Dynamic and concordance-assisted learning for risk stratification with application to Alzheimer's disease.

Dynamic prediction models capable of retaining accuracy by evolving over time could play a significant role for monitoring disease progression in clinical practice. In biomedical studies with long-term follow up, participants are often monitored through periodic clinical visits with repeat measurements until an occurrence of the event of interest (e.g. disease onset) or the study end. Acknowledging the dynamic nature of disease risk and clinical information contained in the longitudinal markers, we propose an innovative concordance-assisted learning algorithm to derive a real-time risk stratification score. The proposed approach bypasses the need to fit regression models, such as joint models of the longitudinal markers and time-to-event outcome, and hence enjoys the desirable property of model robustness. Simulation studies confirmed that the proposed method has satisfactory performance in dynamically monitoring the risk of developing disease and differentiating high-risk and low-risk population over time. We apply the proposed method to the Alzheimer's Disease Neuroimaging Initiative data and develop a dynamic risk score of Alzheimer's Disease for patients with mild cognitive impairment using multiple longitudinal markers and baseline prognostic factors.

Blood biomarkers in dynamic prediction of conversion to Alzheimer's disease: An application of joint modeling.

OBJECTIVES: To investigate the accuracy of longitudinal trajectories of blood biomarkers for predicting future onset of AD among MCI participants as well as to demonstrate dynamic prediction of the individual conversion risk applying joint modeling. METHODS: A total of 446 participants with MCI at baseline from the Alzheimer's Disease Neuroimaging Initiative database were included. We introduced joint modeling to analyze the effects of the longitudinal blood biomarkers on the conversion risk to AD, and further to build individual-specific prediction risk model. RESULTS: During the follow-up, 345 participants remained with MCI and 101 progressed to AD, and were categorized as non-progression and progression group, respectively. Longitudinally, the positive association of the concentration dynamics of plasma p-tau181 and NfL with the conversion risk to AD from MCI was also demonstrated, with Hazard Ratio (HR) = 5.83 and HR = 4.18, respectively. When incorporating plasma p-tau181 and NfL together to predict AD progression, we observed improved performance (AUC = 0.701, Brier Score = 0.119). Two participants were chosen to exemplify the individual-specific risk prediction at different follow-up time for comparative analysis. CONCLUSIONS: Plasma p-tau181 and NfL could serve as biomarkers for the prediction of AD onset, and the individualized prediction opens up the possibility to provide clinical information at a personal level.

A dynamic prediction model for preeclampsia using the sFlt-1/PLGF ratio combined with multiple factors.

OBJECTIVE: Preeclampsia (PE) is a pregnancy-related multi-organ disease and a significant cause of incidence rate and mortality of pregnant women and newborns worldwide. Delivery remains the only available treatment for PE. This study aims to establish a dynamic prediction model for PE. METHODS: A total of 737 patients who visited our hospital from January 2021 to June 2022 were identified according to the inclusion and exclusion criteria, forming the primary dataset. Additionally, 176 singleton pregnant women who visited our hospital from July 2022 to November 2022 comprised the verification set. We investigated different gestational weeks of sFlt-1/PLGF (soluble FMS-like tyrosine kinase-1, placental growth factor) ratio combined with maternal characteristics and routine prenatal laboratory results in order to predict PE in each trimester. Multivariate logistic regression was used to establish the prediction model for PE at different gestational weeks. The discrimination, calibration, and clinical validity were utilized to evaluate predictive models as well as models in external validation queues. RESULTS: At 20-24 weeks, the obtained prediction model for PE yielded an area under the curve of 0.568 (95% confidence interval, 0.479-0.657). At 25-29 weeks, the obtained prediction model for PE yielded an area under the curve of 0.773 (95% confidence interval, 0.703-0.842)and 0.731 (95% confidence interval, 0.653-0.809) at 30-34 weeks. After adding maternal factors, uterine artery pulsation index(Ut-IP), and other laboratory indicators to the sFlt-1/PLGF ratio, the predicted performance of PE improved. It found that the AUC improved to 0.826(95% confidence interval, 0.748 ∼ 0.904) at 20-24 weeks, 0.879 (95% confidence interval, 0.823 ∼ 0.935) at 25-29 weeks, and 0.862(95% confidence interval, 0.799 ∼ 0.925) at 30-34 weeks.The calibration plot of the prediction model indicates good predictive accuracy between the predicted probability of PE and the observed probability. Furthermore, decision-curve analysis showed an excellent clinical application value of the models. CONCLUSION: Using the sFlt-1/PLGF ratio combined with multiple factors at 25-29 weeks can effectively predict PE, but the significance of re-examination in late pregnancy is not significant.

