Adaptive treatment allocation and selection in multi-arm clinical trials: a Bayesian perspective.

BACKGROUND: Adaptive designs offer added flexibility in the execution of clinical trials, including the possibilities of allocating more patients to the treatments that turned out more successful, and early stopping due to either declared success or futility. Commonly applied adaptive designs, such as group sequential methods, are based on the frequentist paradigm and on ideas from statistical significance testing. Interim checks during the trial will have the effect of inflating the Type 1 error rate, or, if this rate is controlled and kept fixed, lowering the power. RESULTS: The purpose of the paper is to demonstrate the usefulness of the Bayesian approach in the design and in the actual running of randomized clinical trials during phase II and III. This approach is based on comparing the performance of the different treatment arms in terms of the respective joint posterior probabilities evaluated sequentially from the accruing outcome data, and then taking a control action if such posterior probabilities fall below a pre-specified critical threshold value. Two types of actions are considered: treatment allocation, putting on hold at least temporarily further accrual of patients to a treatment arm, and treatment selection, removing an arm from the trial permanently. The main development in the paper is in terms of binary outcomes, but extensions for handling time-to-event data, including data from vaccine trials, are also discussed. The performance of the proposed methodology is tested in extensive simulation experiments, with numerical results and graphical illustrations documented in a Supplement to the main text. As a companion to this paper, an implementation of the methods is provided in the form of a freely available R package 'barts'. CONCLUSION: The proposed methods for trial design provide an attractive alternative to their frequentist counterparts.

Predictive Bayesian inference and dynamic treatment regimes.

While optimal dynamic treatment regimes (DTRs) can be estimated without specification of a predictive model, a model-based approach, combined with dynamic programming and Monte Carlo integration, enables direct probabilistic comparisons between the outcomes under the optimal DTR and alternative (dynamic or static) treatment regimes. The Bayesian predictive approach also circumvents problems related to frequentist estimators under the nonregular estimation problem. However, the model-based approach is susceptible to misspecification, in particular of the "null-paradox" type, which is due to the model parameters not having a direct causal interpretation in the presence of latent individual-level characteristics. Because it is reasonable to insist on correct inferences under the null of no difference between the alternative treatment regimes, we discuss how to achieve this through a "null-robust" reparametrization of the problem in a longitudinal setting. Since we argue that causal inference can be entirely understood as posterior predictive inference in a hypothetical population without covariate imbalances, we also discuss how controlling for confounding through inverse probability of treatment weighting can be justified and incorporated in the Bayesian setting.

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective.

This paper was inspired by the studies of Niels Keiding and co-authors on estimating the waiting time-to-pregnancy (TTP) distribution, and in particular on using the current duration design in that context. In this design, a cross-sectional sample of women is collected from those who are currently attempting to become pregnant, and then by recording from each the time she has been attempting. Our aim here is to study the identifiability and the estimation of the waiting time distribution on the basis of current duration data. The main difficulty in this stems from the fact that very short waiting times are only rarely selected into the sample of current durations, and this renders their estimation unstable. We introduce here a Bayesian method for this estimation problem, prove its asymptotic consistency, and compare the method to some variants of the non-parametric maximum likelihood estimators, which have been used previously in this context. The properties of the Bayesian estimation method are studied also empirically, using both simulated data and TTP data on current durations collected by Slama et al. (Hum Reprod 27(5):1489-1498, 2012).

Transcriptomic pan-cancer analysis using rank-based Bayesian inference.

