Bayesian-frequentist hybrid inference framework for single cell RNA-seq analyses.

BACKGROUND: Single cell RNA sequencing technology (scRNA-seq) has been proven useful in understanding cell-specific disease mechanisms. However, identifying genes of interest remains a key challenge. Pseudo-bulk methods that pool scRNA-seq counts in the same biological replicates have been commonly used to identify differentially expressed genes. However, such methods may lack power due to the limited sample size of scRNA-seq datasets, which can be prohibitively expensive. RESULTS: Motivated by this, we proposed to use the Bayesian-frequentist hybrid (BFH) framework to increase the power and we showed in simulated scenario, the proposed BFH would be an optimal method when compared with other popular single cell differential expression methods if both FDR and power were considered. As an example, the method was applied to an idiopathic pulmonary fibrosis (IPF) case study. CONCLUSION: In our IPF example, we demonstrated that with a proper informative prior, the BFH approach identified more genes of interest. Furthermore, these genes were reasonable based on the current knowledge of IPF. Thus, the BFH offers a unique and flexible framework for future scRNA-seq analyses.

A Bayesian platform trial design with hybrid control based on multisource exchangeability modelling.

Enrolling patients to the standard of care (SOC) arm in randomized clinical trials, especially for rare diseases, can be very challenging due to the lack of resources, restricted patient population availability, and ethical considerations. As the therapeutic effect for the SOC is often well documented in historical trials, we propose a Bayesian platform trial design with hybrid control based on the multisource exchangeability modelling (MEM) framework to harness historical control data. The MEM approach provides a computationally efficient method to formally evaluate the exchangeability of study outcomes between different data sources and allows us to make better informed data borrowing decisions based on the exchangeability between historical and concurrent data. We conduct extensive simulation studies to evaluate the proposed hybrid design. We demonstrate the proposed design leads to significant sample size reduction for the internal control arm and borrows more information compared to competing Bayesian approaches when historical and internal data are compatible.

Incorporating historical information to improve dose optimization design with toxicity and efficacy endpoints: iBOIN-ET.

In modern oncology drug development, adaptive designs have been proposed to identify the recommended phase 2 dose. The conventional dose finding designs focus on the identification of maximum tolerated dose (MTD). However, designs ignoring efficacy could put patients under risk by pushing to the MTD. Especially in immuno-oncology and cell therapy, the complex dose-toxicity and dose-efficacy relationships make such MTD driven designs more questionable. Additionally, it is not uncommon to have data available from other studies that target on similar mechanism of action and patient population. Due to the high variability from phase I trial, it is beneficial to borrow historical study information into the design when available. This will help to increase the model efficiency and accuracy and provide dose specific recommendation rules to avoid toxic dose level and increase the chance of patient allocation at potential efficacious dose levels. In this paper, we propose iBOIN-ET design that uses prior distribution extracted from historical studies to minimize the probability of decision error. The proposed design utilizes the concept of skeleton from both toxicity and efficacy data, coupled with prior effective sample size to control the amount of historical information to be incorporated. Extensive simulation studies across a variety of realistic settings are reported including a comparison of iBOIN-ET design to other model based and assisted approaches. The proposed novel design demonstrates the superior performances in percentage of selecting the correct optimal dose (OD), average number of patients allocated to the correct OD, and overdosing control during dose escalation process.

Using Prior Toxicological Data to Support Dose-Response Assessment─Identifying Plausible Prior Distributions for Dichotomous Dose-Response Models.

The benchmark dose (BMD) methodology has significantly advanced the practice of dose-response analysis and created substantial opportunities to enhance the plausibility of BMD estimation by synthesizing dose-response information from different sources. Particularly, integrating existing toxicological information via prior distribution in a Bayesian framework is a promising but not well-studied strategy. The study objective is to identify a plausible way to incorporate toxicological information through informative prior to support BMD estimation using dichotomous data. There are four steps in this study: determine appropriate types of distribution for parameters in common dose-response models, estimate the parameters of the determined distributions, investigate the impact of alternative strategies of prior implementation, and derive endpoint-specific priors to examine how prior-eliciting data affect priors and BMD estimates. A plausible distribution was estimated for each parameter in the common dichotomous dose-response models using a general database. Alternative strategies for implementing informative prior have a limited impact on BMD estimation, but using informative prior can significantly reduce uncertainty in BMD estimation. Endpoint-specific informative priors are substantially different from the general one, highlighting the necessity for guidance on prior elicitation. The study developed a practical way to employ informative prior and laid a foundation for advanced Bayesian BMD modeling.

