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

Joint modeling of tumor dynamics and progression-free survival in advanced breast cancer: Leveraging data from amcenestrant early phase I-II trials

A joint modeling framework was developed using data from 75 patients of early amcenestrant phase I-II AMEERA-1-2 dose escalation and expansion cohorts. A semi-mechanistic tumor growth inhibition (TGI) model was developed. It accounts for the dynamics of sensitive and resistant tumor cells, an exposure-driven effect on tumor proliferation of sensitive cells, and a delay in the initiation of treatment effect to describe the time course of target lesion tumor size (TS) data. Individual treatment exposure overtime was introduced in the model using concentrations predicted by a population pharmacokinetic model of amcenestrant. This joint modeling framework integrated complex RECISTv1.1 criteria information, linked TS metrics to progression-free survival (PFS), and was externally evaluated using the randomized phase II trial AMEERA-3. We demonstrated that the instantaneous rate of change in TS (TS slope) was an important predictor of PFS and the developed joint model was able to predict well the PFS of amcenestrant phase II monotherapy trial using only early phase I-II data. This provides a good modeling and simulation tool to inform early development decisions.

Assessing tilavonemab efficacy in early Alzheimer's disease via longitudinal item response theory modeling

INTRODUCTION

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by declines in cognitive and functional severities. This research utilized the Clinical Dementia Rating (CDR) to assess the influence of tilavonemab on these deteriorations.

METHODS

Longitudinal Item Response Theory (IRT) models were employed to analyze CDR domains in early-stage AD patients. Both unidimensional and multidimensional models were contrasted to elucidate the trajectories of cognitive and functional severities.

RESULTS

We observed significant temporal increases in both cognitive and functional severities, with the cognitive severity deteriorating at a quicker rate. Tilavonemab did not demonstrate a statistically significant effect on the progression in either severity. Furthermore, a significant positive association was identified between the baselines and progression rates of both severities.

DISCUSSION

While tilavonemab failed to mitigate impairment progression, our multidimensional IRT analysis illuminated the interconnected progression of cognitive and functional declines in AD, suggesting a comprehensive perspective on disease trajectories.

Highlights

Utilized longitudinal Item Response Theory (IRT) models to analyze the Clinical Dementia Rating (CDR) domains in early-stage Alzheimer's disease (AD) patients, comparing unidimensional and multidimensional models.Observed significant temporal increases in both cognitive and functional severities, with cognitive severity deteriorating at a faster rate, while tilavonemab showed no statistically significant effect on either domain's progression.Found a significant positive association between the baseline severities and their progression rates, indicating interconnected progression patterns of cognitive and functional declines in AD.Introduced the application of multidimensional longitudinal IRT models to provide a comprehensive perspective on the trajectories of cognitive and functional severities in early AD, suggesting new avenues for future research including the inclusion of time-dependent random effects and data-driven IRT models.

DYNAMIC RISK PREDICTION TRIGGERED BY INTERMEDIATE EVENTS USING SURVIVAL TREE ENSEMBLES

With the availability of massive amounts of data from electronic health records and registry databases, incorporating time-varying patient information to improve risk prediction has attracted great attention. To exploit the growing amount of predictor information over time, we develop a unified framework for landmark prediction using survival tree ensembles, where an updated prediction can be performed when new information becomes available. Compared to conventional landmark prediction with fixed landmark times, our methods allow the landmark times to be subject-specific and triggered by an intermediate clinical event. Moreover, the nonparametric approach circumvents the thorny issue of model incompatibility at different landmark times. In our framework, both the longitudinal predictors and the event time outcome are subject to right censoring, and thus existing tree-based approaches cannot be directly applied. To tackle the analytical challenges, we propose a risk-set-based ensemble procedure by averaging martingale estimating equations from individual trees. Extensive simulation studies are conducted to evaluate the performance of our methods. The methods are applied to the Cystic Fibrosis Foundation Patient Registry (CFFPR) data to perform dynamic prediction of lung disease in cystic fibrosis patients and to identify important prognosis factors.

