A Bayesian basket trial design that borrows information across strata based on the similarity between the posterior distributions of the response probability

Basket trials simultaneously evaluate the effect of one or more drugs on a defined biomarker, genetic alteration, or molecular target in a variety of disease subtypes, often called strata. A conventional approach for analyzing such trials is an independent analysis of each of the strata. This analysis is inefficient as it lacks the power to detect the effect of drugs in each stratum. To address these issues, various designs for basket trials have been proposed, centering on designs using Bayesian hierarchical models. In this article, we propose a novel Bayesian basket trial design that incorporates predictive sample size determination, early termination for inefficacy and efficacy, and the borrowing of information across strata. The borrowing of information is based on the similarity between the posterior distributions of the response probability. In general, Bayesian hierarchical models have many distributional assumptions along with multiple parameters. By contrast, our method has prior distributions for response probability and two parameters for similarity of distributions. The proposed design is easier to implement and less computationally demanding than other Bayesian basket designs. Through a simulation with various scenarios, our proposed design is compared with other designs including one that does not borrow information and one that uses a Bayesian hierarchical model.     

Comparing two methods of calculating the probability of absence: the Negative Predictive Value, and a Credible Interval

If sampling fails to reveal the presence of an invasive species with potential to actually be present, how may we calculate the probability that it is truly absent, e.g. didymo (Didymosphenia geminate) in New Zealand’s North Island. In statistical terms this is a Bayesian question, concerning the probability of a hypothesis (presence/absence), given the obtained data (all results negative). “Classical” theory doesn’t answer this question, because it inverts the required considerations by calculating the probability of all samples being absent if the invasive was actually present. Accordingly, the Bayesian view of “probability” must be adopted in order to answer the question. That definition differs from classical probability in that it always includes an element of subjective belief, particularly in the choice of an appropriate “prior probability” (this is our belief as to the presence of the invasive organism before collecting new data). Bayesian methods can therefore be somewhat controversial – but we seem forced to use them. One Bayesian approach is to use the “Negative Predictive Value”, in which a point estimate of the probability of presence (or absence) prior to sample collection (the “prior probability”) is updated using data once collected using Bayes’ rule. This is in common use in medical studies, where the prior probability is the background disease prevalence, which is generally well understood. It is sometimes used in environmental ‘hot-spot’ investigations. An alternative approach is to recognise the uncertainty in the prior belief by using a distribution of prior probability and updating that using data once collected to give a Credible Interval in which the probability of presence (or absence) should lie – if all our assumptions have been satisfied. We will compare the merits of these approaches considering didymo, southern salt marsh mosquito (Aedes camptorhychus) and the sea squirt Styela clava.     

Exact sample size determination for a single Poisson random sample

Classical power analysis for sample size determination is typically performed in clinical trials. A “hybrid” classical Bayesian or a “fully Bayesian” approach can be alternatively used in order to add flexibility to the design assumptions needed at the planning stage of the study and to explicitly incorporate prior information in the procedure. In this paper, we exploit and compare these approaches to obtain the optimal sample size of a single-arm trial based on Poisson data. We adopt exact methods to establish the rejection of the null hypothesis within a frequentist or a Bayesian perspective and suggest the use of a conservative criterion for sample size determination that accounts for the not strictly monotonic behavior of the power function in the presence of discrete data. A Shiny web app in R has been developed to provide a user-friendly interface to easily compute the optimal sample size according to the proposed criteria and to assure the reproducibility of the results.     

Comparison of Fluorescent Antibody with Cultural Technique for Isolation of Enteropathogenic Escherichia coli from Swine

In an investigation of hogs as possible reservoirs of human strains of enteropathogenic Escherichia coli (EEC), 92 six-month-old grain- and garbage-fed hogs were examined on the farm and again at the packing plant. Of the 331 specimens obtained by swabbing the rectum, cecum, and edible meat carcass of these hogs, 125 were presumptively positive for EEC when screened by the fluorescent-antibody (FA) technique. These “presumptive positive” specimens then underwent extensive bacteriological examination and complete serological typing. The FA technique proved to be an easier, simpler, and more economical procedure than culture when a large number of specimens were examined for possible EEC serogroups. It was found especially valuable for identification of multiple serogroups of EEC within a single specimen. It also appeared to be more sensitive than cultural examination, since results were not dependent on the presence of large numbers of organisms in the specimen, or even on their viability. However, the FA technique was found to be less specific than culture because of cross-reactivity with antigenically related Enterobacteriaceae when fluorescein-labeled antisera were used. Therefore, any specimen found positive on FA examination should be considered as presumptive positive until confirmed by bacteriological examination and complete serological study.     