The analysis of whole genomes of pan-cancer data sets provides a challenge for researchers, and we contribute to the literature concerning the identification of robust subgroups with clear biological interpretation. Specifically, we tackle this unsupervised problem via a novel rank-based Bayesian clustering method. The advantages of our method are the integration and quantification of all uncertainties related to both the input data and the model, the probabilistic interpretation of final results to allow straightforward assessment of the stability of clusters leading to reliable conclusions, and the transparent biological interpretation of the identified clusters since each cluster is characterized by its top-ranked genomic features. We applied our method to RNA-seq data from cancer samples from 12 tumor types from the Cancer Genome Atlas. We identified a robust clustering that mostly reflects tissue of origin but also includes pan-cancer clusters. Importantly, we identified three pan-squamous clusters composed of a mix of lung squamous cell carcinoma, head and neck squamous carcinoma, and bladder cancer, with different biological functions over-represented in the top genes that characterize the three clusters. We also found two novel subtypes of kidney cancer that show different prognosis, and we reproduced known subtypes of breast cancer. Taken together, our method allows the identification of robust and biologically meaningful clusters of pan-cancer samples.

Bayesian integrated modeling of expression data: a case study on RhoG.

BACKGROUND: DNA microarrays provide an efficient method for measuring activity of genes in parallel and even covering all the known transcripts of an organism on a single array. This has to be balanced against that analyzing data emerging from microarrays involves several consecutive steps, and each of them is a potential source of errors. Errors tend to accumulate when moving from the lower level towards the higher level analyses because of the sequential nature. Eliminating such errors does not seem feasible without completely changing the technologies, but one should nevertheless try to meet the goal of being able to realistically assess degree of the uncertainties that are involved when drawing the final conclusions from such analyses. RESULTS: We present a Bayesian hierarchical model for finding differentially expressed genes between two experimental conditions, proposing an integrated statistical approach where correcting signal saturation, systematic array effects, dye effects, and finding differentially expressed genes, are all modeled jointly. The integration allows all these components, and also the associated errors, to be considered simultaneously. The inference is based on full posterior distribution of gene expression indices and on quantities derived from them rather than on point estimates. The model was applied and tested on two different datasets. CONCLUSIONS: The method presents a way of integrating various steps of microarray analysis into a single joint analysis, and thereby enables extracting information on differential expression in a manner, which properly accounts for various sources of potential error in the process.

Bayesian methods for analyzing movements in heterogeneous landscapes from mark-recapture data.

Spatially referenced mark-recapture data are becoming increasingly available, but the analysis of such data has remained difficult for a variety of reasons. One of the fundamental problems is that it is difficult to disentangle inherent movement behavior from sampling artifacts. For example, in a typical study design, short distances are sampled more frequently than long distances. Here we present a modeling-based alternative that combines a diffusion-based process model with an observation model to infer the inherent movement behavior of the species from the data. The movement model is based on classifying the landscape into a number of habitat types, and assuming habitat-specific diffusion and mortality parameters, and habitat selection at edges between the habitat types. As the problem is computationally highly intensive, we provide software that implements adaptive Bayesian methods for effective sampling of the posterior distribution. We illustrate the modeling framework by analyzing individual mark-recapture data on the Glanville fritillary butterfly (Melitaea cinxia), and by comparing our results with earlier ones derived from the same data using a purely statistical approach. We use simulated data to perform an analysis of statistical power, examining how accuracy in parameter estimates depends on the amount of data and on the study design. Obtaining precise estimates for movement rates and habitat preferences turns out to be especially challenging, as these parameters can be highly correlated in the posterior density. We show that the parameter estimates can be considerably improved by alternative study designs, such as releasing some of the individuals into the unsuitable matrix, or spending part of the recapture effort in the matrix.

Estimating genealogies from linked marker data: a Bayesian approach.

BACKGROUND: Answers to several fundamental questions in statistical genetics would ideally require knowledge of the ancestral pedigree and of the gene flow therein. A few examples of such questions are haplotype estimation, relatedness and relationship estimation, gene mapping by combining pedigree and linkage disequilibrium information, and estimation of population structure. RESULTS: We present a probabilistic method for genealogy reconstruction. Starting with a group of genotyped individuals from some population isolate, we explore the state space of their possible ancestral histories under our Bayesian model by using Markov chain Monte Carlo (MCMC) sampling techniques. The main contribution of our work is the development of sampling algorithms in the resulting vast state space with highly dependent variables. The main drawback is the computational complexity that limits the time horizon within which explicit reconstructions can be carried out in practice. CONCLUSION: The estimates for IBD (identity-by-descent) and haplotype distributions are tested in several settings using simulated data. The results appear to be promising for a further development of the method.

