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.

Efficacy of a Dual-Epitope Dendritic Cell Vaccine as Part of Combined Immunotherapy for HER2-Expressing Breast Tumors.

Previous work from our group and others has shown that patients with breast cancer can generate a T cell response against specific human epidermal growth factor 2 (HER2) epitopes. In addition, preclinical work has shown that this T cell response can be augmented by Ag-directed mAb therapy. This study evaluated the activity and safety of a combination of dendritic cell (DC) vaccination given with mAb and cytotoxic therapy. We performed a phase I/II study using autologous DCs pulsed with two different HER2 peptides given with trastuzumab and vinorelbine to a study cohort of patients with HER2-overexpressing and a second with HER2 nonoverexpressing metastatic breast cancer. Seventeen patients with HER2-overexpressing and seven with nonoverexpressing disease were treated. Treatment was well tolerated, with one patient removed from therapy because of toxicity and no deaths. Forty-six percent of patients had stable disease after therapy, with 4% achieving a partial response and no complete responses. Immune responses were generated in the majority of patients but did not correlate with clinical response. However, in one patient, who has survived >14 y since treatment in the trial, a robust immune response was demonstrated, with 25% of her T cells specific to one of the peptides in the vaccine at the peak of her response. These data suggest that autologous DC vaccination when given with anti-HER2-directed mAb therapy and vinorelbine is safe and can induce immune responses, including significant T cell clonal expansion, in a subset of patients.

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.

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 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.

Efficient computation of high-dimensional penalized generalized linear mixed models by latent factor modeling of the random effects.

Modern biomedical datasets are increasingly high-dimensional and exhibit complex correlation structures. Generalized linear mixed models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the fixed and random effects in GLMMs is increasingly difficult in high dimensions, and computational complexity grows with increasing dimension of the random effects. We present a novel reformulation of the GLMM using a factor model decomposition of the random effects, enabling scalable computation of GLMMs in high dimensions by reducing the latent space from a large number of random effects to a smaller set of latent factors. We also extend our prior work to estimate model parameters using a modified Monte Carlo Expectation Conditional Minimization algorithm, allowing us to perform variable selection on both the fixed and random effects simultaneously. We show through simulation that through this factor model decomposition, our method can fit high-dimensional penalized GLMMs faster than comparable methods and more easily scale to larger dimensions not previously seen in existing approaches.

Rejoinder to the discussion on "LEAP: the latent exchangeability prior for borrowing information from historical data".

The discussions of our paper provide insights into the practical considerations of the latent exchangeability prior while also highlighting further extensions. In this rejoinder, we briefly summarize the discussions and provide comments.

LEAP: the latent exchangeability prior for borrowing information from historical data.

It is becoming increasingly popular to elicit informative priors on the basis of historical data. Popular existing priors, including the power prior, commensurate prior, and robust meta-analytic predictive prior, provide blanket discounting. Thus, if only a subset of participants in the historical data are exchangeable with the current data, these priors may not be appropriate. In order to combat this issue, propensity score approaches have been proposed. However, these approaches are only concerned with the covariate distribution, whereas exchangeability is typically assessed with parameters pertaining to the outcome. In this paper, we introduce the latent exchangeability prior (LEAP), where observations in the historical data are classified into exchangeable and non-exchangeable groups. The LEAP discounts the historical data by identifying the most relevant subjects from the historical data. We compare our proposed approach against alternative approaches in simulations and present a case study using our proposed prior to augment a control arm in a phase 3 clinical trial in plaque psoriasis with an unbalanced randomization scheme.

Safety signal detection with control of latent factors.

Postmarket drug safety database like vaccine adverse event reporting system (VAERS) collect thousands of spontaneous reports annually, with each report recording occurrences of any adverse events (AEs) and use of vaccines. We hope to identify signal vaccine-AE pairs, for which certain vaccines are statistically associated with certain adverse events (AE), using such data. Thus, the outcomes of interest are multiple AEs, which are binary outcomes and could be correlated because they might share certain latent factors; and the primary covariates are vaccines. Appropriately accounting for the complex correlation among AEs could improve the sensitivity and specificity of identifying signal vaccine-AE pairs. We propose a two-step approach in which we first estimate the shared latent factors among AEs using a working multivariate logistic regression model, and then use univariate logistic regression model to examine the vaccine-AE associations after controlling for the latent factors. Our simulation studies show that this approach outperforms current approaches in terms of sensitivity and specificity. We apply our approach in analyzing VAERS data and report our findings.

Clinical Outcomes Associated With Diltiazem Use in Heart Failure With Reduced Ejection Fraction After Implementation of a Clinical Support System.

BACKGROUND: Despite atrial fibrillation guideline recommendations, many patients with heart failure with reduced ejection fraction (EF) continue to receive IV diltiazem for acute rate control. OBJECTIVE: Our institution recently implemented a clinical decision support system (CDSS)-based tool that recommends against the use of diltiazem in patients with an EF ≤ 40%. The objective of this study was to evaluate outcomes of adherence to the aforementioned CDSS-based tool. METHODS: This multi-hospital, retrospective study assessed patients who triggered the CDSS alert and compared those who did and did not discontinue diltiazem. The primary outcome was the occurrence of clinical deterioration. The primary endpoint was compared utilizing a Fisher's Exact Test, and a multivariate logistic regression model was developed to confirm the results of the primary analysis. RESULTS: A total of 246 patients were included in this study with 146 patients in the nonadherent group (received diltiazem) and 100 patients in the adherent group (did not receive diltiazem). There was a higher proportion of patients experiencing clinical deterioration in the alert nonadherence group (33% vs 21%, P = 0.044), including increased utilization of inotropes and vasopressors, and higher rate of transfer to ICU. CONCLUSION AND RELEVANCE: In patients with heart failure with reduced EF, diltiazem use after nonadherence to a CDSS alert resulted in an increased risk of clinical deterioration. This study highlights the need for improved provider adherence to diltiazem clinical decision support systems.