Incorporating historical controls in clinical trials with longitudinal outcomes using the modified power prior.

Several dynamic borrowing methods, such as the modified power prior (MPP), the commensurate prior, have been proposed to increase statistical power and reduce the required sample size in clinical trials where comparable historical controls are available. Most methods have focused on cross-sectional endpoints, and appropriate methodology for longitudinal outcomes is lacking. In this study, we extend the MPP to the linear mixed model (LMM). An important question is whether the MPP should use the conditional version of the LMM (given the random effects) or the marginal version (averaged over the distribution of the random effects), which we refer to as the conditional MPP and the marginal MPP, respectively. We evaluated the MPP for one historical control arm via a simulation study and an analysis of the data of Alzheimer's Disease Cooperative Study (ADCS) with the commensurate prior as the comparator. The conditional MPP led to inflated type I error rate when there existed moderate or high between-study heterogeneity. The marginal MPP and the commensurate prior yielded a power gain (3.6%-10.4% vs. 0.6%-4.6%) with the type I error rates close to 5% (5.2%-6.2% vs. 3.8%-6.2%) when the between-study heterogeneity is not excessively high. For the ADCS data, all the borrowing methods improved the precision of estimates and provided the same clinical conclusions. The marginal MPP and the commensurate prior are useful for borrowing historical controls in longitudinal data analysis, while the conditional MPP is not recommended due to inflated type I error rates.

Estimating the effects of copy-number variants on intelligence using hierarchical Bayesian models.

It is challenging to estimate the phenotypic impact of the structural genome changes known as copy-number variations (CNVs), since there are many unique CNVs which are nonrecurrent, and most are too rare to be studied individually. In recent work, we found that CNV-aggregated genomic annotations, that is, specifically the intolerance to mutation as measured by the pLI score (probability of being loss-of-function intolerant), can be strong predictors of intellectual quotient (IQ) loss. However, this aggregation method only estimates the individual CNV effects indirectly. Here, we propose the use of hierarchical Bayesian models to directly estimate individual effects of rare CNVs on measures of intelligence. Annotation information on the impact of major mutations in genomic regions is extracted from genomic databases and used to define prior information for the approach we call HBIQ. We applied HBIQ to the analysis of CNV deletions and duplications from three datasets and identified several genomic regions containing CNVs demonstrating significant deleterious effects on IQ, some of which validate previously known associations. We also show that several CNVs were identified as deleterious by HBIQ even if they have a zero pLI score, and the converse is also true. Furthermore, we show that our new model yields higher out-of-sample concordance (78%) for predicting the consequences of carrying known recurrent CNVs compared with our previous approach.

Unit information prior for adaptive information borrowing from multiple historical datasets.

In clinical trials, there often exist multiple historical studies for the same or related treatment investigated in the current trial. Incorporating historical data in the analysis of the current study is of great importance, as it can help to gain more information, improve efficiency, and provide a more comprehensive evaluation of treatment. Enlightened by the unit information prior (UIP) concept in the reference Bayesian test, we propose a new informative prior called UIP from an information perspective that can adaptively borrow information from multiple historical datasets. We consider both binary and continuous data and also extend the new UIP to linear regression settings. Extensive simulation studies demonstrate that our method is comparable to other commonly used informative priors, while the interpretation of UIP is intuitive and its implementation is relatively easy. One distinctive feature of UIP is that its construction only requires summary statistics commonly reported in the literature rather than the patient-level data. By applying our UIP to phase III clinical trials for investigating the efficacy of memantine in Alzheimer's disease, we illustrate its ability to adaptively borrow information from multiple historical datasets. The Python codes for simulation studies and the real data application are available at https://github.com/JINhuaqing/UIP.

