily temperature in northeastern Spain : This work was partially supported by the Ministerio de Ciencia e Innovación under Grant PID2020-116873GB-I00; Gobierno de Aragón under Research Group E46_20R: Modelos Estocásticos; and JC-M was supported by Gobierno de Aragón under Doctoral Scholarship ORDEN CUS/581/2020.Estimation of the area under the ROC curve with complex survey data / Amaia Iparragirre, Irantzu Barrio, Inmaculada Arostegui : This work was financially supported in part by IT1294-19, PID2020-115882RB-I00, KK-2020/00049. The work of AI was supported by PIF18/213.INLAMSM: Adjusting multivariate lattice models with R and INLA / Francisco Palmí Perales, Virgilio Gómez Rubio and Miguel Ángel Martínez Beneito : This work has been supported by grants PPIC-2014-001-P and SBPLY/17/180501/000491, funded by Consejería de Educación, Cultura y Deportes (Junta de Comunidades de Castilla-La Mancha, Spain) and FEDER, grant MTM2016-77501-P, funded by Ministerio de Economía y Competitividad (Spain), grant PID2019-106341GB-I00 from Ministerio de Ciencia e Innovación (Spain) and a grant to support research groups by the University of Castilla-La Mancha (Spain). F. Palmí-Perales has been supported by a Ph.D. scholarship awarded by the University of Castilla-La Mancha (Spain)