Application of longitudinal item response theory models to modeling Parkinson's disease progression

The Movement Disorder Society revised version of the Unified Parkinson's Disease Rating Scale (MDS-UPDRS) parts 2 and 3 reflect patient-reported functional impact and clinician-reported severity of motor signs of Parkinson's disease (PD), respectively. Total scores are common clinical outcomes but may obscure important time-based changes in items. We aim to analyze longitudinal disease progression based on MDS-UPRDS parts 2 and 3 item-level responses over time and as functions of Hoehn & Yahr (H&Y) stages 1 and 2 for subjects with early PD. The longitudinal item response theory (IRT) modeling is a novel statistical method addressing limitations in traditional linear regression approaches, such as ignoring varying item sensitivities and the sum score balancing out improvements and declines. We utilized a harmonized dataset consisting of six studies with 3573 subjects with early PD and 14,904 visits, and mean follow-up time of 2.5 years (±1.57). We applied both a unidimensional (each part separately) and multidimensional (both parts combined) longitudinal IRT models. We assessed the progression rates for both parts, anchored to baseline H&Y stages 1 and 2. Both the uni- and multidimensional longitudinal IRT models indicate significant worsening time effects in both parts 2 and 3. Baseline H&Y stage 2 was associated with significantly higher baseline severities, but slower progression rates in both parts, as compared with stage 1. Patients with baseline H&Y stage 1 demonstrated slower progression in part 2 severity compared to part 3, whereas patients with baseline H&Y stage 2 progressed faster in part 2 than part 3. The multidimensional model had a superior fit compared to the unidimensional models and it had excellent model performance.

Dissecting the Domains of Parkinson's Disease: Insights from Longitudinal Item Response Theory Modeling

BACKGROUND

Longitudinal item response theory (IRT) models previously suggested that the Movement Disorder Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) motor examination has two salient domains, tremor and nontremor, that progress in time and in response to treatment differently.

OBJECTIVE

Apply longitudinal IRT modeling, separating tremor and nontremor domains, to reanalyze outcomes in the previously published clinical trial (Study of Urate Elevation in Parkinson's Disease, Phase 3) that showed no overall treatment effects.

METHODS

We applied unidimensional and multidimensional longitudinal IRT models to MDS-UPDRS motor examination items in 298 participants with Parkinson's disease from the Study of Urate Elevation in Parkinson's Disease, Phase 3 (placebo vs. inosine) study. We separated 10 tremor items from 23 nontremor items and used Bayesian inference to estimate progression rates and sensitivity to treatment in overall motor severity and tremor and nontremor domains.

RESULTS

The progression rate was faster in the tremor domain than the nontremor domain before levodopa treatment. Inosine treatment had no effect on either domain relative to placebo. Levodopa treatment was associated with greater slowing of progression in the tremor domain than the nontremor domain regardless of inosine exposure. Linear patterns of progression were observed. Despite different domain-specific progression patterns, tremor and nontremor severities at baseline and over time were significantly correlated.

CONCLUSIONS

Longitudinal IRT analysis is a novel statistical method addressing limitations of traditional linear regression approaches. It is particularly useful because it can simultaneously monitor changes in different, but related, domains over time and in response to treatment interventions. We suggest that in neurological diseases with distinct impairment domains, clinical or anatomical, this application may identify patterns of change unappreciated by standard statistical methods. © 2022 International Parkinson and Movement Disorder Society.

Novel Approach to Movement Disorder Society-Unified Parkinson's Disease Rating Scale Monitoring in Clinical Trials: Longitudinal Item Response Theory Models

Background

Although nontremor and tremor Part 3 Movement Disorder Society-Unified Parkinson's Disease Rating Scale items measure different impairment domains, their distinct progression and drug responsivity remain unstudied longitudinally. The total score may obscure important time-based and treatment-based changes occurring in the individual domains.

Objective

Using the unique advantages of item response theory (IRT), we developed novel longitudinal unidimensional and multidimensional models to investigate nontremor and tremor changes occurring in an interventional Parkinson's disease (PD) study.

Method

With unidimensional longitudinal IRT, we assessed the 33 Part 3 item data (22 nontremor and 10 tremor items) of 336 patients with early PD from the STEADY-PD III (Safety, Tolerability, and Efficacy Assessment of Isradipine for PD, placebo vs. isradipine) study. With multidimensional longitudinal IRT, we assessed the progression rates over time and treatment (in overall motor severity, nontremor, and tremor domains) using Markov Chain Monte Carlo implemented in Stan.

Results

Regardless of treatment, patients showed significant but different time-based deterioration rates for total motor, nontremor, and tremor scores. Isradipine was associated with additional significant deterioration over placebo in total score and nontremor scores, but not in tremor score. Further highlighting the 2 separate latent domains, nontremor and tremor severity changes were positively but weakly correlated (correlation coefficient, 0.108).