Dynamic risk score modeling for multiple longitudinal risk factors and survival.

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

Research on Intelligent Vehicle Trajectory Tracking Control Based on Improved Adaptive MPC.

Intelligent vehicle trajectory tracking exhibits problems such as low adaptability, low tracking accuracy, and poor robustness in complex driving environments with uncertain road conditions. Therefore, an improved method of adaptive model predictive control (AMPC) for trajectory tracking was designed in this study to increase the corresponding tracking accuracy and driving stability of intelligent vehicles under uncertain and complex working conditions. First, based on the unscented Kalman filter, longitudinal speed, yaw speed, and lateral acceleration were considered as the observed variables of the measurement equation to estimate the lateral force of the front and rear tires accurately in real time. Subsequently, an adaptive correction estimation strategy for tire cornering stiffness was designed, an AMPC method was established, and a dynamic prediction time-domain adaptive model was constructed for optimization according to vehicle speed and road adhesion conditions. The improved AMPC method for trajectory tracking was then realized. Finally, the control effectiveness and trajectory tracking accuracy of the proposed AMPC technique were verified via co-simulation using CarSim and MATLAB/Simulink. From the results, a low lateral position error and heading angle error in trajectory tracking were obtained under different vehicle driving conditions and road adhesion conditions, producing high trajectory-tracking control accuracy. Thus, this work provides an important reference for improving the adaptability, robustness, and optimization of intelligent vehicle tracking control systems.

Prediction models of colorectal cancer prognosis incorporating perioperative longitudinal serum tumor markers: a retrospective longitudinal cohort study.

BACKGROUND: Current prognostic prediction models of colorectal cancer (CRC) include only the preoperative measurement of tumor markers, with their available repeated postoperative measurements underutilized. CRC prognostic prediction models were constructed in this study to clarify whether and to what extent the inclusion of perioperative longitudinal measurements of CEA, CA19-9, and CA125 can improve the model performance, and perform a dynamic prediction. METHODS: The training and validating cohort included 1453 and 444 CRC patients who underwent curative resection, with preoperative measurement and two or more measurements within 12 months after surgery, respectively. Prediction models to predict CRC overall survival were constructed with demographic and clinicopathological variables, by incorporating preoperative CEA, CA19-9, and CA125, as well as their perioperative longitudinal measurements. RESULTS: In internal validation, the model with preoperative CEA, CA19-9, and CA125 outperformed the model including CEA only, with the better area under the receiver operating characteristic curves (AUCs: 0.774 vs 0.716), brier scores (BSs: 0.057 vs 0.058), and net reclassification improvement (NRI = 33.5%, 95% CI: 12.3 ~ 54.8%) at 36 months after surgery. Furthermore, the prediction models, by incorporating longitudinal measurements of CEA, CA19-9, and CA125 within 12 months after surgery, had improved prediction accuracy, with higher AUC (0.849) and lower BS (0.049). Compared with preoperative models, the model incorporating longitudinal measurements of the three markers had significant NRI (40.8%, 95% CI: 19.6 to 62.1%) at 36 months after surgery. External validation showed similar results to internal validation. The proposed longitudinal prediction model can provide a personalized dynamic prediction for a new patient, with estimated survival probability updated when a new measurement is collected during 12 months after surgery. CONCLUSIONS: Prediction models including longitudinal measurements of CEA, CA19-9, and CA125 have improved accuracy in predicting the prognosis of CRC patients. We recommend repeated measurements of CEA, CA19-9, and CA125 in the surveillance of CRC prognosis.

Dynamic logistic state space prediction model for clinical decision making.

Prediction modeling for clinical decision making is of great importance and needed to be updated frequently with the changes of patient population and clinical practice. Existing methods are either done in an ad hoc fashion, such as model recalibration or focus on studying the relationship between predictors and outcome and less so for the purpose of prediction. In this article, we propose a dynamic logistic state space model to continuously update the parameters whenever new information becomes available. The proposed model allows for both time-varying and time-invariant coefficients. The varying coefficients are modeled using smoothing splines to account for their smooth trends over time. The smoothing parameters are objectively chosen by maximum likelihood. The model is updated using batch data accumulated at prespecified time intervals, which allows for better approximation of the underlying binomial density function. In the simulation, we show that the new model has significantly higher prediction accuracy compared to existing methods. We apply the method to predict 1 year survival after lung transplantation using the United Network for Organ Sharing data.

Analysis of dynamic restricted mean survival time based on pseudo-observations.

