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A Bayesian toolkit for genetic association studies.

We present a range of modelling components designed to facilitate Bayesian analysis of genetic-association-study data. A key feature of our approach is the ability to combine different submodels together, almost arbitrarily, for dealing with the complexities of real data. In particular, we propose various techniques for selecting the "best" subset of genetic predictors for a specific phenotype (or set of phenotypes). At the same time, we may control for complex, non-linear relationships between phenotypes and additional (non-genetic) covariates as well as accounting for any residual correlation that exists among multiple phenotypes. Both of these additional modelling components are shown to potentially aid in detecting the underlying genetic signal. We may also account for uncertainty regarding missing genotype data. Indeed, at the heart of our approach is a novel method for reconstructing unobserved haplotypes and/or inferring the values of missing genotypes. This can be deployed independently or, alternatively, it can be fully integrated into arbitrary genotype- or haplotype-based association models such that the missing data and the association model are "estimated" simultaneously. The impact of such simultaneous analysis on inferences drawn from the association model is shown to be potentially significant. Our modelling components are packaged as an "add-on" interface to the widely used WinBUGS software, which allows Markov chain Monte Carlo analysis of a wide range of statistical models. We illustrate their use with a series of increasingly complex analyses conducted on simulated data based on a real pharmacogenetic example.

Bayes Theorem↗

The use of mixture models for identifying high risks in disease mapping.

Conventional approaches for estimating risks in disease mapping or mortality studies are based on Poisson inference. Frequently, overdispersion is present and this extra variability is modelled by introducing random effects. In this paper we compare two computationally simple approaches for incorporating random effects: one based on a non-parametric mixture model assuming that the population arises from a discrete mixture of Poisson distributions, and the second using a Poisson-normal mixture model which allows for spatial autocorrelation. The comparison is focused on how well each of these methods identify the regions which have high risks. Such identification is important because policy makers may wish to target regions associated with such extreme risks for financial assistance while epidemiologists may wish to target such regions for further study. The Poisson-normal mixture model is presented from both a frequentist, or empirical Bayes, and a fully Bayesian point of view. We compare results obtained with the parametric and non-parametric models specifically in terms of detecting extreme mortality risks, using infant mortality data of British Columbia, Canada, for the period 1981-1985, breast cancer data from Sardinia, for the period 1983-1987, and Scottish lip cancer data for 1975-1980. However, we also investigate the performance of these models in a simulation study. The key finding is that discrete mixture models seem to be able to locate regions which experience high risks; normal mixture models also work well in this regard, and perform substantially better when spatial autocorrelation is present.

Adult↗

Multiple sequence alignment accuracy and phylogenetic inference.

Phylogenies are often thought to be more dependent upon the specifics of the sequence alignment rather than on the method of reconstruction. Simulation of sequences containing insertion and deletion events was performed in order to determine the role that alignment accuracy plays during phylogenetic inference. Data sets were simulated for pectinate, balanced, and random tree shapes under different conditions (ultrametric equal branch length, ultrametric random branch length, nonultrametric random branch length). Comparisons between hypothesized alignments and true alignments enabled determination of two measures of alignment accuracy, that of the total data set and that of individual branches. In general, our results indicate that as alignment error increases, topological accuracy decreases. This trend was much more pronounced for data sets derived from more pectinate topologies. In contrast, for balanced, ultrametric, equal branch length tree shapes, alignment inaccuracy had little average effect on tree reconstruction. These conclusions are based on average trends of many analyses under different conditions, and any one specific analysis, independent of the alignment accuracy, may recover very accurate or inaccurate topologies. Maximum likelihood and Bayesian, in general, outperformed neighbor joining and maximum parsimony in terms of tree reconstruction accuracy. Results also indicated that as the length of the branch and of the neighboring branches increase, alignment accuracy decreases, and the length of the neighboring branches is the major factor in topological accuracy. Thus, multiple-sequence alignment can be an important factor in downstream effects on topological reconstruction.

Base Sequence↗

DNA variation in a 13-Mb region including the F9 gene: inferring the genealogical history and causal role of a hemophilia B mutation (IVS 5+13 A-->G).