A novel c.1037C > G (p.Ala346Gly) mutation in TP63 as cause of the ectrodactyly-ectodermal dysplasia and cleft lip/palate (EEC) syndrome

Ectrodactyly – ectodermal dysplasia and cleft lip/palate (EEC) syndrome (OMIM 604292) is a rare disorder determined by mutations in the TP63 gene. Most cases of EEC syndrome are associated to mutations in the DNA binding domain (DBD) region of the p63 protein. Here we report on a three-generation Brazilian family with three individuals (mother, son and grandfather) affected by EEC syndrome, determined by a novel mutation c.1037C > G (p.Ala346Gly). The disorder in this family exhibits a broad spectrum of phenotypes: two individuals were personally examined, one presenting the complete constellation of EEC syndrome manifestations and the other presenting an intermediate phenotype; the third affected, a deceased individual not examined personally and referred to by his daughter, exhibited only the split-hand/foot malformation (SHFM). Our findings contribute to elucidate the complex phenotype-genotype correlations in EEC syndrome and other related TP63-mutation syndromes. The possibility of the mutation c.1037C > G being related both to acro-dermato-ungual-lacrimal-tooth (ADULT) syndrome and SHFM is also raised by the findings here reported.     

Incorporating prior knowledge induced from stochastic differential equations in the classification of stochastic observations

In classification, prior knowledge is incorporated in a Bayesian framework by assuming that the feature-label distribution belongs to an uncertainty class of feature-label distributions governed by a prior distribution. A posterior distribution is then derived from the prior and the sample data. An optimal Bayesian classifier (OBC) minimizes the expected misclassification error relative to the posterior distribution. From an application perspective, prior construction is critical. The prior distribution is formed by mapping a set of mathematical relations among the features and labels, the prior knowledge, into a distribution governing the probability mass across the uncertainty class. In this paper, we consider prior knowledge in the form of stochastic differential equations (SDEs). We consider a vector SDE in integral form involving a drift vector and dispersion matrix. Having constructed the prior, we develop the optimal Bayesian classifier between two models and examine, via synthetic experiments, the effects of uncertainty in the drift vector and dispersion matrix. We apply the theory to a set of SDEs for the purpose of differentiating the evolutionary history between two species.     

A comparison study of optimal and suboptimal intervention policies for gene regulatory networks in the presence of uncertainty

Perfect knowledge of the underlying state transition probabilities is necessary for designing an optimal intervention strategy for a given Markovian genetic regulatory network. However, in many practical situations, the complex nature of the network and/or identification costs limit the availability of such perfect knowledge. To address this difficulty, we propose to take a Bayesian approach and represent the system of interest as an uncertainty class of several models, each assigned some probability, which reflects our prior knowledge about the system. We define the objective function to be the expected cost relative to the probability distribution over the uncertainty class and formulate an optimal Bayesian robust intervention policy minimizing this cost function. The resulting policy may not be optimal for a fixed element within the uncertainty class, but it is optimal when averaged across the uncertainly class. Furthermore, starting from a prior probability distribution over the uncertainty class and collecting samples from the process over time, one can update the prior distribution to a posterior and find the corresponding optimal Bayesian robust policy relative to the posterior distribution. Therefore, the optimal intervention policy is essentially nonstationary and adaptive.     

Characterization of the arabinogalactan protein 31 (AGP31) of Arabidopsis thaliana: new advances on the Hyp-O-glycosylation of the Pro-rich domain