Bayesian hierarchical model for correcting signal saturation in microarrays using pixel intensities.

Pixel saturation occurs when the pixel intensity exceeds the scanner upper threshold of detection and the recorded pixel intensity is then truncated at the threshold. Truncation of the pixel intensity causes the estimates of gene expression (i.e., intensity) to be biased. Microarray experiments are commonly affected by saturated pixels; as a result all higher level analyses are made on these biased gene expression estimates. In this paper, we propose a method for improving the quality of the signal for cDNA microarrays by making use of several scans at varying scanner sensitivities. For each spot, pixel level intensity readings are given as input to a Bayesian hierarchical model. The model uses the pixel intensities of the spot to provide a posterior distribution of the true expression level of the corresponding genes. The parameters of the hierarchical model are estimated jointly with these expression levels, thus performing an integrated analysis of the measurement data. The method improves in all ranges the accuracy with which intensities can be estimated and extends the dynamic range of measured gene expression at the high end. The method is generic and can be applied to data from any organism and for imaging with any scanner. Results from a real data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan.

Estimating efficacy in the presence of non-ignorable non-trial interventions in the Helsinki Psychotherapy Study.

In a randomised clinical trial with a longitudinal outcome, analyses of the efficacy of the study treatments may be complicated by both non-trial interventions, which have not been administered by the researcher, and sparsely measured outcome values. The delay between the change in outcome and the starting of the non-trial intervention may be much shorter than the time intervals between the actual measurements. We propose a model that accounts for the possible dynamic interdependence between the longitudinal outcome and time-to-event data. The model is based on discretising time into short intervals. This results in a missing data problem, which we tackle using Bayesian inference and data augmentation. The method is based on the assumption that decisions to initiate non-trial interventions are not confounded by unobservable factors. The Helsinki Psychotherapy Study data are used as an illustration. Different psychotherapies were compared, and possible episodes of psychotropic medication were viewed as non-trial interventions. Simulation studies suggest that our method provides reasonable estimates of the effects of both the study treatment and the non-trial intervention also showing some robustness against possible latent background factors. An application of marginal structural modelling, however, appeared to underestimate the differences between the treatments.

Work ability index and perceived work ability as predictors of disability pension: a prospective study among Finnish municipal employees.

OBJECTIVES: We analyzed the work ability index (WAI) and its first item (work ability score, WAS) - and subsequent four-year changes thereof - as predictors of disability pension (DP). METHODS: We linked survey responses of 5251 Finnish municipal employees, aged 44-58 years, to pension and death register data until 2009. Job content (physical, mental, or mixed) was based on observation. Baseline (1981) WAI was divided into poor (<27), moderate (28-36), and good/excellent (>37) and WAS into poor (0-5), moderate (6-7), and good/excellent (8-10). Four-year changes in these scores were classified as strong decline (

Increasing incidence of Type 1 diabetes--role for genes?

BACKGROUND: The incidence of Type 1 diabetes (T1DM) is increasing fast in many populations. The reasons for this are not known, although an increase in the penetrance of the diabetes-associated alleles, through changes in the environment, might be the most plausible mechanism. After the introduction of insulin treatment in 1930s, an increase in the pool of genetically susceptible individuals has been suggested to contribute to the increase in the incidence of Type 1 diabetes. RESULTS: To explore this hypothesis, the authors formulate a simple population genetic model for the incidence change driven by non-Mendelian transmission of a single susceptibility factor, either allele(s) or haplotype(s). A Poisson mixture model is used to model the observed number of cases. Model parameters were estimated by maximizing the log-likelihood function. Based on the Finnish incidence data 1965-1996 the point estimate of the transmission probability was 0.998. Given our current knowledge of the penetrance of the most diabetic gene variants in the HLA region and their transmission probabilities, this value is exceedingly unrealistic. CONCLUSIONS: As a consequence, non-Mendelian transmission of diabetic allele(s)/haplotype(s) if present, could explain only a small part of the increase in incidence in Finland. Hence, the importance of other, probably environmental factors modifying the disease incidence is emphasized.