Conclusions

Longitudinal IRT analysis is a novel statistical method highly applicable to PD clinical trials. It addresses limitations of traditional linear regression approaches and previous IRT investigations that either applied cross-sectional IRT models to longitudinal data or failed to estimate all parameters simultaneously. It is particularly useful because it can separate nontremor and tremor changes both over time and in response to treatment interventions.

Modeling local dependence in latent vector autoregressive models

We propose a Bayesian latent vector autoregressive (LVAR) model to analyze multivariate longitudinal data of binary and ordinal variables (items) as a function of a small number of continuous latent variables. We focus on the evolution of the latent variables while taking into account the correlation structure of the responses. Often local independence is assumed in this context. Local independence implies that, given the latent variables, the responses are assumed mutually independent cross-sectionally and longitudinally. However, in practice conditioning on the latent variables may not remove the dependence of the responses. We address local dependence by further conditioning on item-specific random effects. A simulation study shows that wrongly assuming local independence may give biased estimates for the regression coefficients of the LVAR process as well as the item-specific parameters. Novel features of our proposal include (i) correcting biased estimates of the model parameters, especially the regression coefficients of the LVAR process, obtained when local dependence is ignored and (ii) measuring the magnitude of local dependence. We applied our model on data obtained from a registry on the elderly population in Belgium. The purpose was to examine the values of oral health information on top of general health information.

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.

Predicting Alzheimer's disease based on survival data and longitudinally measured performance on cognitive and functional scales

This study assessed how well longitudinally taken cognitive and functional scales from people with mild cognitive impairment (MCI) predict conversion to Alzheimer's disease (AD). Participants were individuals with baseline MCI from the Alzheimer's Disease Neuroimaging Initiative. Scales included the Alzheimer Disease Assessment Scale-Cognitive (ADAS-Cog) 11 and 13, the Mini Mental State Examination (MMSE), and the Functional Assessment Questionnaire (FAQ). A joint modelling approach compared performance on the four scales for dynamic prediction of risk for AD. The goodness of fit measures included log likelihood, the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC). The area under the curve (AUC) of the receiver operating characteristic assessed predictive accuracy. The parameter α in the ADAS-Cog11, ADAS-Cog13, MMSE, and FAQ joint models was statistically significant. Joint MMSE and FAQ models had better goodness of fit. FAQ had the best predictive accuracy. Cognitive and functional impairment assessment scales are strong screening predictors when repeated measures are available. They could be useful for predicting risk for AD in primary healthcare.

Improved Landmark Dynamic Prediction Model to Assess Cardiovascular Disease Risk in On-Treatment Blood Pressure Patients: A Simulation Study and Post Hoc Analysis on SPRINT Data

Landmark model (LM) is a dynamic prediction model that uses a longitudinal biomarker in time-to-event data to make prognosis prediction. This study was designed to improve this model and to apply it to assess the cardiovascular risk in on-treatment blood pressure patients. A frailty parameter was used in LM, landmark frailty model (LFM), to account the frailty of the patients and measure the correlation between different landmarks. The proposed model was compared with LM in different scenarios respecting data missing status, sample size (100, 200, and 400), landmarks (6, 12, 24, and 48), and failure percentage (30, 50, and 100%). Bias of parameter estimation and mean square error as well as deviance statistic between models were compared. Additionally, discrimination and calibration capability as the goodness of fit of the model were evaluated using dynamic concordance index (DCI), dynamic prediction error (DPE), and dynamic relative prediction error (DRPE). The proposed model was performed on blood pressure data, obtained from systolic blood pressure intervention trial (SPRINT), in order to calculate the cardiovascular risk. Dynpred, coxme, and coxphw packages in the R.3.4.3 software were used. It was proved that our proposed model, LFM, had a better performance than LM. Parameter estimation in LFM was closer to true values in comparison to that in LM. Deviance statistic showed that there was a statistically significant difference between the two models. In the landmark numbers 6, 12, and 24, the LFM had a higher DCI over time and the three landmarks showed better performance in discrimination. Both DPE and DRPE in LFM were lower in comparison to those in LM over time. It was indicated that LFM had better calibration in comparison to its peer. Moreover, real data showed that the structure of prognostic process was predicted better in LFM than in LM. Accordingly, it is recommended to use the LFM model for assessing cardiovascular risk due to its better performance.

