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1. Efficient Algorithms and Implementation of a Semiparametric Joint Model for Longitudinal and Competing Risk Data: With Applications to Massive Biobank Data

   https://doi.org/10.1155/2022/1362913  

   Li, Shanpeng; Li, Ning; Wang, Hong; Zhou, Jin; Zhou, Hua; Li, Gang (February 2022, Computational and Mathematical Methods in Medicine)

   Maex, Reinoud (Ed.)

   Semiparametric joint models of longitudinal and competing risk data are computationally costly, and their current implementations do not scale well to massive biobank data. This paper identifies and addresses some key computational barriers in a semiparametric joint model for longitudinal and competing risk survival data. By developing and implementing customized linear scan algorithms, we reduce the computational complexities from O n 2 or O n 3 to O n in various steps including numerical integration, risk set calculation, and standard error estimation, where n is the number of subjects. Using both simulated and real-world biobank data, we demonstrate that these linear scan algorithms can speed up the existing methods by a factor of up to hundreds of thousands when n > 1 0 4 , often reducing the runtime from days to minutes. We have developed an R package, FastJM, based on the proposed algorithms for joint modeling of longitudinal and competing risk time-to-event data and made it publicly available on the Comprehensive R Archive Network (CRAN). 

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2. Joint analysis of recurrence and termination: A Bayesian latent class approach

   https://doi.org/10.1177/0962280220962522  

   Xu, Zhixing; Sinha, Debajyoti; Bradley, Jonathan R (February 2021, Statistical Methods in Medical Research)

   Like many other clinical and economic studies, each subject of our motivating transplant study is at risk of recurrent events of non-fatal tissue rejections as well as the terminating event of death due to total graft rejection. For such studies, our model and associated Bayesian analysis aim for some practical advantages over competing methods. Our semiparametric latent-class-based joint model has coherent interpretation of the covariate (including race and gender) effects on all functions and model quantities that are relevant for understanding the effects of covariates on future event trajectories. Our fully Bayesian method for estimation and prediction uses a complete specification of the prior process of the baseline functions. We also derive a practical and theoretically justifiable partial likelihood-based semiparametric Bayesian approach to deal with the analysis when there is a lack of prior information about baseline functions. Our model and method can accommodate fixed as well as time-varying covariates. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Our Bayesian analysis of transplant study and simulation study demonstrate practical advantages and improved performance of our approach. 

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3. Longitudinal Omics Data Analysis: A Review on Models, Algorithms, and Tools

   Taheriyoun, Ali R; Ross, Allen; Safikhani, Abolfazl; Soudbakhsh, Damoon; Rahnavard, Ali (June 2025, arxiv)

   Longitudinal omics data (LOD) analysis is essential for understanding the dynamics of biological processes and disease progression over time. This review explores various statistical and computational approaches for analyzing such data, emphasizing their applications and limitations. The main characteristics of longitudinal data, such as imbalancedness, high-dimensionality, and non-Gaussianity are discussed for modeling and hypothesis testing. We discuss the properties of linear mixed models (LMM) and generalized linear mixed models (GLMM) as foundation stones in LOD analyses and highlight their extensions to handle the obstacles in the frequentist and Bayesian frameworks. We differentiate in dynamic data analysis between time-course and longitudinal analyses, covering functional data analysis (FDA) and replication constraints. We explore classification techniques, single-cell as exemplary omics longitudinal studies, survival modeling, and multivariate methods for clinical/biomarker-based applications. Emerging topics, including data integration, clustering, and network-based modeling, are also discussed. We categorized the state-of-the-art approaches applicable to omics data, highlighting how they address the data features. This review serves as a guideline for researchers seeking robust strategies to analyze longitudinal omics data effectively, which is usually complex. 

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4. Quantile regression for survival data with covariates subject to detection limits

   https://doi.org/10.1111/biom.13309  

   Yu, Tonghui; Xiang, Liming; Wang, Huixia Judy (June 2020, Biometrics)

   Abstract With advances in biomedical research, biomarkers are becoming increasingly important prognostic factors for predicting overall survival, while the measurement of biomarkers is often censored due to instruments' lower limits of detection. This leads to two types of censoring: random censoring in overall survival outcomes and fixed censoring in biomarker covariates, posing new challenges in statistical modeling and inference. Existing methods for analyzing such data focus primarily on linear regression ignoring censored responses or semiparametric accelerated failure time models with covariates under detection limits (DL). In this paper, we propose a quantile regression for survival data with covariates subject to DL. Comparing to existing methods, the proposed approach provides a more versatile tool for modeling the distribution of survival outcomes by allowing covariate effects to vary across conditional quantiles of the survival time and requiring no parametric distribution assumptions for outcome data. To estimate the quantile process of regression coefficients, we develop a novel multiple imputation approach based on another quantile regression for covariates under DL, avoiding stringent parametric restrictions on censored covariates as often assumed in the literature. Under regularity conditions, we show that the estimation procedure yields uniformly consistent and asymptotically normal estimators. Simulation results demonstrate the satisfactory finite‐sample performance of the method. We also apply our method to the motivating data from a study of genetic and inflammatory markers of Sepsis. 

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5. Longitudinal Patterns in Clinical and Imaging Measurements Predict Residual Survival in Glioblastoma Patients

   Smedley, Nova F; Ellingson, Benjamin M; Cloughesy, Timothy F; Hsu, William (January 2018, Scientific reports)

   The growing amount of longitudinal data for a large population of patients has necessitated the application of algorithms that can discover patterns that inform patient management. This study demonstrates how temporal patterns generated from a combination of clinical and imaging measurements improve residual survival prediction in glioblastoma patients. Temporal patterns were identified with sequential pattern mining using data from 304 patients. Along with patient covariates, the patterns were incorporated as features in logistic regression models to predict 2-, 6-, or 9-month residual survival at each visit. The modeling approach that included temporal patterns achieved test performances of 0.820, 0.785, and 0.783 area under the receiver operating characteristic curve for predicting 2-, 6-, and 9-month residual survival, respectively. This approach significantly outperformed models that used tumor volume alone (p < 0.001) or tumor volume combined with patient covariates (p < 0.001) in training. Temporal patterns involving an increase in tumor volume above 122 mm3/day, a decrease in KPS across multiple visits, moderate neurologic symptoms, and worsening overall neurologic function suggested lower residual survival. These patterns are readily interpretable and found to be consistent with known prognostic indicators, suggesting they can provide early indicators to clinicians of changes in patient state that inform management decisions. 

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