Optimal dynamic regimes: presenting a case for predictive inference.

Dynamic treatment regime is a decision rule in which the choice of the treatment of an individual at any given time can depend on the known past history of that individual, including baseline covariates, earlier treatments, and their measured responses. In this paper we argue that finding an optimal regime can, at least in moderately simple cases, be accomplished by a straightforward application of nonparametric Bayesian modeling and predictive inference. As an illustration we consider an inference problem in a subset of the Multicenter AIDS Cohort Study (MACS) data set, studying the effect of AZT initiation on future CD4-cell counts during a 12-month follow-up.

Evolution of the capsular regulatory genes in Streptococcus pneumoniae.

The major pneumococcal virulence determinant is its capsule, and pneumococcal epidemiology is based on 91 capsular serotypes, each corresponding to the structure of the capsular polysaccharide determined by the type-specific capsular genome. Here, we provide the beginnings of an approach to intertwine serotype epidemiology, capsular regulatory gene characteristics on the basis of existing sequence information, and the reanalysis of published epidemiological data. We present an approach to explain epidemiological characteristics of serotypes on the basis of genetic differences in their capsular regulatory genes. The part of the capsular genome that regulates capsular expression falls into 2 highly divergent sequence clans: the ancestral pneumococcal capsular regulatory gene sequences (present in 49 serotypes) and laterally transferred sequences (present in 32 serotypes). Our survey of epidemiological data showed a tendency of the ancestral type of the capsular regulatory genome to be associated with carriage and the laterally transferred sequences to be associated with invasive disease isolates. The regulatory gene region shows mosaic structures that have signatures of recent recombination events, reminiscent of structures known from antibiotic resistance genes.

Bayesian quantitative trait locus mapping based on reconstruction of recent genetic histories.

We assume that quantitative measurements on a considered trait and unphased genotype data at certain marker loci are available on a sample of individuals from a background population. Our goal is to map quantitative trait loci by using a Bayesian model that performs, and makes use of, probabilistic reconstructions of the recent unobserved genealogical history (a pedigree and a gene flow at the marker loci) of the sampled individuals. This work extends variance component-based linkage analysis to settings where the unobserved pedigrees are considered as latent variables. In addition to the measured trait values and unphased genotype data at the marker loci, the method requires as an input estimates of the population allele frequencies and of a marker map, as well as some parameters related to the population size and the mating behavior. Given such data, the posterior distribution of the trait parameters (the number, the locations, and the relative variance contributions of the trait loci) is studied by using the reversible-jump Markov chain Monte Carlo methodology. We also introduce two shortcuts related to the trait parameters that allow us to do analytic integration, instead of stochastic sampling, in some parts of the algorithm. The method is tested on two simulated data sets. Comparisons with traditional variance component linkage analysis and association analysis demonstrate the benefits of our approach in a gene mapping context.

A Naive Bayes classifier for protein function prediction.

A Naive Bayes classifier tool is presented for annotating proteins on the basis of amino acid motifs, cellular localization and protein-protein interactions. Annotations take the form of posterior probabilities within the Molecular Function hierarchy of the Gene Ontology (GO). Experiments with the data available for yeast, Saccharomyces cerevisiae, show that our prediction method can yield a relatively high level of accuracy. Several apparent challenges and possibilities for future developments are also discussed. A common approach to functional characterization is to use sequence similarities at varying levels, by utilizing several existing databases and local alignment/identification algorithms. Such an approach is typically quite labor-intensive when performed by an expert in a manual fashion. Integration of several sources of information is in this context generally considered as the only possibility to obtain valuable predictions with practical implications. However, some improvements in the prediction accuracy of the molecular functions, and thereby also savings in the computational effort, can be achieved by restricting attention to only those data sources that involve a higher degree of specificity. We employ here a Naive Bayes model in order to provide probabilistic predictions, and to enable a computationally efficient approach to data integration.