Proteins are important actors in plant cell walls because they contribute to their architecture and their dynamics. Among them, hydroxyproline (Hyp)-rich glycoproteins constitute a complex family of O-glycoproteins with various structures and functions. In this study, we characterized an atypical Hyp-rich glycoprotein, AGP31 (arabinogalactan protein 31), which displays a multidomain organization unique in Arabidopsis thaliana, consisting of a short arabinogalactan protein (AGP) motif, a His stretch, a Pro-rich domain, and a C-terminal PAC (PRP-AGP containing Cys) domain. The use of various mass spectrometry strategies was innovative and powerful: it permitted us to locate Hyp residues, to demonstrate the presence of carbohydrates, and to refine their distribution over the Pro-rich domain. Most Hyp were isolated within repeated motifs such as KAOV, KSOV, K(PO/OP)T, K(PO/OP)V, T(PO/OP)V, and Y(PO/OP)T. A few extensin-like motifs with contiguous Hyp (SOOA and SOOT) were also found. The Pro-rich domain was shown to carry Gal residues on isolated Hyp but also Ara residues. The existence of new type Hyp-O-Gal/Ara-rich motifs not recognized by the β-glucosyl Yariv reagent but interacting with the peanut agglutinin lectin was proposed. In addition, the N-terminal short AGP motif was assumed to be substituted by arabinogalactans. Altogether, AGP31 was found to be highly heterogeneous in cell walls because arabinogalactans could be absent, Hyp-O-Gal/Ara-rich motifs of different sizes were observed, and truncated forms missing the C-terminal PAC domain were found, suggesting degradation in muro and/or partial glycosylation prior to secretion.     

Bayesian nonparametric analysis of restricted mean survival time

The restricted mean survival time (RMST) evaluates the expectation of survival time truncated by a prespecified time point, because the mean survival time in the presence of censoring is typically not estimable. The frequentist inference procedure for RMST has been widely advocated for comparison of two survival curves, while research from the Bayesian perspective is rather limited. For the RMST of both right- and interval-censored data, we propose Bayesian nonparametric estimation and inference procedures. By assigning a mixture of Dirichlet processes (MDP) prior to the distribution function, we can estimate the posterior distribution of RMST. We also explore another Bayesian nonparametric approach using the Dirichlet process mixture model and make comparisons with the frequentist nonparametric method. Simulation studies demonstrate that the Bayesian nonparametric RMST under diffuse MDP priors leads to robust estimation and under informative priors it can incorporate prior knowledge into the nonparametric estimator. Analysis of real trial examples demonstrates the flexibility and interpretability of the Bayesian nonparametric RMST for both right- and interval-censored data.     

Construction of a tissue microarray with two millimeters cores of endometrioid endometrial cancer: factors affecting the quality of the recipient block

The tissue microarray (TMA) method currently is not used to render a primary diagnosis of cancer, but its scientific value has been proved in studies of various cancer types. TMA technology still is not used often for uterine tumors, however. We investigated the repeatability of histological diagnosis of endometrioid endometrial cancer (EEC) using conventional histology and TMA using 2 mm cores. We examined EEC tissues from 171 patients. Formalin fixed, paraffin embedded tissue donor blocks from EEC specimens were selected and examined histologically. Duplicate 2 mm tissue cores were inserted into a TMA recipient block. EEC tissues were examined as hematoxylin-eosin stained sections from the TMAs. EEC tissue was identified in the TMAs in 158 cases (92.4%) and not found in 13 cases (7.6%). On the TMA slides, both EEC positive cores were identified in 129 cases (75.4%), but only one core in 29 cases (17.0%). Among 342 biopsies of the donor blocks (each case in duplicate), EEC was found in 287 cases (83.9%) using the TMA: 124/146 (84.9%) with superficial infiltration, 153/178 (86.0%) with deep myometrial infiltration, and 10/18 (55.6%) without myometrial infiltration. We concluded that two 2 mm tissue cores from a biopsy of a donor block inserted into a TMA recipient block were sufficient to diagnose EEC in more than 90% of cases. EEC was identified in the TMAs with similar frequency with respect to superficial and deep myometrial infiltration. Cases without myometrial infiltration were identified less often.     

From P-Values to Objective Probabilities in Assessing Medical Treatments

The assessment of the effectiveness of a treatment in a clinical trial, depends on calculating p-values. However, p-values are only indirect and partial indicators of a genuine effect. Particularly in situations where publication bias is very likely, assessment using a p-value of 0.05 may not be sufficiently cautious. In other situations it seems reasonable to believe that assessment based on p-values may be unduly conservative. Assessments could be improved by using prior information. This implies using a Bayesian approach to take account of prior probability. However, the use of prior information in the form of expert opinion can allow bias. A method is given here that applies to assessments already included or likely to be included in the Cochrane Collaboration, excluding those reviews concerning new drugs. This method uses prior information and a Bayesian approach, but the prior information comes not from expert opinion but simply from the distribution of effectiveness apparent in a random sample of summary statistics in the Cochrane Collaboration. The method takes certain types of summary statistics and their confidence intervals and with the help of a graph, translates this into probabilities that the treatments being trialled are effective.     