Improving efficiency in the stepped-wedge trial design via Bayesian modeling with an informative prior for the time effects.

BACKGROUND: In a cross-sectional stepped-wedge cluster randomized trial comparing usual care to a new intervention, treatment allocation and time are correlated by design because participants enrolled early in the trial predominantly receive usual care while those enrolled late in the trial predominantly receive the new intervention. Current guidelines recommend adjustment for time effects when analyzing stepped-wedge cluster randomized trials to remove the confounding bias induced by this correlation. However, adjustment for time effects impacts study power. Within the Frequentist framework, adopting a sample size calculation that includes time effects would ensure the trial having adequate power regardless of the magnitude of the effect of time on the outcome. But if in fact time effects were negligible, this would overestimate the required sample size and could lead to the trial being deemed infeasible due to cost or unavailability of the required numbers of clusters or participants. In this study, we explore the use of prior information on time effects to potentially reduce the required sample size of the trial. METHODS: We applied a Bayesian approach to incorporate the prior information on the time effects into cluster-level statistical models (for continuous, binary, or count outcomes) for the stepped-wedge cluster randomized trial. We conducted simulations to illustrate how the bias in the intervention effect estimate and the trial power vary as a function of the prior precision and the mis-specification of the prior means of the time effects in an example scenario. RESULTS: When a nearly flat prior for the time effects was used, the power or sample size calculated using the Bayesian approach matched the result obtained using the Frequentist approach with time effects included. When a highly precise prior for the time effects (with accurately specified prior means) was used, the Bayesian result matched the Frequentist result obtained with time effects excluded. When the prior means of the time effects were nearly correctly specified, including this information improved the efficiency of the trial with little bias introduced into the intervention effect estimate. When the prior means of the time effects were greatly mis-specified and a precise prior was used, this bias was substantial. CONCLUSION: Including prior information on time effects using a Bayesian approach may substantially reduce the required sample size. When the prior can be justified, results from applying this approach could support the conduct of a trial, which would be deemed infeasible if based on the larger sample size obtained using a Frequentist calculation. Caution is warranted as biased intervention effect estimates may arise when the prior distribution for the time effects is concentrated far from their true values.

A natural lead-in approach to response-adaptive allocation for continuous outcomes.

Response-adaptive (RA) allocation designs can skew the allocation of incoming subjects toward the better performing treatment group based on the previously accrued responses. While unstable estimators and increased variability can adversely affect adaptation in early trial stages, Bayesian methods can be implemented with decreasingly informative priors (DIP) to overcome these difficulties. DIPs have been previously used for binary outcomes to constrain adaptation early in the trial, yet gradually increase adaptation as subjects accrue. We extend the DIP approach to RA designs for continuous outcomes, primarily in the normal conjugate family by functionalizing the prior effective sample size to equal the unobserved sample size. We compare this effective sample size DIP approach to other DIP formulations. Further, we considered various allocation equations and assessed their behavior utilizing DIPs. Simulated clinical trials comparing the behavior of these approaches with traditional Frequentist and Bayesian RA as well as balanced designs show that the natural lead-in approaches maintain improved treatment with lower variability and greater power.

Discussion on "Predictively consistent prior effective sample sizes," by Beat Neuenschwander, Sebastian Weber, Heinz Schmidli, and Anthony O'Hagan.

Neuenschwander et al. address a seemingly easy but often complicated problem in applied Bayesian methodology. We discuss some issues that relate to the question of why one might care about the effective sample size ( ESS ) in a Bayesian model and the motivation for reporting the ESS .

Baseline Methods for Bayesian Inference in Gumbel Distribution.

Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.

Model averaging for robust extrapolation in evidence synthesis.

Extrapolation from a source to a target, eg, from adults to children, is a promising approach to utilize external information when data are sparse. In the context of meta-analyses, one is commonly faced with a small number of studies, whereas potentially relevant additional information may also be available. Here, we describe a simple extrapolation strategy using heavy-tailed mixture priors for effect estimation in meta-analysis, which effectively results in a model-averaging technique. The described method is robust in the sense that a potential prior-data conflict, ie, a discrepancy between source and target data, is explicitly anticipated. The aim of this paper is to develop a solution for this particular application to showcase the ease of implementation by providing R code, and to demonstrate the robustness of the general approach in simulations.

