Bayesian joint modeling of multivariate longitudinal and survival outcomes using Gaussian copulas.

There is an increasing interest in the use of joint models for the analysis of longitudinal and survival data. While random effects models have been extensively studied, these models can be hard to implement and the fixed effect regression parameters must be interpreted conditional on the random effects. Copulas provide a useful alternative framework for joint modeling. One advantage of using copulas is that practitioners can directly specify marginal models for the outcomes of interest. We develop a joint model using a Gaussian copula to characterize the association between multivariate longitudinal and survival outcomes. Rather than using an unstructured correlation matrix in the copula model to characterize dependence structure as is common, we propose a novel decomposition that allows practitioners to impose structure (e.g., auto-regressive) which provides efficiency gains in small to moderate sample sizes and reduces computational complexity. We develop a Markov chain Monte Carlo model fitting procedure for estimation. We illustrate the method's value using a simulation study and present a real data analysis of longitudinal quality of life and disease-free survival data from an International Breast Cancer Study Group trial.

Bayesian multiregional clinical trials using model averaging.

Multiregional clinical trials (MRCTs) provide the benefit of more rapidly introducing drugs to the global market; however, small regional sample sizes can lead to poor estimation quality of region-specific effects when using current statistical methods. With the publication of the International Conference for Harmonisation E17 guideline in 2017, the MRCT design is recognized as a viable strategy that can be accepted by regional regulatory authorities, necessitating new statistical methods that improve the quality of region-specific inference. In this article, we develop a novel methodology for estimating region-specific and global treatment effects for MRCTs using Bayesian model averaging. This approach can be used for trials that compare two treatment groups with respect to a continuous outcome, and it allows for the incorporation of patient characteristics through the inclusion of covariates. We propose an approach that uses posterior model probabilities to quantify evidence in favor of consistency of treatment effects across all regions, and this metric can be used by regulatory authorities for drug approval. We show through simulations that the proposed modeling approach results in lower MSE than a fixed-effects linear regression model and better control of type I error rates than a Bayesian hierarchical model.

Bayesian design of clinical trials using joint models for recurrent and terminating events.

Joint models for recurrent event and terminating event data are increasingly used for the analysis of clinical trials. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the effect of an investigational product (IP) on both recurrent event and terminating event processes considered as multiple primary endpoints, using a multifrailty joint model. Dependence between the recurrent and terminating event processes is accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. We propose an approach for sample size determination to ensure the trial design has a high power and a well-controlled type I error rate, with both operating characteristics defined from a Bayesian perspective. We also consider a generalization of the proposed parametric model that uses a nonparametric mixture of Dirichlet processes to model the frailty distributions and compare its performance to the proposed approach. We demonstrate the methodology by designing a colorectal cancer clinical trial with a goal of demonstrating that the IP causes a favorable effect on at least one of the two outcomes but no harm on either.

Bayesian joint models for multi-regional clinical trials.

In recent years, multi-regional clinical trials (MRCTs) have increased in popularity in the pharmaceutical industry due to their ability to accelerate the global drug development process. To address potential challenges with MRCTs, the International Council for Harmonisation released the E17 guidance document which suggests the use of statistical methods that utilize information borrowing across regions if regional sample sizes are small. We develop an approach that allows for information borrowing via Bayesian model averaging in the context of a joint analysis of survival and longitudinal data from MRCTs. In this novel application of joint models to MRCTs, we use Laplace's method to integrate over subject-specific random effects and to approximate posterior distributions for region-specific treatment effects on the time-to-event outcome. Through simulation studies, we demonstrate that the joint modeling approach can result in an increased rejection rate when testing the global treatment effect compared with methods that analyze survival data alone. We then apply the proposed approach to data from a cardiovascular outcomes MRCT.

Case weighted power priors for hybrid control analyses with time-to-event data.

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCTs) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g., unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted power prior provides robust inference under various forms of incompatibility between the external controls and RCT population.

Bayesian design of clinical trials using the scale transformed power prior.

There are many Bayesian design methods allowing for the incorporation of historical data for sample size determination (SSD) in situations where the outcome in the historical data is the same as the outcome of a new study. However, there is a dearth of methods supporting the incorporation of data from a previously completed clinical trial that investigated the same or similar treatment as the new trial but had a primary outcome that is different. We propose a simulation-based Bayesian SSD framework using the partial-borrowing scale transformed power prior (straPP). The partial-borrowing straPP is developed by applying a novel scale transformation to a traditional power prior on the parameters from the historical data model to make the information better align with the new data model. The scale transformation is based on the assumption that the standardized parameters (i.e., parameters multiplied by the square roots of their respective Fisher information matrices) are equal. To illustrate the method, we present results from simulation studies that use real data from a previously completed clinical trial to design a new clinical trial with a primary time-to-event endpoint.

