A novel nonparametric time-dependent precision-recall curve estimator for right-censored survival data

In order to assess prognostic risk for individuals in precision health research, risk prediction models are increasingly used, in which statistical models are used to estimate the risk of future outcomes based on clinical and nonclinical characteristics. The predictive accuracy of a risk score must be assessed before it can be used in routine clinical decision making, where the receiver operator characteristic curves, precision-recall curves, and their corresponding area under the curves are commonly used metrics to evaluate the discriminatory ability of a continuous risk score. Among these the precision-recall curves have been shown to be more informative when dealing with unbalanced biomarker distribution between classes, which is common in rare event, even though except one, all existing methods are proposed for classic uncensored data. This paper is therefore to propose a novel nonparametric estimation approach for the time-dependent precision-recall curve and its associated area under the curve for right-censored data. A simulation is conducted to show the better finite sample property of the proposed estimator over the existing method and a real-world data from primary biliary cirrhosis trial is used to demonstrate the practical applicability of the proposed estimator.

Time-dependent receiver operating characteristic curve estimator for correlated right-censored time-to-event data

In clinical trials, evaluating the accuracy of risk scores (markers) derived from prognostic models for prediction of survival outcomes is of major concern. The time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve are appealing measures to evaluate the predictive accuracy. Several estimation methods have been proposed in the context of classical right-censored data which assumes the event time of individuals are independent. In many applications, however, this may not hold true if, for example, individuals belong to clusters or experience recurrent events. Estimates may be biased if this correlated nature is not taken into account. This paper is then aimed to fill this knowledge gap to introduce a time-dependent receiver operating characteristic curve and the corresponding area under the receiver operating characteristic curve estimation method for right-censored data that take the correlated nature into account. In the proposed method, the unknown status of censored subjects is imputed using conditional survival functions given the marker and frailty of the subjects. An extensive simulation study is conducted to evaluate and demonstrate the finite sample performance of the proposed method. Finally, the proposed method is illustrated using two real-world examples of lung cancer and kidney disease.

A semi-parametric approach for time-dependent ROC curves with nonignorable missing biomarker

The main purpose of this paper is to survey the statistical inference for covariate-specific time-dependent receiver operating characteristic (ROC) curves with nonignorable missing continuous biomarker values. To construct time-dependent ROC curves, we consider a joint model which assumes that the failure time depends on the continuous biomarker and the covariates through a Cox proportional hazards model and that the continuous biomarker depends on the covariates through a semiparametric location model. Assuming a purely parametric model on the propensity score, we utilize instrumental variables to deal with the identifiable issue and estimate the unknown parameters of the propensity score by a simple and efficient method. In addition, when the propensity score is estimated, we develop HT and AIPW approaches to estimate our interested quantities. In the presence of nonignorable missing biomarker, our AIPW estimators of the interested quantities are still doubly robust when the true propensity score is a special parametric logistic model. At last, simulation studies are conducted to assess the performance of our proposed approaches, and a real data analysis is also carried out to illustrate its application.

BAYESIAN INFERENCE AND DYNAMIC PREDICTION FOR MULTIVARIATE LONGITUDINAL AND SURVIVAL DATA

Alzheimer's disease (AD) is a complex neurological disorder impairing multiple domains such as cognition and daily functions. To better understand the disease and its progression, many AD research studies collect multiple longitudinal outcomes that are strongly predictive of the onset of AD dementia. We propose a joint model based on a multivariate functional mixed model framework (referred to as MFMM-JM) that simultaneously models the multiple longitudinal outcomes and the time to dementia onset. We develop six functional forms to fully investigate the complex association between longitudinal outcomes and dementia onset. Moreover, we use the Bayesian methods for statistical inference and develop a dynamic prediction framework that provides accurate personalized predictions of disease progressions based on new subject-specific data. We apply the proposed MFMM-JM to two large ongoing AD studies: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and National Alzheimer's Coordinating Center (NACC), and identify the functional forms with the best predictive performance. our method is also validated by extensive simulation studies with five settings.

A comparison of two approaches to dynamic prediction: Joint modeling and landmark modeling

Joint modeling and landmark modeling are two mainstream approaches to dynamic prediction in longitudinal studies, that is, the prediction of a clinical event using longitudinally measured predictor variables available up to the time of prediction. It is an important research question to the methodological research field and also to practical users to understand which approach can produce more accurate prediction. There were few previous studies on this topic, and the majority of results seemed to favor joint modeling. However, these studies were conducted in scenarios where the data were simulated from the joint models, partly due to the widely recognized methodological difficulty on whether there exists a general joint distribution of longitudinal and survival data so that the landmark models, which consists of infinitely many working regression models for survival, hold simultaneously. As a result, the landmark models always worked under misspecification, which caused difficulty in interpreting the comparison. In this paper, we solve this problem by using a novel algorithm to generate longitudinal and survival data that satisfies the working assumptions of the landmark models. This innovation makes it possible for a "fair" comparison of joint modeling and landmark modeling in terms of model specification. Our simulation results demonstrate that the relative performance of these two modeling approaches depends on the data settings and one does not always dominate the other in terms of prediction accuracy. These findings stress the importance of methodological development for both approaches. The related methodology is illustrated with a kidney transplantation dataset.

A novel prognostic nomogram for adult acute lymphoblastic leukemia: a comprehensive analysis of 321 patients

The cure rate of acute lymphoblastic leukemia (ALL) in adolescents and adults remains poor. This study aimed to establish a prognostic model for ≥14-year-old patients with ALL to guide treatment decisions. We retrospectively analyzed the data of 321 ALL patients between January 2017 and June 2020. Patients were randomly (2:1 ratio) divided into either the training or validation set. A nomogram was used to construct a prognostic model. Multivariate Cox analysis of the training set showed that age > 50 years, white blood cell count > 28.52×10⁹/L, and MLL rearrangement were independent risk factors for overall survival (OS), while platelet count >37×10⁹/L was an independent protective factor. The nomogram was established according to these independent prognostic factors in the training set, where patients were grouped into two categories: low-risk (≤13.15) and high-risk (>13.15). The survival analysis, for either total patients or sub-group patients, showed that both OS and progression-free survival (PFS) of low-risk patients was significantly better than that of high-risk patients. Moreover, treatment analysis showed that both OS and progression-free survival (PFS) of ALL with stem cell transplantation (SCT) were significantly better than that of ALL without SCT. Further stratified analysis showed that in low-risk patients, the OS and PFS of patients with SCT were significantly better than those of patients without SCT. In contrast, in high-risk patients, compared with non-SCT patients, receiving SCT can only significantly prolong the PFS, but it does not benefit the OS. We established a simple and effective prognostic model for ≥ 14-year-old patients with ALL that can provide accurate risk stratification and determine the clinical strategy.