In clinical follow-up studies with a time-to-event end point, the difference in the restricted mean survival time (RMST) is a suitable substitute for the hazard ratio (HR). However, the RMST only measures the survival of patients over a period of time from the baseline and cannot reflect changes in life expectancy over time. Based on the RMST, we study the conditional restricted mean survival time (cRMST) by estimating life expectancy in the future according to the time that patients have survived, reflecting the dynamic survival status of patients during follow-up. In this paper, we introduce the estimation method of cRMST based on pseudo-observations, the statistical inference concerning the difference between two cRMSTs (cRMSTd), and the establishment of the robust dynamic prediction model using the landmark method. Simulation studies are conducted to evaluate the statistical properties of these methods. The results indicate that the estimation of the cRMST is accurate, and the dynamic RMST model has high accuracy in coefficient estimation and good predictive performance. In addition, an example of patients with chronic kidney disease who received renal transplantations is employed to illustrate that the dynamic RMST model can predict patients' expected survival times from any prediction time, considering the time-dependent covariates and time-varying effects of covariates.

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.

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.

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.

Dynamic Prediction of Patient Outcomes in the Intensive Care Unit: A Scoping Review of the State-of-the-Art.

INTRODUCTION: Intensive care units (ICUs) are high-pressure, complex, technology-intensive medical environments where patient physiological data are generated continuously. Due to the complexity of interpreting multiple signals at speed, there are substantial opportunities and significant potential benefits in providing ICU staff with additional decision support and predictive modeling tools that can support and aid decision-making in real-time.This scoping review aims to synthesize the state-of-the-art dynamic prediction models of patient outcomes developed for use in the ICU. We define "dynamic" models as those where predictions are regularly computed and updated over time in response to updated physiological signals. METHODS: Studies describing the development of predictive models for use in the ICU were searched, using PubMed. The studies were screened as per Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) guidelines, and the data regarding predicted outcomes, methods used to develop the predictive models, preprocessing the data and dealing with missing values, and performance measures were extracted and analyzed. RESULTS: A total of n = 36 studies were included for synthesis in our review. The included studies focused on the prediction of various outcomes, including mortality (n = 17), sepsis-related complications (n = 12), cardiovascular complications (n = 5), and other complications (respiratory, renal complications, and bleeding, n = 5). The most common classification methods include logistic regression, random forest, support vector machine, and neural networks. CONCLUSION: The included studies demonstrated that there is a strong interest in developing dynamic prediction models for various ICU patient outcomes. Most models reported focus on mortality. As such, the development of further models focusing on a range of other serious and well-defined complications-such as acute kidney injury-would be beneficial. Furthermore, studies should improve the reporting of key aspects of model development challenges.

Illustration of association between change in prostate-specific antigen (PSA) values and time to tumor status after treatment for prostate cancer patients: a joint modelling approach.

BACKGROUND: Prostate cancer (PCa) is the most prevalent tumor in men, and Prostate-Specific Antigen (PSA) serves as the primary marker for diagnosis, recurrence, and disease-free status. PSA levels post-treatment guide physicians in gauging disease progression and tumor status (low or high). Clinical follow-up relies on monitoring PSA over time, forming the basis for dynamic prediction. Our study proposes a joint model of longitudinal PSA and time to tumor shrinkage, incorporating baseline variables. The research aims to assess tumor status post-treatment for dynamic prediction, utilizing joint assessment of PSA measurements and time to tumor status. METHODS: We propose a joint model for longitudinal PSA and time to tumor shrinkage, taking into account baseline BMI and post-treatment factors, including external beam radiation therapy (EBRT), androgen deprivation therapy (ADT), prostatectomy, and various combinations of these interventions. The model employs a mixed-effect sub-model for longitudinal PSA and an event time sub-model for tumor shrinkage. RESULTS: Results emphasize the significance of baseline factors in understanding the relationship between PSA trajectories and tumor status. Patients with low tumor status consistently exhibit low PSA values, decreasing exponentially within one month post-treatment. The correlation between PSA levels and tumor shrinkage is evident, with the considered factors proving to be significant in both sub-models. CONCLUSIONS: Compared to other treatment options, ADT is the most effective in achieving a low tumor status, as evidenced by a decrease in PSA levels after months of treatment. Patients with an increased BMI were more likely to attain a low tumor status. The research enhances dynamic prediction for PCa patients, utilizing joint analysis of PSA and time to tumor shrinkage post-treatment. The developed model facilitates more effective and personalized decision-making in PCa care.

Predicting age at Alzheimer's dementia onset with the cognitive clock.