Association of generalized aggressive periodontitis and ectrodactyly-ectodermal dysplasia-cleft syndrome

Ectrodactyly-ectodermal dysplasia-cleft (EEC) syndrome is an autosomal dominant disorder characterized by the triad of ectrodactyly, ectodermal dysplasia, and facial clefting. Even though literature has documented the association of various genetic disorders with aggressive periodontitis, the periodontal manifestations in patients with EEC syndrome have never been addressed. This case report presents the periodontal status of three patients in a family with EEC syndrome. The presence of generalized aggressive periodontitis was noticed in these patients. EEC syndrome could be a new addition to the group of genetic disorders associated with aggressive periodontitis.     

Evaluating the Impact of Prior Assumptions in Bayesian Biostatistics

A common concern in Bayesian data analysis is that an inappropriately informative prior may unduly influence posterior inferences. In the context of Bayesian clinical trial design, well chosen priors are important to ensure that posterior-based decision rules have good frequentist properties. However, it is difficult to quantify prior information in all but the most stylized models. This issue may be addressed by quantifying the prior information in terms of a number of hypothetical patients, i.e., a prior effective sample size (ESS). Prior ESS provides a useful tool for understanding the impact of prior assumptions. For example, the prior ESS may be used to guide calibration of prior variances and other hyperprior parameters. In this paper, we discuss such prior sensitivity analyses by using a recently proposed method to compute a prior ESS. We apply this in several typical settings of Bayesian biomedical data analysis and clinical trial design. The data analyses include cross-tabulated counts, multiple correlated diagnostic tests, and ordinal outcomes using a proportional-odds model. The study designs include a phase I trial with late-onset toxicities, a phase II trial that monitors event times, and a phase I/II trial with dose-finding based on efficacy and toxicity.     

Quantification of prior impact in terms of effective current sample size

Bayesian methods allow borrowing of historical information through prior distributions. The concept of prior effective sample size (prior ESS) facilitates quantification and communication of such prior information by equating it to a sample size. Prior information can arise from historical observations; thus, the traditional approach identifies the ESS with such a historical sample size. However, this measure is independent of newly observed data, and thus would not capture an actual “loss of information” induced by the prior in case of prior-data conflict. We build on a recent work to relate prior impact to the number of (virtual) samples from the current data model and introduce the effective current sample size (ECSS) of a prior, tailored to the application in Bayesian clinical trial designs. Special emphasis is put on robust mixture, power, and commensurate priors. We apply the approach to an adaptive design in which the number of recruited patients is adjusted depending on the effective sample size at an interim analysis. We argue that the ECSS is the appropriate measure in this case, as the aim is to save current (as opposed to historical) patients from recruitment. Furthermore, the ECSS can help overcome lack of consensus in the ESS assessment of mixture priors and can, more broadly, provide further insights into the impact of priors. An R package accompanies the paper.     

No fallacies in the formulation of the paternity index

In a recent publication, Li and Chakravarti claim to have shown that the paternity index is not a likelihood ratio. They present a method of estimating the prior probability of paternity from a sample of previous court cases on the basis of exclusions and nonexclusions. They propose calculating the posterior probability on the basis of this estimated prior and the test result expressed as exclusion/nonexclusion. Their claim is wrong--the paternity index is a likelihood-ratio, that is, the ratio of the likelihood of the observation conditional on the two mutually exclusive hypotheses. Their proposed method of estimating the prior has been long known, has been applied to several samples, and is inferior (in terms of variance of the estimate) to maximum likelihood estimation based on all the phenotypic information available. Their proposed "new method" of calculating a posterior probability is based on the use of a less informative likelihood ratio 1/(1-PE) instead of Gürtler's fully informative paternity index X/Y (Acta Med Leg Soc Liege 9:83-93, 1956), but is otherwise identical to the Bayesian approach originally introduced by Essen-M?ller in 1938.     

A bayesian approach to the design of phase II clinical trials

A new strategy for the design of Phase II clinical trials is presented which utilizes the information provided by the prior distribution of the response rate, the costs of treating a patient, and the losses or gains resulting from the decisions taken at the completion of the study. A risk function is derived from which one may determine the optimal Bayes sampling plan. The decision theoretic/Bayesian approach is shown to provide a formal justification for the sample sizes often used in practice and shows the conditions under which such sample sizes are clearly inappropriate.     