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.

MRLocus: Identifying causal genes mediating a trait through Bayesian estimation of allelic heterogeneity.

Expression quantitative trait loci (eQTL) studies are used to understand the regulatory function of non-coding genome-wide association study (GWAS) risk loci, but colocalization alone does not demonstrate a causal relationship of gene expression affecting a trait. Evidence for mediation, that perturbation of gene expression in a given tissue or developmental context will induce a change in the downstream GWAS trait, can be provided by two-sample Mendelian Randomization (MR). Here, we introduce a new statistical method, MRLocus, for Bayesian estimation of the gene-to-trait effect from eQTL and GWAS summary data for loci with evidence of allelic heterogeneity, that is, containing multiple causal variants. MRLocus makes use of a colocalization step applied to each nearly-LD-independent eQTL, followed by an MR analysis step across eQTLs. Additionally, our method involves estimation of the extent of allelic heterogeneity through a dispersion parameter, indicating variable mediation effects from each individual eQTL on the downstream trait. Our method is evaluated against other state-of-the-art methods for estimation of the gene-to-trait mediation effect, using an existing simulation framework. In simulation, MRLocus often has the highest accuracy among competing methods, and in each case provides more accurate estimation of uncertainty as assessed through interval coverage. MRLocus is then applied to five candidate causal genes for mediation of particular GWAS traits, where gene-to-trait effects are concordant with those previously reported. We find that MRLocus's estimation of the causal effect across eQTLs within a locus provides useful information for determining how perturbation of gene expression or individual regulatory elements will affect downstream traits. The MRLocus method is implemented as an R package available at https://mikelove.github.io/mrlocus.

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.

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.

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 design of multi-regional clinical trials with time-to-event endpoints.

Sponsors often rely on multi-regional clinical trials (MRCTs) to introduce new treatments more rapidly into the global market. Many commonly used statistical methods do not account for regional differences, and small regional sample sizes frequently result in lower estimation quality of region-specific treatment effects. The International Council for Harmonization E17 guidelines suggest consideration of methods that allow for information borrowing across regions to improve estimation. In response to these guidelines, we develop a novel methodology to estimate global and region-specific treatment effects from MRCTs with time-to-event endpoints using Bayesian model averaging (BMA). This approach accounts for the possibility of heterogeneous treatment effects between regions, and we discuss how to assess the consistency of these effects using posterior model probabilities. We obtain posterior samples of the treatment effects using a Laplace approximation, and we show through simulation studies that the proposed modeling approach estimates region-specific treatment effects with lower mean squared error than a Cox proportional hazards model while resulting in a similar rejection rate of the global treatment effect. We then apply the BMA approach to data from the LEADER trial, an MRCT designed to evaluate the cardiovascular safety of an anti-diabetic treatment.

Estimating cell type composition using isoform expression one gene at a time.

Human tissue samples are often mixtures of heterogeneous cell types, which can confound the analyses of gene expression data derived from such tissues. The cell type composition of a tissue sample may itself be of interest and is needed for proper analysis of differential gene expression. A variety of computational methods have been developed to estimate cell type proportions using gene-level expression data. However, RNA isoforms can also be differentially expressed across cell types, and isoform-level expression could be equally or more informative for determining cell type origin than gene-level expression. We propose a new computational method, IsoDeconvMM, which estimates cell type fractions using isoform-level gene expression data. A novel and useful feature of IsoDeconvMM is that it can estimate cell type proportions using only a single gene, though in practice we recommend aggregating estimates of a few dozen genes to obtain more accurate results. We demonstrate the performance of IsoDeconvMM using a unique data set with cell type-specific RNA-seq data across more than 135 individuals. This data set allows us to evaluate different methods given the biological variation of cell type-specific gene expression data across individuals. We further complement this analysis with additional simulations.

Bayesian generalized linear low rank regression models for the detection of vaccine-adverse event associations.

We propose a generalized linear low-rank mixed model (GLLRM) for the analysis of both high-dimensional and sparse responses and covariates where the responses may be binary, counts, or continuous. This development is motivated by the problem of identifying vaccine-adverse event associations in post-market drug safety databases, where an adverse event is any untoward medical occurrence or health problem that occurs during or following vaccination. The GLLRM is a generalization of a generalized linear mixed model in that it integrates a factor analysis model to describe the dependence among responses and a low-rank matrix to approximate the high-dimensional regression coefficient matrix. A sampling procedure combining the Gibbs sampler and Metropolis and Gamerman algorithms is employed to obtain posterior estimates of the regression coefficients and other model parameters. Testing of response-covariate pair associations is based on the posterior distribution of the corresponding regression coefficients. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed procedures on binary and count outcomes. We further illustrate the GLLRM via a real data example based on the Vaccine Adverse Event Reporting System.

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.

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.