About 5.5% of all UK hemophilia B patients have the base substitution IVS 5+13 A-->G as the only change in their factor (F)IX gene (F9). This generates a novel donor splice site which fits the consensus better than the normal intron 5 donor splice. Use of the novel splice site should result in a missense mutation followed by the abnormal addition of four amino acids to the patients' FIX. In order to explain the prevalence of this mutation, its genealogical history is examined. Analysis of restriction fragment length polymorphism in the 21 reference UK individuals (from different families) with the above mutation showed identical haplotypes in 19 while two differed from the rest and from each other. In order to investigate the history of the mutation and to verify that it had occurred independently more than once, the sequence variation in 1.5-kb segments scattered over a 13-Mb region including F9 was examined in 18 patients and 15 controls. This variation was then analyzed with a recently developed Bayesian approach that reconstructs the genealogy of the gene investigated while providing evidence of independent mutations that contribute disconnected branches to the genealogical tree. The method also provides minimum estimates of the age of the mutation inherited by the members of coherent trees. This revealed that 17 or 18 mutant genes descend from a founder who probably lived 450 years ago, while one patient carries an independent mutation. The independent recurrence of the IVS5+13 A-->G mutation strongly supports the conclusion that it is the cause of these patients' mild hemophilia.

Base Sequence↗

A Bayesian change-point analysis of electromyographic data: detecting muscle activation patterns and associated applications.

Many facets of neuromuscular activation patterns and control can be assessed via electromyography and are important for understanding the control of locomotion. After spinal cord injury, muscle activation patterns can affect locomotor recovery. We present a novel application of reversible jump Markov chain Monte Carlo simulation to estimate activation patterns from electromyographic data. We assume the data to be a zero-mean, heteroscedastic process. The variance is explicitly modeled using a step function. The number and location of points of discontinuity, or change-points, in the step function, the inter-change-point variances, and the overall mean are jointly modeled along with the mean and variance from baseline data. The number of change-points is considered a nuisance parameter and is integrated out of the posterior distribution. Whereas current methods of detecting activation patterns are deterministic or provide only point estimates, ours provides distributional estimates of muscle activation. These estimates, in turn, are used to estimate physiologically relevant quantities such as muscle coactivity, total integrated energy, and average burst duration and to draw valid statistical inferences about these quantities.

Bayes Theorem↗

FINEX: a Probabilistic Expert System for forensic identification.

A series of recent papers have shown how to formulate complex problems of forensic DNA identification inference, such as occur in disputed paternity or criminal identification cases, in terms of Probabilistic Expert Systems (PESs). However, at the present time, general purpose PES software is not particularly well suited to the repetitive tasks of: specifying an appropriate set of marker networks for a specific problem; for editing the many local conditional probability tables; and combining evidence from several genetic markers to evaluate likelihoods. Here, I describe a user-friendly prototype software tool called FINEX developed both to automate such tasks and also to evaluate likelihoods of interest. Ease of use is achieved by a graphical specification language that enables a user to quickly specify a range of forensic DNA problems. I describe the algorithms by which FINEX converts the user input in the graphical specification language and data on observed markers to the Bayesian networks used in PES.

Algorithms↗

Profiling providers on use of adjuvant chemotherapy by combining cancer registry and medical record data.

PURPOSE: Treatment information collected by cancer registries can be used to monitor the provision of guideline-recommended chemotherapy to colorectal cancer patients. Incomplete information may bias comparisons of these rates. We developed statistical methods that combine data from a registry and physicians' records to assess hospital quality. DATA: From California Cancer Registry data, we selected all patients (n=12,594) newly diagnosed with stage III colon cancer or stage II or III rectal cancer from 428 hospitals during the years 1994 to 1998. To assess rates and predictors of underreporting of chemotherapy, we surveyed physicians treating 1449 of these patients from 98 hospitals during the years 1996 to 1997. METHODS: Using Bayesian statistical models, we imputed unobserved treatments. We studied the impact of underreporting on provider profiling by comparing rankings, estimates, and credible intervals based only on registry data to those incorporating physician survey data. RESULTS: Analyses that account for incompleteness of reporting yielded wider credible intervals for provider profiles than those that ignored such incompleteness. Among the 109 (25%) hospitals in the highest quartile of chemotherapy rates according to the registry data, 16 were not so classified when incomplete reporting was taken into account. With the more comprehensive model, 12 hospitals could be identified that ranked in the top quartile with probability>0.90. CONCLUSION: Estimates of adjusted hospital chemotherapy rates based solely on cancer registry data overstate the precision of assessments of hospital quality. Using additional information from a physician survey and applying rigorous statistical models, better inferences can be drawn about provider quality.