Identification of enteroendocrine cells that express TRPA1 channels in the mouse intestine

TRPA1 is an ion channel that detects specific chemicals in food and also transduces mechanical, cold and chemical stimulation. Its presence in sensory nerve endings is well known and recent evidence indicates that it is expressed by some gastrointestinal enteroendocrine cells (EEC). The purpose of the present work is to identify and quantify EEC that express TRPA1 in the mouse gastrointestinal tract. Combined in situ hybridisation histochemistry for TRPA1 and immunofluorescence for EEC hormones was used. TRPA1 expressing EEC were common in the duodenum and jejunum, were rare in the distal small intestine and were absent from the stomach and large intestine. In the duodenum and jejunum, TRPA1 occurred in EEC that contained both cholecystokinin (CCK) and 5-hydroxytryptamine (5HT) and in a small number of cells expressing 5HT but not CCK. TRPA1 was absent from CCK cells that did not express 5HT and from EEC containing glucagon-like insulinotropic peptide. Thus TRPA1 is contained in very specific EEC populations. It is suggested that foods such as garlic and cinnamon that contain TRPA1 stimulants may aid digestion by facilitating the release of CCK.     

Estimating diversifying selection and functional constraint in the presence of recombination

Models of molecular evolution that incorporate the ratio of nonsynonymous to synonymous polymorphism (dN/dS ratio) as a parameter can be used to identify sites that are under diversifying selection or functional constraint in a sample of gene sequences. However, when there has been recombination in the evolutionary history of the sequences, reconstructing a single phylogenetic tree is not appropriate, and inference based on a single tree can give misleading results. In the presence of high levels of recombination, the identification of sites experiencing diversifying selection can suffer from a false-positive rate as high as 90%. We present a model that uses a population genetics approximation to the coalescent with recombination and use reversible-jump MCMC to perform Bayesian inference on both the dN/dS ratio and the recombination rate, allowing each to vary along the sequence. We demonstrate that the method has the power to detect variation in the dN/dS ratio and the recombination rate and does not suffer from a high false-positive rate. We use the method to analyze the porB gene of Neisseria meningitidis and verify the inferences using prior sensitivity analysis and model criticism techniques.     

pH dependence of amide chemical shifts in natively disordered polypeptides detects medium-range interactions with ionizable residues

A growing number of natively disordered proteins undergo a folding/binding process that is essential for their biological function. An interesting question is whether these proteins have incompletely solvated regions that drive the folding/binding process. Although the presence of predominantly hydrophobic buried regions can be easily ascertained by high-sensitivity differential scanning calorimetry analysis, the identification of those residues implicated in the burial requires NMR analysis. We have selected a partially solvated natively disordered fragment of Escherichia coli, thioredoxin, C37 (38-108), for full NMR spectral assignment. The secondary chemical shifts, temperature coefficients, and relaxation rates (R(1) and R(2)) of this fragment indicate the presence of a flexible backbone without a stable hydrogen bond network near neutral pH. (1)H-(15)N heteronuclear single quantum coherence analysis of the pH dependence of amide chemical shifts in fragment C37 within pH 2.0 and 7.0 suggests the presence of interactions between nonionizable residues and the carboxylate groups of four Asp and four Glu residues. The pH midpoints (pH(m)) of the amides in the ionizable residues (Asp or Glu) and, consequently, the shifts in the pH(m) (DeltapH(m)) of these residues with respect to model tetrapeptides, are sequence-dependent; and the nonionizable residues that show pH dependence cluster around the ionizable ones. The same pH dependence has been observed in two fragments: M37 (38-73) and C73 (74-108), ruling out the participation of long-range interactions. Our studies indicate the presence of a 15-residue pH-dependent segment with the highest density of ionizable sites in the disordered ensembles of fragments C37 and M37. The observed correlations between ionizable and nonionizable residues in this segment suggest the organization of the backbone and side chains through local and medium-range interactions up to nine residues apart, in contrast to only a few interactions in fragment C73. These results agree qualitatively with the predominantly hydrophobic buried surface detected only in fragments C37 and M37 by highly sensitive differential scanning calorimetry analysis. This work offers a sensitive and rapid new tool to obtain clues about local and nonlocal interactions between ionizable and nonionizable residues in the growing family of natively disordered small proteins with full NMR assignments.