Multivariate functional mixed model with MRI data: An application to Alzheimer's disease

Alzheimer's Disease (AD) is the leading cause of dementia and impairment in various domains. Recent AD studies, (ie, Alzheimer's Disease Neuroimaging Initiative (ADNI) study), collect multimodal data, including longitudinal neurological assessments and magnetic resonance imaging (MRI) data, to better study the disease progression. Adopting early interventions is essential to slow AD progression for subjects with mild cognitive impairment (MCI). It is of particular interest to develop an AD predictive model that leverages multimodal data and provides accurate personalized predictions. In this article, we propose a multivariate functional mixed model with MRI data (MFMM-MRI) that simultaneously models longitudinal neurological assessments, baseline MRI data, and the survival outcome (ie, dementia onset) for subjects with MCI at baseline. Two functional forms (the random-effects model and instantaneous model) linking the longitudinal and survival process are investigated. We use Markov Chain Monte Carlo (MCMC) method based on No-U-Turn Sampling (NUTS) algorithm to obtain posterior samples. We develop a dynamic prediction framework that provides accurate personalized predictions of longitudinal trajectories and survival probability. We apply MFMM-MRI to the ADNI study and identify significant associations among longitudinal outcomes, MRI data, and the risk of dementia onset. The instantaneous model with voxels from the whole brain has the best prediction performance among all candidate models. The simulation study supports the validity of the estimation and dynamic prediction method.

Increases prognostic value of clinical-pathological nomogram in patients with esophageal squamous cell carcinoma

Background

This study was intended to construct a brand new prognostic nomogram after combine clinical and pathological characteristics to increases prognostic value in patients with esophageal squamous cell carcinoma.

Methods

A total of 1,634 patients were included. Subsequently, the tumor tissues of all patients were prepared into tissue microarrays. AIPATHWELL software was employed to explore tissue microarrays and calculate the tumor-stroma ratio. X-tile was adopted to find the optimal cut-off value. Univariate and multivariate Cox analyses were used to screen out remarkable characteristics for constructing the nomogram in the total populations. A novel prognostic nomogram with clinical and pathological characteristics was constructed on the basis of the training cohort (n=1,144). What's more performance was validated in the validation cohort (n=490). Clinical-pathological nomogram were assessed by concordance index, time-dependent receiver operating characteristic, calibration curve and decision curve analysis.

Results

The patients can divide into two groups with cut-off value of 69.78 for the tumor-stroma ratio. It is noteworthy that the survival difference was noticeable (P<0.001). A clinical-pathological nomogram was constructed by combining clinical and pathological characteristics to predict the overall survival. In comparison with TNM stage, the concordance index and time-dependent receiver operating characteristic of the clinical-pathological nomogram showed better predictive value (P<0.001). High quality of calibration plots in overall survival was noticed. As demonstrated by the decision curve analysis, the nomogram has better value than the TNM stage.

Conclusions

As evidently revealed by the research findings, tumor-stroma ratio is an independent prognostic factor in patients with esophageal squamous cell carcinoma. The clinical-pathological nomogram has an incremental value compared TNM stage in predicting overall survival.

Predicting the risk of a clinical event using longitudinal data: the generalized landmark analysis

BACKGROUND

In the development of prediction models for a clinical event, it is common to use the static prediction modeling (SPM), a regression model that relates baseline predictors to the time to event. In many situations, the data used in training and validation are from longitudinal studies, where predictor variables are time-varying and measured at clinical visits. But these data are not used in SPM. The landmark analysis (LA), previously proposed for dynamic prediction with longitudinal data, has interpretational difficulty when the baseline is not a risk-changing clinical milestone, as is often the case in observational studies of chronic disease without intervention.

METHODS

This paper studies the generalized landmark analysis (GLA), a statistical framework to develop prediction models for longitudinal data. The GLA includes the LA as a special case, and generalizes it to situations where the baseline is not a risk-changing clinical milestone with a more useful interpretation. Unlike the LA, the landmark variable does not have to be time since baseline in the GLA, but can be any time-varying prognostic variable. The GLA can also be viewed as a longitudinal generalization of localized prediction, which has been studied in the context of low-dimensional cross-sectional data. We studied the GLA using data from the Chronic Renal Insufficiency Cohort (CRIC) Study and the Wisconsin Allograft Replacement Database (WisARD) and compared the prediction performance of SPM and GLA.

RESULTS

In various validation populations from longitudinal data, the GLA generally had similarly or better predictive performance than SPM, with notable improvement being seen when the validation population deviated from the baseline population. The GLA also demonstrated similar or better predictive performance than LA, due to its more general model specification.

CONCLUSIONS

GLA is a generalization of the LA such that the landmark variable does not have to be the time since baseline. It has better interpretation when the baseline is not a risk-changing clinical milestone. The GLA is more adaptive to the validation population than SPM and is more flexible than LA, which may help produce more accurate prediction.

Accommodating population differences when validating risk prediction models

Validation of risk prediction models in independent data provides a more rigorous assessment of model performance than internal assessment, for example, done by cross-validation in the data used for model development. However, several differences between the populations that gave rise to the training and the validation data can lead to seemingly poor performance of a risk model. In this paper we formalize the notions of "similarity" or "relatedness" of the training and validation data, and define reproducibility and transportability. We address the impact of different distributions of model predictors and differences in verifying the disease status or outcome on measures of calibration, accuracy and discrimination of a model. When individual level information from both the training and validation data sets is available, we propose and study weighted versions of the validation metrics that adjust for differences in the risk factor distributions and in outcome verification between the training and validation data to provide a more comprehensive assessment of model performance. We provide conditions on the risk model and the populations that gave rise to the training and validation data that ensure a model's reproducibility or transportability, and show how to check these conditions using weighted and unweighted performance measures. We illustrate the method by developing and validating a model that predicts the risk of developing prostate cancer using data from two large prostate cancer screening trials.