Predicting the Survival of AIDS Patients Using Two Frameworks of Statistical Joint Modeling and Comparing Their Predictive Accuracy

BACKGROUND

The present study aimed to estimate the survival of HIV-positive patients and compare the accuracy of two commonly used models, Shared Random-Effect Model (SREM) and Joint Latent Class Model (JLCM) for the analysis of time to death among these patients.

METHODS

Data on a retrospective survey among HIV-positive patients diagnosed during 1989-2014 who referred to the Behavioral Diseases Consultation Center of Mashhad University of Medical Sciences was used in this study. Participants consisted of HIV-positive high-risk volunteers, referrals of new HIV cases from prisons, blood transfusion organization and hospitals. Subjects were followed from diagnosis until death or the end of study. SREM and JLCM were used to predict the survival of HIV/AIDS patients. In both models age, sex and addiction were included as covariates. To compare the accuracy of these alternative models, dynamic predictions were calculated at specific time points. The receiver operating characteristic (ROC) curve was used to select the more accurate model.

RESULTS

Overall, 213 patients were eligible that met entry conditions for the present analysis. Based on BIC criteria, three heterogeneous sub-populations of patients were identified by JLCM and individuals were categorized in these classes ("High Risk", "Moderate Risk" and "Low Risk") according to their health status. JLCM had a better predictive accuracy than SREM. The average area under ROC curve for JLCM and SREM was 0.75 and 0.64 respectively. In both models CD4 count decreased with time. Based on the result of JLCM, men had higher hazard rate than women and the CD4 counts levels of patients decreased with increasing age.

CONCLUSION

Predicting risk of death (or survival) is vital for patients care in most medical research. In a heterogeneous population, such as HIV-positive patients fitting JLCM can significantly improve the accuracy of the risk prediction. Therefore, this model is preferred for these populations.

Bayesian joint modelling of longitudinal and time to event data: a methodological review

BACKGROUND

In clinical research, there is an increasing interest in joint modelling of longitudinal and time-to-event data, since it reduces bias in parameter estimation and increases the efficiency of statistical inference. Inference and prediction from frequentist approaches of joint models have been extensively reviewed, and due to the recent popularity of data-driven Bayesian approaches, a review on current Bayesian estimation of joint model is useful to draw recommendations for future researches.

METHODS

We have undertaken a comprehensive review on Bayesian univariate and multivariate joint models. We focused on type of outcomes, model assumptions, association structure, estimation algorithm, dynamic prediction and software implementation.

RESULTS

A total of 89 articles have been identified, consisting of 75 methodological and 14 applied articles. The most common approach to model the longitudinal and time-to-event outcomes jointly included linear mixed effect models with proportional hazards. A random effect association structure was generally used for linking the two sub-models. Markov Chain Monte Carlo (MCMC) algorithms were commonly used (93% articles) to estimate the model parameters. Only six articles were primarily focused on dynamic predictions for longitudinal or event-time outcomes.

CONCLUSION

Methodologies for a wide variety of data types have been proposed; however the research is limited if the association between the two outcomes changes over time, and there is also lack of methods to determine the association structure in the absence of clinical background knowledge. Joint modelling has been proved to be beneficial in producing more accurate dynamic prediction; however, there is a lack of sufficient tools to validate the prediction.

Developing and Validating Risk Assessment Models of Clinical Outcomes in Modern Oncology

The identification of prognostic factors and building of risk assessment prognostic models will continue to play a major role in 21st century medicine in patient management and decision making. Investigators are often interested in examining the relationship between host, tumor-related, and environmental variables in predicting clinical outcomes. We make a distinction between static and dynamic prediction models. In static prediction modelling, typically variables collected at baseline are utilized in building models. On the other hand, dynamic predictive models leverage the longitudinal data of covariates collected during treatment or follow-up, and hence provide accurate predictions of patients prognoses. To date, most risk assessment models in oncology have been based on static models. In this article, we cover topics that are related to the analysis of prognostic factors, centering on factors that are both relevant at the time of diagnosis or initial treatment and during treatment. We describe the types of risk prediction and then provide a brief description of the penalized regression methods. We then review the state-of-the art methods for dynamic prediction and compare the strengths and the limitations of these methods. While static models will continue to play an important role in oncology, developing and validating dynamic models of clinical outcomes need to take a higher priority. It is apparent that a framework for developing and validating dynamic tools in oncology is still needed. One of the limitations in oncology that modelers may be constrained by the lack of access to the longitudinal biomarker data. It is highly recommended that the next generation of risk assessments consider the longitudinal biomarker data and outcomes so that prediction can be continually updated.