INTRODUCTION: Intervention of Alzheimer's dementia hinges on early diagnosis and advanced planning. This work utilizes the cognitive clock, a novel indicator of brain health, to develop a dementia prediction model that can be easily applied in broad settings. METHODS: Data came from over 3000 community-dwelling older adults. Cognitive age was estimated by aligning Mini-Mental State Examination (MMSE) scores to a clock that represents the typical cognitive aging profile. We identified a mean cognitive age at Alzheimer's dementia onset and predicted the corresponding chronological age at person-specific level. RESULTS: The mean chronological age at baseline was 78 years. A total of 881 (28%) participants developed Alzheimer's dementia. The mean cognitive age at onset was 91 years. The predicted chronological age at onset had a mean (standard deviation) of 87.6 (6.7) years. The model's prediction accuracy was supported by multiple testing statistics. DISCUSSION: Our model offers an easy-to-use tool for predicting person-specific age at Alzheimer's dementia onset.

Dynamic and static predictive modelling of psychotherapy outcome-Comparison of two statistical approaches.

OBJECTIVE: Improving prediction abilities in the therapy process can increase therapeutic success for a variety of reasons, such as more personalised treatment or resource optimisation. The increasingly applied methods of dynamic prediction seem to be very promising for this purpose. Prediction models are usually based on static approaches of frequentist statistics. However, the application of this statistical approach has been widely criticised in this research area. Bayesian statistics has been proposed in the literature as an alternative, especially for the task of dynamic modelling. In this study, we compare the performance of predicting therapy outcome over the course of therapy between both statistical approaches. METHOD: Based on a sample of 341 patients, a logistic regression analysis was performed using both statistical approaches. Therapy success was conceptualised as reliable pre-post improvement in brief symptom inventory (BSI) scores. As predictors, we used the subscales of the Outcome Questionnaire (OQ-30) and the Helping Alliance Questionnaire (HAQ) measured every fifth session, as well as baseline BSI scores. RESULTS: The influence of the predictors during therapy differs between the frequentist and the Bayesian approach. In contrast, predictive validity is comparable with a mean area under the curve (AUC) of 0.76 in both model types. CONCLUSION: Bayesian statistic provides an innovative and useful alternative to the frequentist approach in predicting therapy outcome. The theoretical foundation is particularly well suited for dynamic prediction. Nevertheless, no differences in predictive validity were found in this study. More complex methodology as well as further research seems necessary to exploit the potential of Bayesian statistics in this area.

A Gaussian copula approach for dynamic prediction of survival with a longitudinal biomarker.

Dynamic prediction uses patient information collected during follow-up to produce individualized survival predictions at given time points beyond treatment or diagnosis. This allows clinicians to obtain updated predictions of a patient's prognosis that can be used in making personalized treatment decisions. Two commonly used approaches for dynamic prediction are landmarking and joint modeling. Landmarking does not constitute a comprehensive probability model, and joint modeling often requires strong distributional assumptions and computationally intensive methods for estimation. We introduce an alternative approximate approach for dynamic prediction that aims to overcome the limitations of both methods while achieving good predictive performance. We separately specify the marker and failure time distributions conditional on surviving up to a prediction time of interest and use standard variable selection and goodness-of-fit techniques to identify the best-fitting models. Taking advantage of its analytic tractability and easy two-stage estimation, we use a Gaussian copula to link the marginal distributions smoothly at each prediction time with an association function. With simulation studies, we examine the proposed method's performance. We illustrate its use for dynamic prediction in an application to predicting death for heart valve transplant patients using longitudinal left ventricular mass index information.

Dynamic prediction with time-dependent marker in survival analysis using supervised functional principal component analysis.

Time-varying biomarkers reflect important information on disease progression over time. Dynamic prediction for event occurrence on a real-time basis, utilizing time-varying information, is crucial in making accurate clinical decisions. Functional principal component analysis (FPCA) has been widely adopted in the literature for extracting features from time-varying biomarker trajectories. However, feature extraction via FPCA is conducted independent of the time-to-event response, which may not produce optimal results when the goal lies in prediction. With this consideration, we propose a novel supervised FPCA, where the functional principal components are determined to optimize the association between the time-varying biomarker and time-to-event outcome. The proposed framework also accommodates irregularly spaced and sparse longitudinal data. Our method is empirically shown to retain better discrimination and calibration performance than the unsupervised FPCA method in simulation studies. Application of the proposed method is also illustrated in the Alzheimer's Disease Neuroimaging Initiative database.

Dynamic prediction of global monthly burned area with hybrid deep neural networks.