An easy-to-use nomogram predicting overall survival of adult acute lymphoblastic leukemia

Adult acute lymphoblastic leukemia (ALL) is heterogeneous both biologically and clinically. The outcomes of ALL have been improved with the application of children-like regimens and novel agents including immune therapy in young adults. The refractory to therapy and relapse of ALL have occurred in most adult cases. Factors affecting the prognosis of ALL include age and white blood cell (WBC) count at diagnosis. The clinical implications of genetic biomarkers, including chromosome translocation and gene mutation, have been explored in ALL. The interactions of these factors on the prediction of prognosis have not been evaluated in adult ALL. A prognostic model based on clinical and genetic abnormalities is necessary for clinical practice in the management of adult ALL. The newly diagnosed adult ALL patients were divided into the training and the validation cohort at 7:3 ratio. Factors associated with overall survival (OS) were assessed by univariate/multivariate Cox regression analyses and a signature score was assigned to each independent factor. A nomogram based on the signature score was developed and validated. The receiver operating characteristic (ROC) curve, calibration curve, and decision curve analysis (DCA) were used to assess the performance of the nomogram model. This study included a total of 229 newly diagnosed ALL patients. Five independent variables including age, WBC, bone marrow (BM) blasts, MLL rearrangement, and ICT gene mutations (carried any positive mutation of IKZF1, CREBBP and TP53) were identified as independent adverse factors for OS evaluated by the univariate, Kaplan-Meier survival and multivariate Cox regression analyses. A prognostic nomogram was built based on these factors. The areas under the ROC curve and calibration curve showed good accuracy between the predicted and observed values. The DCA curve showed that the performance of our model was superior to current risk factors. A nomogram was developed and validated based on the clinical and laboratory factors in newly diagnosed ALL patients. This model is effective to predict the overall survival of adult ALL. It is a simple and easy-to-use model that could efficiently predict the prognosis of adult ALL and is useful for decision making of treatment.

A necroptosis-related prognostic model for predicting prognosis, immune landscape, and drug sensitivity in hepatocellular carcinoma based on single-cell sequencing analysis and weighted co-expression network

Background: Hepatocellular carcinoma (HCC) is a highly lethal cancer and is the second leading cause of cancer-related deaths worldwide. Unlike apoptosis, necroptosis (NCPS) triggers an immune response by releasing damage-related molecular factors. However, the clinical prognostic features of necroptosis-associated genes in HCC are still not fully explored.

Methods: We analyzed the single-cell datasets GSE125449 and GSE151530 from the GEO database and performed weighted co-expression network analysis on the TCGA data to identify the necroptosis genes. A prognostic model was built using COX and Lasso regression. In addition, we performed an analysis of survival, immunity microenvironment, and mutation. Furthermore, the hub genes and pathways associated with HCC were localized within the single-cell atlas.

Results: Patients with HCC in the TCGA and ICGC cohorts were classified using a necroptosis-related model with significant differences in survival times between high- and low-NCPS groups (p &lt; 0.05). High-NCPS patients expressed more immune checkpoint-related genes, suggesting immunotherapy and some chemotherapies might prove beneficial to them. In addition, a single-cell sequencing approach was conducted to investigate the expression of hub genes and associated signaling pathways in different cell types.

Conclusion: Through the analysis of single-cell and bulk multi-omics sequencing data, we constructed a prognostic model related to necroptosis and explored the relationship between high- and low-NCPS groups and immune cell infiltration in HCC. This provides a new reference for further understanding the role of necroptosis in HCC.

Identification of the KCNQ1OT1/ miR-378a-3p/ RBMS1 Axis as a Novel Prognostic Biomarker Associated With Immune Cell Infiltration in Gastric Cancer

Background: Gastric cancer (GC) is the second leading cause of cancer-related mortality and the fifth most common cancer worldwide. However, the underlying mechanisms of competitive endogenous RNAs (ceRNAs) in GC are unclear. This study aimed to construct a ceRNA regulation network in correlation with prognosis and explore a prognostic model associated with GC.

Methods: In this study, 1,040 cases of GC were obtained from TCGA and GEO datasets. To identify potential prognostic signature associated with GC, Cox regression analysis and the least absolute shrinkage and selection operator (LASSO) regression were employed. The prognostic value of the signature was validated in the GEO84437 training set, GEO84437 test set, GEO15459 set, and TCGA-STAD. Based on the public databases, TargetScan and starBase, an mRNA-miRNA-lncRNA regulatory network was constructed, and hub genes were identified using the CytoHubba plugin. Furthermore, the clinical outcomes, immune cell infiltration, genetic variants, methylation, and somatic copy number alteration (sCNA) associated with the ceRNA network were derived using bioinformatics methods.

Results: A total of 234 prognostic genes were identified. GO and GSEA revealed that the biological pathways and modules related to immune response and fibroblasts were considerably enriched in GC. A nomogram was generated to provide accurate prognostic outcomes and individualized risk estimates, which were validated in the training, test dataset, and two independent validation datasets. Thereafter, an mRNA-miRNA-lncRNA regulatory network containing 4 mRNAs, 22 miRNAs, 201 lncRNAs was constructed. The KCNQ1OT1/hsa-miR-378a-3p/RBMS1 ceRNA network associated with the prognosis was obtained by hub gene analysis and correlation analysis. Importantly, we found that the KCNQ1OT1/miR-378a-3p/RBMS1 axis may play a vital role in the diagnosis and prognosis of GC patients based on Cox regression analyses. Furthermore, our findings demonstrated that mutations and sCNA of the KCNQ1OT1/miR-378a-3p/RBMS1 axis were associated with increased immune infiltration, while the abnormal upregulation of the axis was primarily a result of hypomethylation.

Conclusion: Our findings suggest that the KCNQ1OT1/miR-378a-3p/RBMS1 axis may be a potential prognostic biomarker and therapeutic target for GC. Moreover, such findings provide insights into the molecular mechanisms of GC pathogenesis.

A Whole Exon Screening-Based Score Model Predicts Prognosis and Immune Checkpoint Inhibitor Therapy Effects in Low-Grade Glioma

Objective

This study aims to identify prognostic factors for low-grade glioma (LGG) via different machine learning methods in the whole genome and to predict patient prognoses based on these factors. We verified the results through in vitro experiments to further screen new potential therapeutic targets.

Method

A total of 940 glioma patients from The Cancer Genome Atlas (TCGA) and The Chinese Glioma Genome Atlas (CGGA) were included in this study. Two different feature extraction algorithms – LASSO and Random Forest (RF) – were used to jointly screen genes significantly related to the prognosis of patients. The risk signature was constructed based on these screening genes, and the K-M curve and ROC curve evaluated it. Furthermore, we discussed the differences between the high- and low-risk groups distinguished by the signature in detail, including differential gene expression (DEG), single-nucleotide polymorphism (SNP), copy number variation (CNV), immune infiltration, and immune checkpoint. Finally, we identified the function of a novel molecule, METTL7B, which was highly correlated with PD-L1 expression on tumor cell, as verified by in vitro experiments.