Adolescent↗

Confounder selection in environmental epidemiology: assessment of health effects of prenatal mercury exposure.

PURPOSE: The purpose of the study is to compare different approaches to the identification of confounders needed for analyzing observational data. Whereas standard analysis usually is conducted as if the confounders were known a priori, selection uncertainty also must be taken into account. METHODS: Confounders were selected by using backward elimination (BE), change in estimate (CIE) method, Akaike information criterion, Bayesian information criterion (BIC), and an empirical approach using a priori information. A modified ridge regression estimator, which shrinks effects of confounders toward zero, also was considered. For each criterion, uncertainty in the estimated exposure effect was assessed by using bootstrap simulations for which confounders were selected in each sample. These methods were illustrated by using data for mercury neurotoxicity in Faroe Islands children. Point estimates and standard errors of mercury effects on confounder-sensitive neurobehavioral outcomes were calculated for each selection procedure. RESULTS: The full model and the empirical a priori model showed approximately the same precision, and these methods were (slightly) inferior to only modified ridge regression. Lower precisions were obtained by using BE with a low cutoff level, BIC, and CIE. CONCLUSIONS: Standard analysis ignores model selection uncertainty and is likely to yield overoptimistic inferences. Thus, the traditional BE procedure with p = 5% should be avoided. If data-dependent procedures are required for confounder identification, we recommend that inferences be based on bootstrap statistics to describe the selection process.

Animals↗

On the relationship between deterministic and probabilistic directed Graphical models: from Bayesian networks to recursive neural networks.

Machine learning methods that can handle variable-size structured data such as sequences and graphs include Bayesian networks (BNs) and Recursive Neural Networks (RNNs). In both classes of models, the data is modeled using a set of observed and hidden variables associated with the nodes of a directed acyclic graph. In BNs, the conditional relationships between parent and child variables are probabilistic, whereas in RNNs they are deterministic and parameterized by neural networks. Here, we study the formal relationship between both classes of models and show that when the source nodes variables are observed, RNNs can be viewed as limits, both in distribution and probability, of BNs with local conditional distributions that have vanishing covariance matrices and converge to delta functions. Conditions for uniform convergence are also given together with an analysis of the behavior and exactness of Belief Propagation (BP) in 'deterministic' BNs. Implications for the design of mixed architectures and the corresponding inference algorithms are briefly discussed.

Bayes Theorem↗

The cost-effectiveness of basiliximab induction in "old-to-old" kidney transplant programs: Bayesian estimation, simulation, and uncertainty analysis.

INTRODUCTION: Markov models are employed in economic analyses to evaluate all possible expectations in a dilemna. The introduction of a new clinical protocol (Basiliximab induction with calcineurin-sparing protocols) for a group of kidney transplant recipients receiving organs from marginal donors was validated with a Markov simulation model, demonstrating the usefulness of combining simulation with Bayesian estimation methods for analysis of cost-effectiveness data collected alongside a clinical trial. We sought to determine whether calcineurin-sparing protocols using anti-interleukin-2/antibody induction (Simulect) would show a beneficial effect on initial kidney function and reduce transplantation costs upon admission, clinical incidences, graft function, and complications during the first month after transplant. PATIENTS AND METHODS: A Markov Chain Monte Carlo (MCMC) was used to estimate a system of generalized linear models relating costs and outcomes to a kidney transplant process affected by treatment under alternative therapies. The Markov simulation model was established following three chains: a calcineurin-free regimen with Basiliximab induction (chain A); a calcineurin-sparing protocol with Basiliximab induction (chain B); and a conventional immunosuppressive regimen (chain C). The MCMC draws were used as parameters in simulations that yielded inferences about the relative cost-effectiveness of the novel therapy under a variety of scenarios. After designing the Markov chain and cohorts, 31 patients from the "old-to-old" program were assigned; eight to chain A; eight to chain B; and 15 to chain C. A year after transplantation a cost-benefit study was performed guided by the three branches of the Markov model. RESULTS: The Markov model showed a benefit of induction therapies in elderly patients. A cost-benefit model showed that after a year, there was a clear benefit from calcineurin-free plus Basiliximab induction therapies, with a slight benefit from calcineurin-sparing protocols. CONCLUSIONS: Markov models are extremely useful when introducing new clinical therapies. The approach allows flexibility in assessing treatment using various premises and quantifies the global effect of parametric uncertainty on a decision maker's confidence to adopt one therapy over another. In our transplant program, a cost-effective analysis of outcomes in old patients using the Markov model showed a clear benefit of calcineurin-sparing protocols with Basixilimab induction.