Bayesian design of clinical trials using joint models for longitudinal and time-to-event data.

Joint models for longitudinal and time-to-event data are increasingly used for the analysis of clinical trial data. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on the time-to-event endpoint using a flexible trajectory joint model. By incorporating the longitudinal outcome trajectory into the hazard model for the time-to-event endpoint, the joint modeling framework allows for non-proportional hazards (e.g., an increasing hazard ratio over time). Inference for the time-to-event endpoint is based on an average of a time-varying hazard ratio which can be decomposed according to the treatment's direct effect on the time-to-event endpoint and its indirect effect, mediated through the longitudinal outcome. We propose an approach for sample size determination for a trial such that the design has high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint and where predictive longitudinal outcome measures are also collected periodically during follow-up.

A hierarchical prior for generalized linear models based on predictions for the mean response.

There has been increased interest in using prior information in statistical analyses. For example, in rare diseases, it can be difficult to establish treatment efficacy based solely on data from a prospective study due to low sample sizes. To overcome this issue, an informative prior to the treatment effect may be elicited. We develop a novel extension of the conjugate prior of Chen and Ibrahim (2003) that enables practitioners to elicit a prior prediction for the mean response for generalized linear models, treating the prediction as random. We refer to the hierarchical prior as the hierarchical prediction prior (HPP). For independent and identically distributed settings and the normal linear model, we derive cases for which the hyperprior is a conjugate prior. We also develop an extension of the HPP in situations where summary statistics from a previous study are available. The HPP allows for discounting based on the quality of individual level predictions, and simulation results suggest that, compared to the conjugate prior and the power prior, the HPP efficiency gains (e.g., lower mean squared error) where predictions are incompatible with the data. An efficient Monte Carlo Markov chain algorithm is developed. Applications illustrate that inferences under the HPP are more robust to prior-data conflict compared to selected nonhierarchical priors.

Bayesian multivariate probability of success using historical data with type I error rate control.

In clinical trials, it is common to have multiple clinical outcomes (e.g., coprimary endpoints or a primary and multiple secondary endpoints). It is often desirable to establish efficacy in at least one of multiple clinical outcomes, which leads to a multiplicity problem. In the frequentist paradigm, the most popular methods to correct for multiplicity are typically conservative. Moreover, despite guidance from regulators, it is difficult to determine the sample size of a future study with multiple clinical outcomes. In this article, we introduce a Bayesian methodology for multiple testing that asymptotically guarantees type I error control. Using a seemingly unrelated regression model, correlations between outcomes are specifically modeled, which enables inference on the joint posterior distribution of the treatment effects. Simulation results suggest that the proposed Bayesian approach is more powerful than the method of Holm (1979), which is commonly utilized in practice as a more powerful alternative to the ubiquitous Bonferroni correction. We further develop multivariate probability of success, a Bayesian method to robustly determine sample size in the presence of multiple outcomes.

Post-acute Ambulatory Care Service Use Among Patients Discharged Home After Stroke or TIA: The Cluster-randomized COMPASS Study.

BACKGROUND AND OBJECTIVES: We examined transitional care management within 90 days and 1 year following discharge home among acute stroke and transient ischemic attack patients from the Comprehensive Post-Acute Stroke Services (COMPASS) Study, a cluster-randomized pragmatic trial of early supported discharge conducted in 41 hospitals (40 hospital units) in North Carolina, United States. METHODS: Data for 2262 of the total 6024 (37.6%; 1069 intervention and 1193 usual care) COMPASS patients were linked with the Centers for Medicare and Medicaid Services fee-for-service Medicare claims. Time to the first ambulatory care visit was examined using Cox proportional hazard models adjusted for patient characteristics not included in the randomization protocol. RESULTS: Only 6% of the patients [mean (SD) age 74.9 (10.2) years, 52.1% women, 80.3% White)] did not have an ambulatory care visit within 90 days postdischarge. Mean time (SD) to first ambulatory care visit was 12.0 (26.0) and 16.3 (35.1) days in intervention and usual care arms, respectively, with the majority of visits in both study arms to primary care providers. The COMPASS intervention resulted in a 27% greater use of ambulatory care services within 1 year postdischarge, relative to usual care [HR=1.27 (95% CI: 1.14-1.41)]. The use of transitional care billing codes was significantly greater in the intervention arm as compared with usual care [OR=1.87 (95% CI: 1.54-2.27)]. DISCUSSION: The COMPASS intervention, which was aimed at improving stroke post-acute care, was associated with an increase in the use of ambulatory care services by stroke and transient ischemic attack patients discharged home and an increased use of transitional care billing codes by ambulatory providers.