Results

We constructed an accurate prediction model based on seven genes (AUC at 1, 3, 5 years= 0.91, 0.85, 0.74). Further analysis showed that extracellular matrix remodeling and cytokine and chemokine release were activated in the high-risk group. The proportion of multiple immune cell infiltration was upregulated, especially macrophages, accompanied by the high expression of most immune checkpoints. According to the in vitro experiment, we preliminarily speculate that METTL7B affects the stability of PD-L1 mRNA by participating in the modification of m6A.

Conclusion

The seven gene signatures we constructed can predict the prognosis of patients and identify the potential benefits of immune checkpoint inhibitors (ICI) therapy for LGG. More importantly, METTL7B, one of the risk genes, is a crucial molecule that regulates PD-L1 and could be used as a new potential therapeutic target.

Modelling time-varying covariates effect on survival via functional data analysis: application to the MRC BO06 trial in osteosarcoma

Time-varying covariates are of great interest in clinical research since they represent dynamic patterns which reflect disease progression. In cancer studies biomarkers values change as functions of time and chemotherapy treatment is modified by delaying a course or reducing the dose intensity, according to patient’s toxicity levels. In this work, a Functional covariate Cox Model (FunCM) to study the association between time-varying processes and a time-to-event outcome is proposed. FunCM first exploits functional data analysis techniques to represent time-varying processes in terms of functional data. Then, information related to the evolution of the functions over time is incorporated into functional regression models for survival data through functional principal component analysis. FunCM is compared to a standard time-varying covariate Cox model, commonly used despite its limiting assumptions that covariate values are constant in time and measured without errors. Data from MRC BO06/EORTC 80931 randomised controlled trial for treatment of osteosarcoma are analysed. Time-varying covariates related to alkaline phosphatase levels, white blood cell counts and chemotherapy dose during treatment are investigated. The proposed method allows to detect differences between patients with different biomarkers and treatment evolutions, and to include this information in the survival model. These aspects are seldom addressed in the literature and could provide new insights into the clinical research.

Prognostic accuracy of inflammatory markers in predicting risk of ICU admission for COVID-19: application of time-dependent receiver operating characteristic curves

Objective

Intensive care unit (ICU) admission occurs at different times during hospitalization among patients with COVID-19. We aimed to evaluate the time-dependent receive operating characteristic (ROC) curve and area under the ROC curve, AUC(t), and accuracy of baseline levels of inflammatory markers C-reactive protein (CRP) and neutrophil-to-lymphocyte ratio (NLR) in predicting time to an ICU admission event in patients with severe COVID-19 infection.

Methods

In this observational study, we evaluated 724 patients with confirmed severe COVID-19 referred to Ayatollah Rohani Hospital, affiliated with Babol University of Medical Sciences, Iran.

Results

The AUC(t) of CRP and NLR reached 0.741 (95% confidence interval [CI]: 0.661–0.820) and 0.690 (95% CI: 0.607–0.772), respectively, in the first 3 days after hospital admission. The optimal cutoff values of CRP and NLR for stratification of ICU admission outcomes in patients with severe COVID-19 were 78 mg/L and 5.13, respectively. The risk of ICU admission was significantly greater for patients with these cutoff values (CRP hazard ratio = 2.98; 95% CI: 1.58–5.62; NLR hazard ratio = 2.90; 95% CI: 1.45–5.77).

Conclusions

Using time-dependent ROC curves, CRP and NLR values at hospital admission were important predictors of ICU admission. This approach is more efficient than using standard ROC curves.

Time-dependent ROC curve estimation for interval-censored data

The receiver-operating characteristic (ROC) curve is the most popular graphical method for evaluating the classification accuracy of a diagnostic marker. In time-to-event studies, the subject's event status is time-dependent, and hence, time-dependent extensions of ROC curve have been proposed. However, in practice, the calculation of this curve is not straightforward due to the presence of censoring that may be of different types. Existing methods focus on the more standard and simple case of right-censoring and neglect the general case of mixed interval-censored data that may involve left-, right-, and interval-censored observations. In this context, we propose and study a new time-dependent ROC curve estimator. We also consider some summary measures (area under the ROC curve and Youden index) traditionally associated with ROC as well as the Youden-based cutoff estimation method. The proposed method uses available data very efficiently. To this end, the unknown status (positive or negative) of censored subjects are estimated from the data via the estimation of the conditional survival function given the marker. For that, we investigate both model-based and nonparametric approaches. We also provide variance estimates and confidence intervals using Bootstrap. A simulation study is conducted to investigate the finite sample behavior of the proposed methods and to compare their performance with a competitor. Globally, we observed better finite sample performances for the proposed estimators. Finally, we illustrate the methods using two data sets one from a hypobaric decompression sickness study and the other from an oral health study. The proposed methods are implemented in the R package cenROC.

Increased prognostic value of clinical–reproductive model in Chinese female patients with esophageal squamous cell carcinoma

BACKGROUND

In China, it has been well recognized that some female patients with esophageal squamous cell carcinoma (ESCC) have different overall survival (OS) time, even with the same tumor-node-metastasis (TNM) stage, challenging the prognostic value of the TNM system alone. An effective predictive model is needed to accurately evaluate the prognosis of female ESCC patients.

AIM

To construct a novel prognostic model with clinical and reproductive data for Chinese female patients with ESCC, and to assess the incremental prognostic value of the full model compared with the clinical model and TNM stage.

METHODS

A new prognostic nomogram incorporating clinical and reproductive features was constructed based on univariatie and Cox proportional hazards survival analysis from a training cohort (n = 175). The results were recognized using the internal (n = 111) and independent external (n = 85) validation cohorts. The capability of the clinical–reproductive model was evaluated by Harrell’s concordance index (C-index), Kaplan–Meier curve, time-dependent receiver operating characteristic (ROC), calibration curve and decision curve analysis. The correlations between estrogen response and immune-related pathways and some gene markers of immune cells were analyzed using the TIMER 2.0 database.

RESULTS

A clinical–reproductive model including incidence area, age, tumor differentiation, lymph node metastasis (N) stage, estrogen receptor alpha (ESR1) and beta (ESR2) expression, menopausal age, and pregnancy number was constructed to predict OS in female ESCC patients. Compared to the clinical model and TNM stage, the time-dependent ROC and C-index of the clinical–reproductive model showed a good discriminative ability for predicting 1-, 3-, and 5-years OS in the primary training, internal and external validation sets. Based on the optimal cut-off value of total prognostic scores, patients were classified into high- and low-risk groups with significantly different OS. The estrogen response was significantly associated with p53 and apoptosis pathways in esophageal cancer.