Informative priors on fetal fraction increase power of the noninvasive prenatal screen.

PURPOSE: Noninvasive prenatal screening (NIPS) sequences a mixture of the maternal and fetal cell-free DNA. Fetal trisomy can be detected by examining chromosomal dosages estimated from sequencing reads. The traditional method uses the Z-test, which compares a subject against a set of euploid controls, where the information of fetal fraction is not fully utilized. Here we present a Bayesian method that leverages informative priors on the fetal fraction. METHOD: Our Bayesian method combines the Z-test likelihood and informative priors of the fetal fraction, which are learned from the sex chromosomes, to compute Bayes factors. Bayesian framework can account for nongenetic risk factors through the prior odds, and our method can report individual positive/negative predictive values. RESULTS: Our Bayesian method has more power than the Z-test method. We analyzed 3,405 NIPS samples and spotted at least 9 (of 51) possible Z-test false positives. CONCLUSION: Bayesian NIPS is more powerful than the Z-test method, is able to account for nongenetic risk factors through prior odds, and can report individual positive/negative predictive values.

Bayesian methods for analysis of biosimilar phase III trials.

A biologic is a product made from living organisms. A biosimilar is a new version of an already approved branded biologic. Regulatory guidelines recommend a totality-of-the-evidence approach with stepwise development for a new biosimilar. Initial steps for biosimilar development are (a) analytical comparisons to establish similarity in structure and function followed by (b) potential animal studies and a human pharmacokinetics/pharmacodynamics equivalence study. The last step is a phase III clinical trial to confirm similar efficacy, safety, and immunogenicity between the biosimilar and the biologic. A high degree of analytical and pharmacokinetics/pharmacodynamics similarity could provide justification for an eased statistical threshold in the phase III trial, which could then further facilitate an overall abbreviated approval process for biosimilars. Bayesian methods can help in the analysis of clinical trials, by adding proper prior information into the analysis, thereby potentially decreasing required sample size. We develop proper prior information for the analysis of a phase III trial for showing that a proposed biosimilar is similar to a reference biologic. For the reference product, we use a meta-analysis of published results to set a prior for the probability of efficacy, and we propose priors for the proposed biosimilar informed by the strength of the evidence generated in the earlier steps of the approval process. A simulation study shows that with few exceptions, the Bayesian relative risk analysis provides greater power, shorter 90% credible intervals with more than 90% frequentist coverage, and better root mean squared error.

Informative prior distributions for ELISA analyses.

Immunoassays are capable of measuring very small concentrations of substances in solutions and have an immense range of application. Enzyme-linked immunosorbent assay (ELISA) tests in particular can detect the presence of an infection, of drugs, or hormones (as in the home pregnancy test). Inference of an unknown concentration via ELISA usually involves a non-linear heteroscedastic regression and subsequent prediction, which can be carried out in a Bayesian framework. For such a Bayesian inference, we are developing informative prior distributions based on extensive historical ELISA tests as well as theoretical considerations. One consideration regards the quality of the immunoassay leading to two practical requirements for the applicability of the priors. Simulations show that the additional prior information can lead to inferences which are robust to reasonable perturbations of the model and changes in the design of the data. On real data, the applicability is demonstrated across different laboratories, for different analytes and laboratory equipment as well as for previous and current ELISAs with sigmoid regression function. Consistency checks on real data (similar to cross-validation) underpin the adequacy of the suggested priors. Altogether, the new priors may improve concentration estimation for ELISAs that fulfill certain design conditions, by extending the range of the analyses, decreasing the uncertainty, or giving more robust estimates. Future use of these priors is straightforward because explicit, closed-form expressions are provided. This work encourages development and application of informative, yet general, prior distributions for other types of immunoassays.

On the prior distribution of extinction time.