Association Between Tumor Size Kinetics and Survival in Patients With Urothelial Carcinoma Treated With Atezolizumab: Implication for Patient Follow-Up

We characterized the association between tumor size kinetics and survival in patients with advanced urothelial carcinoma treated with atezolizumab (anti-programmed death-ligand 1, Tecentriq) using a joint model. The model, developed on data from 309 patients of a phase II clinical trial, identified the time-to-tumor growth and the instantaneous changes in tumor size as the best on-treatment predictors of survival. On the validation dataset containing data from 457 patients from a phase III study, the model predicted individual survival probability using 3-month or 6-month tumor size follow-up data with an area under the receptor-occupancy curve between 0.75 and 0.84, as compared with values comprised between 0.62 and 0.75 when the model included only information available at treatment initiation. Including tumor size kinetics in a relevant statistical framework improves the prediction of survival probability during immunotherapy treatment and may be useful to identify most-at-risk patients in "real-time."

A Bayesian approach for individual-level drug benefit-risk assessment

In existing benefit-risk assessment (BRA) methods, benefit and risk criteria are usually identified and defined separately based on aggregated clinical data and therefore ignore the individual-level differences as well as the association among the criteria. We proposed a Bayesian multicriteria decision-making method for BRA of drugs using individual-level data. We used a multidimensional latent trait model to account for the heterogeneity of treatment effects with latent variables introducing the dependencies among outcomes. We then applied the stochastic multicriteria acceptability analysis approach for BRA incorporating imprecise and heterogeneous patient preference information. We adopted an efficient Markov chain Monte Carlo algorithm when implementing the proposed method. We applied our method to a case study to illustrate how individual-level benefit-risk profiles could inform decision-making.

Joint modeling of multiple repeated measures and survival data using multidimensional latent trait linear mixed model

Impairment caused by Amyotrophic lateral sclerosis (ALS) is multidimensional (e.g. bulbar, fine motor, gross motor) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of ALS use multiple longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow-up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we develop a joint model consisting of a multidimensional latent trait linear mixed model (MLTLMM) for the multiple longitudinal outcomes, and a proportional hazards model with piecewise constant baseline hazard for the event time data. Shared random effects are used to link together two models. The model inference is conducted using a Bayesian framework via Markov chain Monte Carlo simulation implemented in Stan language. Our proposed model is evaluated by simulation studies and is applied to the Ceftriaxone study, a motivating clinical trial assessing the effect of ceftriaxone on ALS patients.

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.

Predicting the multi-domain progression of Parkinson's disease: a Bayesian multivariate generalized linear mixed-effect model

BACKGROUND

It is challenging for current statistical models to predict clinical progression of Parkinson's disease (PD) because of the involvement of multi-domains and longitudinal data.

METHODS

Past univariate longitudinal or multivariate analyses from cross-sectional trials have limited power to predict individual outcomes or a single moment. The multivariate generalized linear mixed-effect model (GLMM) under the Bayesian framework was proposed to study multi-domain longitudinal outcomes obtained at baseline, 18-, and 36-month. The outcomes included motor, non-motor, and postural instability scores from the MDS-UPDRS, and demographic and standardized clinical data were utilized as covariates. The dynamic prediction was performed for both internal and external subjects using the samples from the posterior distributions of the parameter estimates and random effects, and also the predictive accuracy was evaluated based on the root of mean square error (RMSE), absolute bias (AB) and the area under the receiver operating characteristic (ROC) curve.

RESULTS

First, our prediction model identified clinical data that were differentially associated with motor, non-motor, and postural stability scores. Second, the predictive accuracy of our model for the training data was assessed, and improved prediction was gained in particularly for non-motor (RMSE and AB: 2.89 and 2.20) compared to univariate analysis (RMSE and AB: 3.04 and 2.35). Third, the individual-level predictions of longitudinal trajectories for the testing data were performed, with ~80% observed values falling within the 95% credible intervals.

CONCLUSIONS

Multivariate general mixed models hold promise to predict clinical progression of individual outcomes in PD.

TRIAL REGISTRATION

The data was obtained from Dr. Xuemei Huang's NIH grant R01 NS060722 , part of NINDS PD Biomarker Program (PDBP). All data was entered within 24 h of collection to the Data Management Repository (DMR), which is publically available ( https://pdbp.ninds.nih.gov/data-management ).