CONCLUSION

The clinical–reproductive prognostic nomogram has an incremental prognostic value compared with the clinical model and TNM stage in predicting OS in Chinese female ESCC patients.

Deep learning for the dynamic prediction of multivariate longitudinal and survival data

The joint model for longitudinal and survival data improves time-to-event predictions by including longitudinal outcome variables in addition to baseline covariates. However, in practice, joint models may be limited by parametric assumptions in both the longitudinal and survival submodels. In addition, computational difficulties arise when considering multiple longitudinal outcomes due to the large number of random effects to be integrated out in the full likelihood. In this article, we discuss several recent machine learning methods for incorporating multivariate longitudinal data for time-to-event prediction. The presented methods use functional data analysis or convolutional neural networks to model the longitudinal data, both of which scale well to multiple longitudinal outcomes. In addition, we propose a novel architecture based on the transformer neural network, named TransformerJM, which jointly models longitudinal and time-to-event data. The prognostic abilities of each model are assessed and compared through both simulation and real data analysis on Alzheimer's disease datasets. Specifically, the models were evaluated based on their ability to dynamically update predictions as new longitudinal data becomes available. We showed that TransformerJM improves upon the predictive performance of existing methods across different scenarios.

Clonal and subclonal TP53 molecular impairment is associated with prognosis and progression in multiple myeloma

Aberrations on TP53, either as deletions of chromosome 17p (del17p) or mutations, are associated with poor outcome in multiple myeloma (MM), but conventional detection methods currently in use underestimate their incidence, hindering an optimal risk assessment and prognostication of MM patients. We have investigated the altered status of TP53 gene by SNPs array and sequencing techniques in a homogenous cohort of 143 newly diagnosed MM patients, evaluated both at diagnosis and at first relapse: single-hit on TP53 gene, either deletion or mutation, detected both at clonal and sub-clonal level, had a minor effect on outcomes. Conversely, the coexistence of both TP53 deletion and mutation, which defined the so-called double-hit patients, was associated with the worst clinical outcome (PFS: HR 3.34 [95% CI: 1.37–8.12] p = 0.008; OS: HR 3.47 [95% CI: 1.18–10.24] p = 0.02). Moreover, the analysis of longitudinal samples pointed out that TP53 allelic status might increase during the disease course. Notably, the acquisition of TP53 alterations at relapse dramatically worsened the clinical course of patients. Overall, our analyses showed these techniques to be highly sensitive to identify TP53 aberrations at sub-clonal level, emphasizing the poor prognosis associated with double-hit MM patients.

Bayesian inference and dynamic prediction of multivariate joint model with functional data: An application to Alzheimer's disease

Alzheimer's disease (AD) is a severe neurodegenerative disorder impairing multiple domains, for example, cognition and behavior. Assessing the risk of AD progression and initiating timely interventions at early stages are critical to improve the quality of life for AD patients. Due to the heterogeneous nature and complex mechanisms of AD, one single longitudinal outcome is insufficient to assess AD severity and disease progression. Therefore, AD studies collect multiple longitudinal outcomes, including cognitive and behavioral measurements, as well as structural brain images such as magnetic resonance imaging (MRI). How to utilize the multivariate longitudinal outcomes and MRI data to make efficient statistical inference and prediction is an open question. In this article, we propose a multivariate joint model with functional data (MJM-FD) framework that relates multiple correlated longitudinal outcomes to a survival outcome, and use the scalar-on-function regression method to include voxel-based whole-brain MRI data as functional predictors in both longitudinal and survival models. We adopt a Bayesian paradigm to make statistical inference and develop a dynamic prediction framework to predict an individual's future longitudinal outcomes and risk of a survival event. We validate the MJM-FD framework through extensive simulation studies and apply it to the motivating Alzheimer's Disease Neuroimaging Initiative (ADNI) study.

Future Prediction of COVID-19 Vaccine Trends Using a Voting Classifier

Machine learning (ML)-based prediction is considered an important technique for improving decision making during the planning process. Modern ML models are used for prediction, prioritization, and decision making. Multiple ML algorithms are used to improve decision-making at different aspects after forecasting. This study focuses on the future prediction of the effectiveness of the COVID-19 vaccine effectiveness which has been presented as a light in the dark. People bear several reservations, including concerns about the efficacy of the COVID-19 vaccine. Under these presumptions, the COVID-19 vaccine would either lower the risk of developing the malady after injection, or the vaccine would impose side effects, affecting their existing health condition. In this regard, people have publicly expressed their concerns regarding the vaccine. This study intends to estimate what perception the masses will establish about the role of the COVID-19 vaccine in the future. Specifically, this study exhibits people’s predilection toward the COVID-19 vaccine and its results based on the reviews. Five models, e.g., random forest (RF), a support vector machine (SVM), decision tree (DT), K-nearest neighbor (KNN), and an artificial neural network (ANN), were used for forecasting the overall predilection toward the COVID-19 vaccine. A voting classifier was used at the end of this study to determine the accuracy of all the classifiers. The results prove that the SVM produces the best forecasting results and that artificial neural networks (ANNs) produce the worst prediction toward the individual aptitude to be vaccinated by the COVID-19 vaccine. When using the voting classifier, the proposed system provided an overall accuracy of 89.9% for the random dataset and 45.7% for the date-wise dataset. Thus, the results show that the studied prediction technique is a promising and encouraging procedure for studying the future trends of the COVID-19 vaccine.

Upregulation of the APOBEC3 Family Is Associated with a Poor Prognosis and Influences Treatment Response to Raf Inhibitors in Low Grade Glioma

Apolipoprotein B mRNA-editing enzyme catalytic polypeptide-like 3 (APOBEC3) has been identified as a group of enzymes that catalyze cytosine deamination in single-stranded (ss) DNA to form uracil, causing somatic mutations in some cancers. We analyzed the APOBEC3 family in 33 TCGA cancer types and the results indicated that APOBEC3s are upregulated in multiple cancers and strongly correlate with prognosis, particularly in low grade glioma (LGG). Then we constructed a prognostic model based on family expression in LGG where the APOBEC3 family signature is an accurate predictive model (AUC of 0.85). Gene mutation, copy number variation (CNV), and a differential gene expression (DEG) analysis were performed in different risk groups, and the weighted gene co-expression network analysis (WGCNA) was employed to clarify the role of various members in LGG; CIBERSORT algorithm was deployed to evaluate the landscape of LGG immune infiltration. We found that upregulation of the APOBEC3 family expression can strengthen Ras/MAPK signaling pathway, promote tumor progression, and ultimately reduce the treatment benefits of Raf inhibitors. Moreover, the APOBEC3 family was shown to enhance the immune response mediated by myeloid cells and interferon gamma, as well as PD-L1 and PD-L2 expression, implying that they have immunotherapy potential. Therefore, the APOBEC3 signature enables an efficient assessment of LGG patient survival outcomes and expansion of clinical benefits by selecting appropriate individualized treatment strategies.