Wildfires not only severely damage the natural environment and global ecological balance but also cause substantial losses to global forest resources and human lives and property. Unprecedented fire events such as Australia's bushfires have alerted us to the fact that wildfire prediction is a critical scientific problem for fire management. Therefore, robust, long-lead models and dynamic predictions of wildfire are valuable for global fire prevention. However, despite decades of effort, the dynamic, effective, and accurate prediction of wildfire remains problematic. There is great uncertainty in predicting the future based on historical and existing spatiotemporal sequence data, but with advances in deep learning algorithms, solutions to prediction problems are being developed. Here, we present a dynamic prediction model of global burned area of wildfire employing a deep neural network (DNN) approach that produces effective wildfire forecasts based on historical time series predictors and satellite-based burned area products. A hybrid DNN that combines long short-term memory and a two-dimensional convolutional neural network (CNN2D-LSTM) was proposed, and CNN2D-LSTM model candidates with four different architectures were designed and compared to construct the optimal architecture for fire prediction. The proposed model was also shown to outperform convolutional neural networks (CNNs) and the fully connected long short-term memory (FcLSTM) approach using the refined index of agreement and evaluation metrics. We produced monthly global burned area spatiotemporal prediction maps and adequately reflected the seasonal peak in fire activity and highly fire-prone areas. Our combined CNN2D-LSTM approach can effectively predict the global burned area of wildfires 1 month in advance and can be generalized to provide seasonal estimates of global fire risk.

Joint models for dynamic prediction in localised prostate cancer: a literature review.

BACKGROUND: Prostate cancer is a very prevalent disease in men. Patients are monitored regularly during and after treatment with repeated assessment of prostate-specific antigen (PSA) levels. Prognosis of localised prostate cancer is generally good after treatment, and the risk of having a recurrence is usually estimated based on factors measured at diagnosis. Incorporating PSA measurements over time in a dynamic prediction joint model enables updates of patients' risk as new information becomes available. We review joint model strategies that have been applied to model time-dependent PSA trajectories to predict time-to-event outcomes in localised prostate cancer. METHODS: We identify articles that developed joint models for prediction of localised prostate cancer recurrence over the last two decades. We report, compare, and summarise the methodological approaches and applications that use joint modelling accounting for two processes: the longitudinal model (PSA), and the time-to-event process (clinical failure). The methods explored differ in how they specify the association between these two processes. RESULTS: Twelve relevant articles were identified. A range of methodological frameworks were found, and we describe in detail shared-parameter joint models (9 of 12, 75%) and joint latent class models (3 of 12, 25%). Within each framework, these articles presented model development, estimation of dynamic predictions and model validations. CONCLUSIONS: Each framework has its unique principles with corresponding advantages and differing interpretations. Regardless of the framework used, dynamic prediction models enable real-time prediction of individual patient prognosis. They utilise all available longitudinal information, in addition to baseline prognostic risk factors, and are superior to traditional baseline-only prediction models.

A dynamic predictive nomogram of long-term survival in primary gastric lymphoma: a retrospective study.

BACKGROUND: Primary gastric lymphoma (PGL) is the most common extranodal non-Hodgkin lymphoma (NHL). Due to the rarity of the disease, it is important to create a predictive model that provides treatment and prognosis for patients with PGL and physicians. METHODS: A total of 8898 and 127 patients diagnosed with PGL were obtained from the SEER database and from our Cancer Center as training and validation cohorts, respectively. Univariate and multivariate Cox proportional hazards models were used to investigate independent risk factors for the construction of predictive survival nomograms, and a web nomogram was developed for the dynamic prediction of survival of patients with PGL. The concordance index (C-index), calibration plot, and receiver operating characteristics (ROC) curve were used to evaluate and validate the nomogram models. RESULTS: There were 8898 PGL patients in the SEER cohort, most of whom were married men over the age of 60, 16.1% of the primary tumors were localized in the antrum and pylori of the stomach, which was similar to the composition of 127 patients in the Chinese cohort, making both groups comparable. The Nomogram of overall survival (OS) was compiled based on eight variables, including age at diagnosis, sex, race, marital status, histology, stage, radiotherapy and chemotherapy. Cancer-specific survival (CSS) nomogram was developed with eight variables, including age at diagnosis, sex, marital status, primary tumor site, histology, stage, radiotherapy and chemotherapy. The C-index of OS prediction nomogram was 0.948 (95% CI: 0.901-0.995) in the validation cohort, the calibration plots showed an optimal match and a high area below the ROC curve (AUC) was observed in both training and validation sets. Also, we established the first web-based PGL survival rate calculator ( https://yangjinru.shinyapps.io/DynNomapp/ ). CONCLUSION: The web dynamic nomogram provided an insightful and applicable tool for evaluating PGL prognosis in OS and CSS, and can effectively guide individual treatment and monitoring.