Full likelihood analysis of genetic risk with variable age at onset disease--combining population-based registry data and demographic information.

BACKGROUND: In genetic studies of rare complex diseases it is common to ascertain familial data from population based registries through all incident cases diagnosed during a pre-defined enrollment period. Such an ascertainment procedure is typically taken into account in the statistical analysis of the familial data by constructing either a retrospective or prospective likelihood expression, which conditions on the ascertainment event. Both of these approaches lead to a substantial loss of valuable data. METHODOLOGY AND FINDINGS: Here we consider instead the possibilities provided by a Bayesian approach to risk analysis, which also incorporates the ascertainment procedure and reference information concerning the genetic composition of the target population to the considered statistical model. Furthermore, the proposed Bayesian hierarchical survival model does not require the considered genotype or haplotype effects be expressed as functions of corresponding allelic effects. Our modeling strategy is illustrated by a risk analysis of type 1 diabetes mellitus (T1D) in the Finnish population-based on the HLA-A, HLA-B and DRB1 human leucocyte antigen (HLA) information available for both ascertained sibships and a large number of unrelated individuals from the Finnish bone marrow donor registry. The heterozygous genotype DR3/DR4 at the DRB1 locus was associated with the lowest predictive probability of T1D free survival to the age of 15, the estimate being 0.936 (0.926; 0.945 95% credible interval) compared to the average population T1D free survival probability of 0.995. SIGNIFICANCE: The proposed statistical method can be modified to other population-based family data ascertained from a disease registry provided that the ascertainment process is well documented, and that external information concerning the sizes of birth cohorts and a suitable reference sample are available. We confirm the earlier findings from the same data concerning the HLA-DR3/4 related risks for T1D, and also provide here estimated predictive probabilities of disease free survival as a function of age.

Nested case-control data utilized for multiple outcomes: a likelihood approach and alternatives.

Suppose a nested case-control design has been applied for collecting covariate data when studying a specific disease. With possible new outcomes of interest it would be sensible to utilize the previously selected control group instead of (or in addition to) a new control selection, given that the same covariate data were relevant and available, and that their measurements had adequate stability and quality. We formulate this problem in the framework of the competing risks survival model. In this approach covariate information collected for all outcomes can be utilized in the analysis. We not only propose likelihood-based parameter estimation but we also review alternative methods based on weighted partial/pseudolikelihoods. The methods discussed here are closely related to the analysis of a case-cohort design, where the control group is not tied to cases of a specific disease. The different methods are compared in a simulation study.

Bayesian hierarchical model for estimating gene expression intensity using multiple scanned microarrays.

We propose a method for improving the quality of signal from DNA microarrays by using several scans at varying scanner sensitivities. A Bayesian latent intensity model is introduced for the analysis of such data. The method improves the accuracy at which expressions can be measured in all ranges and extends the dynamic range of measured gene expression at the high end. Our method is generic and can be applied to data from any organism, for imaging with any scanner that allows varying the laser power, and for extraction with any image analysis software. Results from a self-self hybridization data set illustrate an improved precision in the estimation of the expression of genes compared to what can be achieved by applying standard methods and using only a single scan.

Estimating genealogies from unlinked marker data: a Bayesian approach.

An issue often encountered in statistical genetics is whether, or to what extent, it is possible to estimate the degree to which individuals sampled from a background population are related to each other, on the basis of the available genotype data and some information on the demography of the population. In this article, we consider this question using explicit modelling of the pedigrees and gene flows at unlinked marker loci, but then restricting ourselves to a relatively recent history of the population, that is, considering the genealogy at most some tens of generations backwards in time. As a computational tool we use a Markov chain Monte Carlo numerical integration on the state space of genealogies of the sampled individuals. As illustrations of the method, we consider the question of relatedness at the level of genes/genomes (IBD estimation), using both simulated and real data.