Backward joint model and dynamic prediction of survival with multivariate longitudinal data

An important approach to dynamic prediction of time-to-event outcomes using longitudinal data is based on modeling the joint distribution of longitudinal and time-to-event data. The widely used joint model for this purpose is the shared random effect model. Presumably, adding more longitudinal predictors improves the predictive accuracy. However, the shared random effect model can be computationally difficult or prohibitive when a large number of longitudinal variables are used. In this paper, we study an alternative way of modeling the joint distribution of longitudinal and time-to-event data. Under this formulation, the log-likelihood involves no more than one-dimensional integration, regardless of the number of longitudinal variables in the model. Therefore, this model is particularly suitable in dynamic prediction problems with large number of longitudinal predictors. The model fitting can be implemented with tractable and stable computation by using a combination of pseudo maximum likelihood estimation, Expectation-Maximization algorithm, and convex optimization. We evaluate the proposed methodology and its predictive accuracy with varying number of longitudinal variables using simulations and data from a primary biliary cirrhosis study.

Developing and validating an individualized breast cancer risk prediction model for women attending breast cancer screening

BACKGROUND

Several studies have proposed personalized strategies based on women's individual breast cancer risk to improve the effectiveness of breast cancer screening. We designed and internally validated an individualized risk prediction model for women eligible for mammography screening.

METHODS

Retrospective cohort study of 121,969 women aged 50 to 69 years, screened at the long-standing population-based screening program in Spain between 1995 and 2015 and followed up until 2017. We used partly conditional Cox proportional hazards regression to estimate the adjusted hazard ratios (aHR) and individual risks for age, family history of breast cancer, previous benign breast disease, and previous mammographic features. We internally validated our model with the expected-to-observed ratio and the area under the receiver operating characteristic curve.

RESULTS

During a mean follow-up of 7.5 years, 2,058 women were diagnosed with breast cancer. All three risk factors were strongly associated with breast cancer risk, with the highest risk being found among women with family history of breast cancer (aHR: 1.67), a proliferative benign breast disease (aHR: 3.02) and previous calcifications (aHR: 2.52). The model was well calibrated overall (expected-to-observed ratio ranging from 0.99 at 2 years to 1.02 at 20 years) but slightly overestimated the risk in women with proliferative benign breast disease. The area under the receiver operating characteristic curve ranged from 58.7% to 64.7%, depending of the time horizon selected.

CONCLUSIONS

We developed a risk prediction model to estimate the short- and long-term risk of breast cancer in women eligible for mammography screening using information routinely reported at screening participation. The model could help to guiding individualized screening strategies aimed at improving the risk-benefit balance of mammography screening programs.

Assessing risk model calibration with missing covariates

When validating a risk model in an independent cohort, some predictors may be missing for some subjects. Missingness can be unplanned or by design, as in case-cohort or nested case-control studies, in which some covariates are measured only in subsampled subjects. Weighting methods and imputation are used to handle missing data. We propose methods to increase the efficiency of weighting to assess calibration of a risk model (i.e. bias in model predictions), which is quantified by the ratio of the number of observed events, $\mathcal{O}$, to expected events, $\mathcal{E}$, computed from the model. We adjust known inverse probability weights by incorporating auxiliary information available for all cohort members. We use survey calibration that requires the weighted sum of the auxiliary statistics in the complete data subset to equal their sum in the full cohort. We show that a pseudo-risk estimate that approximates the actual risk value but uses only variables available for the entire cohort is an excellent auxiliary statistic to estimate $\mathcal{E}$. We derive analytic variance formulas for $\mathcal{O}/\mathcal{E}$ with adjusted weights. In simulations, weight adjustment with pseudo-risk was much more efficient than inverse probability weighting and yielded consistent estimates even when the pseudo-risk was a poor approximation. Multiple imputation was often efficient but yielded biased estimates when the imputation model was misspecified. Using these methods, we assessed calibration of an absolute risk model for second primary thyroid cancer in an independent cohort.

Smoothed time-dependent receiver operating characteristic curve for right censored survival data

The prediction reliability is of primary concern in many clinical studies when the objective is to develop new predictive models or improve existing risk scores. In fact, before using a model in any clinical decision making, it is very important to check its ability to discriminate between subjects who are at risk of, for example, developing certain disease in a near future from those who will not. To that end, the time-dependent receiver operating characteristic (ROC) curve is the most commonly used method in practice. Several approaches have been proposed in the literature to estimate the ROC nonparametrically in the context of survival data. But, except one recent approach, all the existing methods provide a nonsmooth ROC estimator whereas, by definition, the ROC curve is smooth. In this article we propose and study a new nonparametric smooth ROC estimator based on a weighted kernel smoother. More precisely, our approach relies on a well-known kernel method used to estimate cumulative distribution functions of random variables with bounded supports. We derived some asymptotic properties for the proposed estimator. As bandwidth is the main parameter to be set, we present and study different methods to appropriately select one. A simulation study is conducted, under different scenarios, to prove the consistency of the proposed method and to compare its finite sample performance with a competitor. The results show that the proposed method performs better and appear to be quite robust to bandwidth choice. As for inference purposes, our results also reveal the good performances of a proposed nonparametric bootstrap procedure. Furthermore, we illustrate the method using a real data example.

Dynamic prediction of time to a clinical event with sparse and irregularly measured longitudinal biomarkers

In clinical research and practice, landmark models are commonly used to predict the risk of an adverse future event, using patients' longitudinal biomarker data as predictors. However, these data are often observable only at intermittent visits, making their measurement times irregularly spaced and unsynchronized across different subjects. This poses challenges to conducting dynamic prediction at any post-baseline time. A simple solution is the last-value-carry-forward method, but this may result in bias for the risk model estimation and prediction. Another option is to jointly model the longitudinal and survival processes with a shared random effects model. However, when dealing with multiple biomarkers, this approach often results in high-dimensional integrals without a closed-form solution, and thus the computational burden limits its software development and practical use. In this article, we propose to process the longitudinal data by functional principal component analysis techniques, and then use the processed information as predictors in a class of flexible linear transformation models to predict the distribution of residual time-to-event occurrence. The measurement schemes for multiple biomarkers are allowed to be different within subject and across subjects. Dynamic prediction can be performed in a real-time fashion. The advantages of our proposed method are demonstrated by simulation studies. We apply our approach to the African American Study of Kidney Disease and Hypertension, predicting patients' risk of kidney failure or death by using four important longitudinal biomarkers for renal functions.