Age Factors↗

Variance-modeled posterior inference of microarray data: detecting gene-expression changes in 3T3-L1 adipocytes.

MOTIVATION: Microarrays are becoming an increasingly common tool for observing changes in gene expression over a large cross section of the genome. This experimental tool is particularly valuable for understanding the genome-wide changes in gene transcription in response to thiazolidinedione (TZD) treatment. The TZD class of drugs is known to improve insulin-sensitivity in diabetic patients, and is clinically used in treatment regimens. In cells, TZDs bind to and activate the transcriptional activity of peroxisome proliferator-activated receptor gamma (PPAR-gamma). Large-scale array analyses will provide some insight into the mechanisms of TZD-mediated insulin sensitization. Unfortunately, a theoretical basis for analyzing array data has not kept pace with the rapid adoption of this tool. The methods that are commonly used, particularly the fold-change approach and the standard t-test, either lack statistical rigor or resort to generalized statistical models that do not accurately estimate variability at low replicate numbers. RESULTS: We introduce a statistical framework that models the dependence of measurement variance on the level of gene expression in the context of a Bayesian hierarchical model. We compare several methods of parameter estimation and subsequently apply these to determine a set of genes in 3T3-L1 adipocytes that are differentially regulated in response to TZD treatment. When the number of experimental replicates is low (n = 2-3), this approach appears to qualitatively preserve an equivalent degree of specificity, while vastly improving sensitivity over other comparable methods. In addition, the statistical framework developed here can be readily applied to understand the implicit assumptions made in traditional fold-change approaches to array analysis.

3T3-L1 Cells↗

Identifying interventional and pathogenic mechanisms by generative inverse modeling of gene expression profiles.

MOTIVATION: The characterization of genetic mechanisms underlying normal cellular function, cancer development, pathogenesis, and the effect of drug treatment is one of the most challenging topics for cancer research and molecular biology. Existing methods for inferring genetic regulatory networks from genome-wide expression profiles provide important information about gene interactions and regulatory relationships. However, these methods do not provide information about the impact of possible interventions or changes on such regulatory networks to study cause-effect relationships at a systems-biology level. RESULTS: We present a data-driven method called generative inverse modeling, which simulates the effect of local genetic changes on the global cellular state, as reflected by an altered genome-wide expression profile. For each genetic change we define a pathogenic score by calculating to what extent it transforms the simulated expression patterns into patterns measured for pathologically altered tissues. The method can be used to estimate the relevance of genes for disease-specific genetic mechanisms, e.g., as presented here for pathogenesis. Generative inverse modeling is based on a Bayesian probability density estimation from a set of measured gene-expression patterns.

Computational Biology↗

Cell-type-specific genetic associations in Lewy body dementia identified using single-cell eQTL-based Mendelian randomization.