The scale transformed power prior for use with historical data from a different outcome model.

We develop the scale transformed power prior for settings where historical and current data involve different data types, such as binary and continuous data. This situation arises often in clinical trials, for example, when historical data involve binary responses and the current data involve some other type of continuous or discrete outcome. The power prior, proposed by Ibrahim and Chen, does not address the issue of different data types. Herein, we develop a new type of power prior, which we call the scale transformed power prior (straPP). The straPP is constructed by transforming the power prior for the historical data by rescaling the parameter using a function of the Fisher information matrices for the historical and current data models, thereby shifting the scale of the parameter vector from that of the historical to that of the current data. Examples are presented to motivate the need for such a transformation, and simulation studies are presented to illustrate the performance advantages of the straPP over the power prior and other informative and noninformative priors. A real dataset from a clinical trial undertaken to study a novel transitional care model for stroke survivors is used to illustrate the methodology.

A Bayesian approach to study design and analysis with type I error rate control for response variables of mixed types.

There has been increased interest in the design and analysis of studies consisting of multiple response variables of mixed types. For example, in clinical trials, it is desirable to establish efficacy for a treatment effect in primary and secondary outcomes. In this article, we develop Bayesian approaches for hypothesis testing and study planning for data consisting of multiple response variables of mixed types with covariates. We assume that the responses are correlated via a Gaussian copula, and that the model for each response is, marginally, a generalized linear model (GLM). Taking a fully Bayesian approach, the proposed method enables inference based on the joint posterior distribution of the parameters. Under some mild conditions, we show that the joint distribution of the posterior probabilities under any Bayesian analysis converges to a Gaussian copula distribution as the sample size tends to infinity. Using this result, we develop an approach to control the type I error rate under multiple testing. Simulation results indicate that the method is more powerful than conducting marginal regression models and correcting for multiplicity using the Bonferroni-Holm Method. We also develop a Bayesian approach to sample size determination in the presence of response variables of mixed types, extending the concept of probability of success (POS) to multiple response variables of mixed types.

Magnetic Resonance Imaging of the Lumbar Spine: Recommendations for Acquisition and Image Evaluation from the BACPAC Spine Imaging Working Group.

Management of patients suffering from low back pain (LBP) is challenging and requires development of diagnostic techniques to identify specific patient subgroups and phenotypes in order to customize treatment and predict clinical outcome. The Back Pain Consortium (BACPAC) Research Program Spine Imaging Working Group has developed standard operating procedures (SOPs) for spinal imaging protocols to be used in all BACPAC studies. These SOPs include procedures to conduct spinal imaging assessments with guidelines for standardizing the collection, reading/grading (using structured reporting with semi-quantitative evaluation using ordinal rating scales), and storage of images. This article presents the approach to image acquisition and evaluation recommended by the BACPAC Spine Imaging Working Group. While the approach is specific to BACPAC studies, it is general enough to be applied at other centers performing magnetic resonance imaging (MRI) acquisitions in patients with LBP. The herein presented SOPs are meant to improve understanding of pain mechanisms and facilitate patient phenotyping by codifying MRI-based methods that provide standardized, non-invasive assessments of spinal pathologies. Finally, these recommended procedures may facilitate the integration of better harmonized MRI data of the lumbar spine across studies and sites within and outside of BACPAC studies.

The Back Pain Consortium (BACPAC) Research Program Data Harmonization: Rationale for Data Elements and Standards.