Assessing cure status prediction from survival data using receiver operating characteristic curves

Survival analysis relies on the hypothesis that, if the follow-up is long enough, the event of interest will eventually be observed for all observations. This assumption, however, is often not realistic. The survival data then contain a cure fraction. A common approach to modelling and analysing this type of data consists in using cure models. Two types of information can therefore be obtained: the survival at a given time and the cure status, both possibly modelled as a function of the covariates. The cure status is often of interest to medical practitioners, and one is usually interested in predicting it based on markers. Receiver operating characteristic, Roc, curves are one way to evaluate the predicted performance; however, the classical Roc curve method is not appropriate since the cure status is partially unobserved due to the presence of censoring in survival data. We propose a Roc curve estimator that aims to evaluate the cured/noncured status classification performance from cure survival data. This estimator, which handles the presence of censoring, decomposes sensitivity and specificity by means of the definition of conditional probability, and estimates these two quantities by means of weighted empirical distribution functions. The mixture cure model is used to calculate the weights. Based on simulations, we demonstrate good performance of the proposed method, and compare it with the classical Roc curve nonparametric estimator that would be obtained if the cure status was fully observed. We also compare our proposed method with the Roc curves of Heagerty et al. (2000) for classical survival analysis. Finally, we illustrate the methodology on a breast cancer dataset.

Two-stage receiver operating-characteristic curve estimator for cohort studies

The receiver operating-characteristic (ROC) curve is a graphical statistical tool routinely used for studying the classification accuracy in both, diagnostic and prognosis problems. Given the different nature of these situations, ROC curve estimation has been separately considered for binary (diagnostic) and time-to-event (prognosis) outcomes, even for data coming from the same study design. In this work, the authors propose a two-stage ROC curve estimator which allows to link both contexts through a general prediction model (first-stage) and the empirical cumulative estimator of the distribution function (second-stage) of the considered test (marker) on the total population. The so-called two-stage Mixed-Subject (sMS) approach proves its behavior on both, large-samples (theoretically) and finite-samples (via Monte Carlo simulations). Besides, a useful asymptotic distribution for the concomitant area under the curve is also computed. Results show the ability of the proposed estimator to fit non-standard situations by considering flexible predictive models. Two real-world examples, one with binary and one with time-dependent outcomes, help us to a better understanding of the proposed methodology on usual practical circumstances. The R code used for the practical implementation of the proposed methodology and its documentation is provided as supplementary material.

Radiomics-based prediction of survival in patients with head and neck squamous cell carcinoma based on pre- and post-treatment 18F-PET/CT

BACKGROUND

18-fluorodeoxyglucose positron emission tomography/computed tomography (18F-PET/CT) has been widely applied for the imaging of head and neck squamous cell carcinoma (HNSCC). This study examined whether pre- and post-treatment 18F-PET/CT features can help predict the survival of HNSCC patients.

RESULTS

Three radiomics features were identified as prognostic factors. Radiomics score calculated from these features significantly predicted overall survival (OS) and disease-free disease (DFS). The clinicopathological characteristics combined with pre- or post-treatment nomograms showed better ROC curves and decision curves than the nomogram based only on clinicopathological characteristics.

CONCLUSIONS

Combining clinicopathological characteristics with radiomics features of pre-treatment PET/CT or post-treatment PET/CT assessment of primary tumor sites as positive or negative may substantially improve prediction of OS and DFS of HNSCC patients.

METHODS

171 patients who received pre-treatment 18F-PET/CT scans and 154 patients who received post-treatment 18F-PET/CT scans with HNSCC in the Cancer Imaging Achieve (TCIA) were included. Nomograms that combined clinicopathological features with either pre-treatment PET/CT radiomics features or post-treatment assessment of primary tumor sites were constructed using data from 154 HNSCC patients. Receiver operating characteristic (ROC) curves and decision curves were used to compare the predictions of these models with those of a model incorporating only clinicopathological features.

Validation of discrete time-to-event prediction models in the presence of competing risks

Clinical prediction models play a key role in risk stratification, therapy assignment and many other fields of medical decision making. Before they can enter clinical practice, their usefulness has to be demonstrated using systematic validation. Methods to assess their predictive performance have been proposed for continuous, binary, and time-to-event outcomes, but the literature on validation methods for discrete time-to-event models with competing risks is sparse. The present paper tries to fill this gap and proposes new methodology to quantify discrimination, calibration, and prediction error (PE) for discrete time-to-event outcomes in the presence of competing risks. In our case study, the goal was to predict the risk of ventilator-associated pneumonia (VAP) attributed to Pseudomonas aeruginosa in intensive care units (ICUs). Competing events are extubation, death, and VAP due to other bacteria. The aim of this application is to validate complex prediction models developed in previous work on more recently available validation data.

The area between ROC curves, a non-parametric method to evaluate a biomarker for patient treatment selection

Treatment selection markers are generally sought for when the benefit of an innovative treatment in comparison with a reference treatment is considered, and this benefit is suspected to vary according to the characteristics of the patients. Classically, such quantitative markers are detected through testing a marker-by-treatment interaction in a parametric regression model. Most alternative methods rely on modeling the risk of event occurrence in each treatment arm or the benefit of the innovative treatment over the marker values, but with assumptions that may be difficult to verify. Herein, a simple non-parametric approach is proposed to detect and assess the general capacity of a quantitative marker for treatment selection when no overall difference in efficacy could be demonstrated between two treatments in a clinical trial. This graphical method relies on the area between treatment-arm-specific receiver operating characteristic curves (ABC), which reflects the treatment selection capacity of the marker. A simulation study assessed the inference properties of the ABC estimator and compared them with other parametric and non-parametric indicators. The simulations showed that the estimate of the ABC had low bias, power comparable to parametric indicators, and that its confidence interval had a good coverage probability (better than the other non-parametric indicator in some cases). Thus, the ABC is a good alternative to parametric indicators. The ABC method was applied to data of the PETACC-8 trial that investigated FOLFOX4 versus FOLFOX4 + cetuximab in stage III colon adenocarcinoma. It enabled the detection of a treatment selection marker: the DDR2 gene.