Bayesian inference about the extinction of a species based on a record of its sightings requires the specification of a prior distribution for extinction time. Here, I critically review some specifications in the context of a specific model of the sighting record. The practical implication of the choice of prior distribution is illustrated through an application to the sighting record of the Caribbean monk seal.

Statistical considerations for a trial of Ebola virus disease therapeutics.

The 2014 West African outbreak of Ebola virus ravaged Liberia, Sierra Leone, and Guinea, causing hemorrhagic fever and death. The need to identify effective therapeutics was acute. The usual drug development paradigm of phase I, followed by phase II, and then phase III trials would take too long. These and other factors led to the design of a clinical trial of Ebola virus disease therapeutics that differs from more conventional clinical trial designs. This article describes the Ebola virus disease medical countermeasures trial design and the thinking behind it.

Using Bayesian analysis in repeated preclinical in vivo studies for a more effective use of animals.

Whilst innovative Bayesian approaches are increasingly used in clinical studies, in the preclinical area Bayesian methods appear to be rarely used in the reporting of pharmacology data. This is particularly surprising in the context of regularly repeated in vivo studies where there is a considerable amount of data from historical control groups, which has potential value. This paper describes our experience with introducing Bayesian analysis for such studies using a Bayesian meta-analytic predictive approach. This leads naturally either to an informative prior for a control group as part of a full Bayesian analysis of the next study or using a predictive distribution to replace a control group entirely. We use quality control charts to illustrate study-to-study variation to the scientists and describe informative priors in terms of their approximate effective numbers of animals. We describe two case studies of animal models: the lipopolysaccharide-induced cytokine release model used in inflammation and the novel object recognition model used to screen cognitive enhancers, both of which show the advantage of a Bayesian approach over the standard frequentist analysis. We conclude that using Bayesian methods in stable repeated in vivo studies can result in a more effective use of animals, either by reducing the total number of animals used or by increasing the precision of key treatment differences. This will lead to clearer results and supports the "3Rs initiative" to Refine, Reduce and Replace animals in research. Copyright © 2016 John Wiley & Sons, Ltd.

Addressing potential prior-data conflict when using informative priors in proof-of-concept studies.

Bayesian methods are increasingly used in proof-of-concept studies. An important benefit of these methods is the potential to use informative priors, thereby reducing sample size. This is particularly relevant for treatment arms where there is a substantial amount of historical information such as placebo and active comparators. One issue with using an informative prior is the possibility of a mismatch between the informative prior and the observed data, referred to as prior-data conflict. We focus on two methods for dealing with this: a testing approach and a mixture prior approach. The testing approach assesses prior-data conflict by comparing the observed data to the prior predictive distribution and resorting to a non-informative prior if prior-data conflict is declared. The mixture prior approach uses a prior with a precise and diffuse component. We assess these approaches for the normal case via simulation and show they have some attractive features as compared with the standard one-component informative prior. For example, when the discrepancy between the prior and the data is sufficiently marked, and intuitively, one feels less certain about the results, both the testing and mixture approaches typically yield wider posterior-credible intervals than when there is no discrepancy. In contrast, when there is no discrepancy, the results of these approaches are typically similar to the standard approach. Whilst for any specific study, the operating characteristics of any selected approach should be assessed and agreed at the design stage; we believe these two approaches are each worthy of consideration.

The power prior: theory and applications.

The power prior has been widely used in many applications covering a large number of disciplines. The power prior is intended to be an informative prior constructed from historical data. It has been used in clinical trials, genetics, health care, psychology, environmental health, engineering, economics, and business. It has also been applied for a wide variety of models and settings, both in the experimental design and analysis contexts. In this review article, we give an A-to-Z exposition of the power prior and its applications to date. We review its theoretical properties, variations in its formulation, statistical contexts for which it has been used, applications, and its advantages over other informative priors. We review models for which it has been used, including generalized linear models, survival models, and random effects models. Statistical areas where the power prior has been used include model selection, experimental design, hierarchical modeling, and conjugate priors. Frequentist properties of power priors in posterior inference are established, and a simulation study is conducted to further examine the empirical performance of the posterior estimates with power priors. Real data analyses are given illustrating the power prior as well as the use of the power prior in the Bayesian design of clinical trials.