OBJECTIVE: One aim of the Back Pain Consortium (BACPAC) Research Program is to develop an integrated model of chronic low back pain that is informed by combined data from translational research and clinical trials. We describe efforts to maximize data harmonization and accessibility to facilitate Consortium-wide analyses. METHODS: Consortium-wide working groups established harmonized data elements to be collected in all studies and developed standards for tabular and nontabular data (eg, imaging and omics). The BACPAC Data Portal was developed to facilitate research collaboration across the Consortium. RESULTS: Clinical experts developed the BACPAC Minimum Dataset with required domains and outcome measures to be collected by use of questionnaires across projects. Other nonrequired domain-specific measures are collected by multiple studies. To optimize cross-study analyses, a modified data standard was developed on the basis of the Clinical Data Interchange Standards Consortium Study Data Tabulation Model to harmonize data structures and facilitate integration of baseline characteristics, participant-reported outcomes, chronic low back pain treatments, clinical exam, functional performance, psychosocial characteristics, quantitative sensory testing, imaging, and biomechanical data. Standards to accommodate the unique features of chronic low back pain data were adopted. Research units submit standardized study data to the BACPAC Data Portal, developed as a secure cloud-based central data repository and computing infrastructure for researchers to access and conduct analyses on data collected by or acquired for BACPAC. CONCLUSIONS: BACPAC harmonization efforts and data standards serve as an innovative model for data integration that could be used as a framework for other consortia with multiple, decentralized research programs.

The Back Pain Consortium (BACPAC) Research Program: Structure, Research Priorities, and Methods.

In 2019, the National Health Interview survey found that nearly 59% of adults reported pain some, most, or every day in the past 3 months, with 39% reporting back pain, making back pain the most prevalent source of pain, and a significant issue among adults. Often, identifying a direct, treatable cause for back pain is challenging, especially as it is often attributed to complex, multifaceted issues involving biological, psychological, and social components. Due to the difficulty in treating the true cause of chronic low back pain (cLBP), an over-reliance on opioid pain medications among cLBP patients has developed, which is associated with increased prevalence of opioid use disorder and increased risk of death. To combat the rise of opioid-related deaths, the National Institutes of Health (NIH) initiated the Helping to End Addiction Long-TermSM (HEAL) initiative, whose goal is to address the causes and treatment of opioid use disorder while also seeking to better understand, diagnose, and treat chronic pain. The NIH Back Pain Consortium (BACPAC) Research Program, a network of 14 funded entities, was launched as a part of the HEAL initiative to help address limitations surrounding the diagnosis and treatment of cLBP. This paper provides an overview of the BACPAC research program's goals and overall structure, and describes the harmonization efforts across the consortium, define its research agenda, and develop a collaborative project which utilizes the strengths of the network. The purpose of this paper is to serve as a blueprint for other consortia tasked with the advancement of pain related science.

Bayesian Design of Clinical Trials Using Joint Cure Rate Models for Longitudinal and Time-to-Event Data.

For clinical trial design and analysis, there has been extensive work related to using joint models for longitudinal and time-to-event data without a cure fraction (i.e., when all patients are at risk for the event of interest), but comparatively little treatment has been given to design and analysis of clinical trials using joint models that incorporate a cure fraction. In this paper, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on a time-to-event endpoint using a promotion time cure rate model, where the longitudinal process is incorporated into the hazard model for the promotion times. A piecewise linear hazard model for the period after assessment of the longitudinal measure ends is proposed as an alternative to extrapolating the longitudinal trajectory. This may be advantageous in scenarios where the period of time from the end of longitudinal measurements until the end of observation is substantial. Inference for the time-to-event endpoint is based on a novel estimand which combines the treatment's effect on the probability of cure and its effect on the promotion time distribution, mediated by the longitudinal outcome. We propose an approach for sample size determination such that the design has a high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint where longitudinal outcomes are measured periodically during follow up.

Bayesian adaptive basket trial design using model averaging.

In this article, we develop a Bayesian adaptive design methodology for oncology basket trials with binary endpoints using a Bayesian model averaging framework. Most existing methods seek to borrow information based on the degree of homogeneity of estimated response rates across all baskets. In reality, an investigational product may only demonstrate activity for a subset of baskets, and the degree of activity may vary across the subset. A key benefit of our Bayesian model averaging approach is that it explicitly accounts for the possibility that any subset of baskets may have similar activity and that some may not. Our proposed approach performs inference on the basket-specific response rates by averaging over the complete model space for the response rates, which can include thousands of models. We present results that demonstrate that this computationally feasible Bayesian approach performs favorably compared to existing state-of-the-art approaches, even when held to stringent requirements regarding false positive rates.

Skilled Nursing and Inpatient Rehabilitation Facility Use by Medicare Fee-for-Service Beneficiaries Discharged Home After a Stroke: Findings From the COMPASS Trial.