On the validity of time-dependent AUC estimation in the presence of cure fraction

During the last decades, several approaches have been proposed to estimate the time-dependent area under the receiver operating characteristic curve (AUC) of risk tools derived from survival data. The validity of these estimators relies on some regularity assumptions among which a survival function being proper. In practice, this assumption is not always satisfied because a fraction of the population may not be susceptible to experience the event of interest even for long follow-up. Studying the sensitivity of the proposed estimators to the violation of this assumption is of substantial interest. In this paper, we investigate the performance of a nonparametric simple estimator, developed for classical survival data, in the case when the population exhibits a cure fraction. Motivated from the current practice of deriving risk tools in oncology and cardiovascular disease prevention, we also assess the loss, in terms of predictive performance, when deriving risk tools from survival models that do not acknowledge the presence of cure. The simulation results show that the investigated method is valid even under the presence of cure. They also show that risk tools derived from survival models that ignore the presence of cure have smaller AUC compared to those derived from survival models that acknowledge the presence of cure. This was also attested with a real data analysis from a breast cancer study.

Landmark Linear Transformation Model for Dynamic Prediction with Application to a Longitudinal Cohort Study of Chronic Disease

Dynamic prediction of the risk of a clinical event using longitudinally measured biomarkers or other prognostic information is important in clinical practice. We propose a new class of landmark survival models. The model takes the form of a linear transformation model, but allows all the model parameters to vary with the landmark time. This model includes many published landmark prediction models as special cases. We propose a unified local linear estimation framework to estimate time-varying model parameters. Simulation studies are conducted to evaluate the finite sample performance of the proposed method. We apply the methodology to a dataset from the African American Study of Kidney Disease and Hypertension and predict individual patient's risk of an adverse clinical event.

Are tumor size changes predictive of survival for checkpoint blockade based immunotherapy in metastatic melanoma?

BACKGROUND

In oncology clinical development, objective response rate, disease control rate and early tumor size changes are commonly used as efficacy metrics for early decision-making. However, for immunotherapy trials, it is unclear whether these early efficacy metrics are still predictive of long-term clinical benefit such as overall survival. The goal of this paper is to identify appropriate early efficacy metrics predictive of overall survival for immunotherapy trials.

METHODS

Based on several checkpoint blockade based immunotherapy studies in metastatic melanoma, we evaluated the predictive value of early tumor size changes and RECIST-based efficacy metrics at various time points on overall survival. The cut-off values for tumor size changes to predict survival were explored via tree based recursive partitioning and validated by external data. Sensitivity analyses were performed for the cut-offs.

RESULTS

The continuous tumor size change metric and RECIST-based trichotomized response metric at different landmark time points were found to be statistically significantly associated with overall survival. The predictive values were higher at Week 12 and 18 than those at Week 24. The percentage of tumor size changes appeared to have comparable or lower predictive values than the RECIST-based trichotomized metric, and a cut-off of approximately 10% tumor reduction appeared to be reasonable for predicting survival.

CONCLUSIONS

An approximate 10% tumor reduction may be a reasonable cut-off for early decision-making while the RECIST-based efficacy metric remains the primary tool. Early landmark analysis is especially useful for decision making when accrual is fast. Composite response rate (utilizing different weights for PR/CR and SD) may be worth further investigation.

TRIAL REGISTRATION

Clinical trials gov, NCT01295827 , Registered February 15, 2011; NCT01704287 , Registered October 11, 2012; NCT01866319 , Registered May 31, 2013.

Bayesian Functional Joint Models for Multivariate Longitudinal and Time-to-Event Data

A multivariate functional joint model framework is proposed which enables the repeatedly measured functional outcomes, scalar outcomes, and survival process to be modeled simultaneously while accounting for association among the multiple (functional and scalar) longitudinal and survival processes. This data structure is increasingly common across medical studies of neurodegenerative diseases and is exemplified by the motivating Alzheimer's Disease Neuroimaging Initiative (ADNI) study, in which serial brain imaging, clinical and neuropsychological assessments are collected to measure the progression of Alzheimer's disease (AD). The proposed functional joint model consists of a longitudinal function-on-scalar submodel, a regular longitudinal submodel, and a survival submodel which allows time-dependent functional and scalar covariates. A Bayesian approach is adopted for parameter estimation and a dynamic prediction framework is introduced for predicting the subjects' future health outcomes and risk of AD conversion. The proposed model is evaluated by a simulation study and is applied to the motivating ADNI study.

DYNAMIC PREDICTION FOR MULTIPLE REPEATED MEASURES AND EVENT TIME DATA: AN APPLICATION TO PARKINSON'S DISEASE

In many clinical trials studying neurodegenerative diseases such as Parkinson's disease (PD), multiple longitudinal outcomes are collected to fully explore the multidimensional impairment caused by this disease. If the outcomes deteriorate rapidly, patients may reach a level of functional disability sufficient to initiate levodopa therapy for ameliorating disease symptoms. An accurate prediction of the time to functional disability is helpful for clinicians to monitor patients' disease progression and make informative medical decisions. In this article, we first propose a joint model that consists of a semiparametric multilevel latent trait model (MLLTM) for the multiple longitudinal outcomes, and a survival model for event time. The two submodels are linked together by an underlying latent variable. We develop a Bayesian approach for parameter estimation and a dynamic prediction framework for predicting target patients' future outcome trajectories and risk of a survival event, based on their multivariate longitudinal measurements. Our proposed model is evaluated by simulation studies and is applied to the DATATOP study, a motivating clinical trial assessing the effect of deprenyl among patients with early PD.

Dynamic predictions in Bayesian functional joint models for longitudinal and time-to-event data: An application to Alzheimer's disease

In the study of Alzheimer's disease, researchers often collect repeated measurements of clinical variables, event history, and functional data. If the health measurements deteriorate rapidly, patients may reach a level of cognitive impairment and are diagnosed as having dementia. An accurate prediction of the time to dementia based on the information collected is helpful for physicians to monitor patients' disease progression and to make early informed medical decisions. In this article, we first propose a functional joint model to account for functional predictors in both longitudinal and survival submodels in the joint modeling framework. We then develop a Bayesian approach for parameter estimation and a dynamic prediction framework for predicting the subjects' future outcome trajectories and risk of dementia, based on their scalar and functional measurements. The proposed Bayesian functional joint model provides a flexible framework to incorporate many features both in joint modeling of longitudinal and survival data and in functional data analysis. Our proposed model is evaluated by a simulation study and is applied to the motivating Alzheimer's Disease Neuroimaging Initiative study.