OBJECTIVES: To examine the effect of a comprehensive transitional care model on the use of skilled nursing facility (SNF) and inpatient rehabilitation facility (IRF) care in the 12 months after acute care discharge home following stroke; and to identify predictors of experiencing a SNF or IRF admission following discharge home after stroke. DESIGN: Cluster randomized pragmatic trial SETTING: Forty-one acute care hospitals in North Carolina. PARTICIPANTS: 2262 Medicare fee-for-service beneficiaries with transient ischemic attack or stroke discharged home. The sample was 80.3% White and 52.1% female, with a mean (SD) age of 74.9 (10.2) years and a mean ± SD National Institutes of Health stroke scale score of 2.3 (3.7). INTERVENTION: Comprehensive transitional care model (COMPASS-TC), which consisted of a 2-day follow-up phone call from the postacute care coordinator and 14-day in-person visit with the postacute care coordinator and advanced practice provider. MAIN OUTCOME MEASURES: Time to first SNF or IRF and SNF or IRF admission (yes/no) in the 12 months following discharge home. All analyses utilized multivariable mixed models including a hospital-specific random effect to account for the non-independence of measures within hospital. Intent to treat analyses using Cox proportional hazards regression assessed the effect of COMPASS-TC on time to SNF/IRF admission. Logistic regression was used to identify clinical and non-clinical predictors of SNF/IRF admission. RESULTS: Only 34% of patients in the intervention arm received COMPASS-TC per protocol. COMPASS-TC was not associated with a reduced hazard of a SNF/ IRF admission in the 12 months post-discharge (hazard ratio, 1.20, with a range of 0.95-1.52) compared to usual care. This estimate was robust to additional covariate adjustment (hazard ratio, 1.23) (0.93-1.64). Both clinical and non-clinical factors (ie, insurance, geography) were predictors of SNF/IRF use. CONCLUSIONS: COMPASS-TC was not consistently incorporated into real-world clinical practice. The use of a comprehensive transitional care model for patients discharged home after stroke was not associated with SNF or IRF admissions in a 12-month follow-up period. Non-clinical factors predictive of SNF/IRF use suggest potential issues with access to this type of care.

A structured framework for adaptively incorporating external evidence in sequentially monitored clinical trials.

We present a Bayesian framework for sequential monitoring that allows for use of external data, and that can be applied in a wide range of clinical trial applications. The basis for this framework is the idea that, in many cases, specification of priors used for sequential monitoring and the stopping criteria can be semi-algorithmic byproducts of the trial hypotheses and relevant external data, simplifying the process of prior elicitation. Monitoring priors are defined using the family of generalized normal distributions, which comprise a flexible class of priors, naturally allowing one to construct a prior that is peaked or flat about the parameter values thought to be most likely. External data are incorporated into the monitoring process through mixing an a priori skeptical prior with an enthusiastic prior using a weight that can be fixed or adaptively estimated. In particular, we introduce an adaptive monitoring prior for efficacy evaluation that dynamically weighs skeptical and enthusiastic prior components based on the degree to which observed data are consistent with an enthusiastic perspective. The proposed approach allows for prospective and pre-specified use of external data in the monitoring procedure. We illustrate the method for both single-arm and two-arm randomized controlled trials. For the latter case, we also include a retrospective analysis of actual trial data using the proposed adaptive sequential monitoring procedure. Both examples are motivated by completed pediatric trials, and the designs incorporate information from adult trials to varying degrees. Preposterior analysis and frequentist operating characteristics of each trial design are discussed.

Bayesian adaptive design for concurrent trials involving biologically related diseases.

We develop a Bayesian design method for a clinical program where an investigational product is to be studied concurrently in a set of clinical trials involving related diseases with the goal of demonstrating superiority to a control in each. The approach borrows information on treatment effectiveness using correlated mixture priors using an analysis procedure that is closely related Bayesian model averaging. Mixture priors are constructed by eliciting conjugate priors based on pessimistic and enthusiastic predictions for the data to be observed for each disease and then by eliciting mixture weights for all possible configurations of the pessimistic and enthusiastic priors across the diseases to be studied. The proposed approach provides a robust framework for information borrowing in settings where the diseases may have endpoints based on different data types. We show via simulation that operating characteristics based on the proposed design framework are favorable compared to those based on information borrowing designs using the Bayesian hierarchical model which is poorly suited for information borrowing when there are different data types underpinning the endpoints across which information is to be borrowed.