BACKGROUND: Lewy body dementia (LBD) is a complex neurodegenerative disorder marked by α-synuclein aggregation and dual impairment of cognitive and motor function.While genome-wide association studies have identified risk loci, the cellular mechanisms linking genetic variation to disease susceptibility remain largely unexplored. METHODS: We performed single-cell transcriptome-wide Mendelian randomization using brain cell-type-specific eQTLs across eight major cell types. Genetic associations were evaluated using inverse-variance weighted models, followed by Bayesian colocalization analysis. Replication was performed in independent stratified LBD cohorts based on APOE ε4 carrier status. Phenome-wide association analysis was included as a supplementary, descriptive assessment of cross-trait associations. RESULTS: Expression of ANKRD65 in excitatory neurons was significantly associated with reduced LBD risk (odds ratio = 0.65, 95 % CI: 0.52-0.81, p = 0.00013). This association passed a false discovery rate of 0.1 and showed strong evidence of colocalization (posterior probability = 0.93). Effect direction was consistent across APOE ε4+ and ε4- LBD subgroups in independent cohorts. No genome-wide significant associations were observed with non-neurological traits in the phenome-wide analysis. CONCLUSIONS: Our findings identify a genetically supported, cell-type-resolved association between ANKRD65 expression in excitatory neurons and LBD risk. This study demonstrates the value of integrating cell-resolved transcriptomic regulation with genetic inference to pinpoint functionally relevant targets in neurodegenerative diseases.

Humans↗

Improved pairwise alignments of proteins in the Twilight Zone using local structure predictions.

MOTIVATION: In recent years, advances have been made in the ability of computational methods to discriminate between homologous and non-homologous proteins in the 'twilight zone' of sequence similarity, where the percent sequence identity is a poor indicator of homology. To make these predictions more valuable to the protein modeler, they must be accompanied by accurate alignments. Pairwise sequence alignments are inferences of orthologous relationships between sequence positions. Evolutionary distance is traditionally modeled using global amino acid substitution matrices. But real differences in the likelihood of substitutions may exist for different structural contexts within proteins, since structural context contributes to the selective pressure. RESULTS: HMMSUM (HMMSTR-based substitution matrices) is a new model for structural context-based amino acid substitution probabilities consisting of a set of 281 matrices, each for a different sequence-structure context. HMMSUM does not require the structure of the protein to be known. Instead, predictions of local structure are made using HMMSTR, a hidden Markov model for local structure. Alignments using the HMMSUM matrices compare favorably to alignments carried out using the BLOSUM matrices or structure-based substitution matrices SDM and HSDM when validated against remote homolog alignments from BAliBASE. HMMSUM has been implemented using local Dynamic Programming and with the Bayesian Adaptive alignment method.

Algorithms↗

High variation in developmental instability under non-normal developmental error: a Bayesian perspective.

The developmental mechanisms behind developmental instability (DI) are only poorly understood. Nevertheless, fluctuating asymmetry (FA) is often used a surrogate for DI. Based on statistical arguments it is often assumed that individual levels of FA are only weakly associated with the underlying DI. Patterns in FA therefore need to be interpreted with caution, and should ideally be transformed into patterns in DI. In order to be able to achieve that, assumptions about the distribution of developmental errors must be made. Current models assume that errors during development are additive and independent such that they yield a normal distribution. The observation that the distribution of FA is often leptokurtic has been interpreted as evidence for between-individual variation in DI. This approach has led to unrealistically high estimates of between-individual variation in DI, and potentially incorrect interpretations of patterns in FA, especially at the individual level. Recently, it has been suggested that the high estimates of variation in DI may be biased upward because either developmental errors are log-normal or gamma distributed and/or low measurement resolution of FA. A proper estimation of the amount (and shape) of heterogeneity in DI is crucial for the interpretation of patterns in FA and their transformation into patterns in DI. Yet, incorrect model assumptions may render misleading inferences. We therefore develop a statistical model to evaluate the sensitivity of results under the normal error model against the two alternative distributions as well as to investigate the importance of low measurement resolution. An analysis of simulated and empirical data sets indicated that bias due to misspecification of the developmental error distribution can be substantial, yet, did not appear to reduce estimates of variation in DI in empirical data sets to a large extent. Effects of low measurement resolution were neglectable. The importance of these results are discussed in the context of the interpretation of patterns in FA.

Animals↗

Phylogenetic relationships of Hynobius naevius (Amphibia: Caudata) as revealed by mitochondrial 12S and 16S rRNA genes.

Using mitochondrial 12S and 16S rRNA sequences, we investigated phylogenetic relationships among populations of the endemic Japanese salamander Hynobius naevius. Monophyly of this species was recovered only in the maximum parsimony tree and was unresolved in maximum likelihood and Bayesian trees. Instead the following four haplotype clades consistently emerged clearly: Clade 1 from northwestern Kyushu, Clade 2 from Chugoku and northeastern Kyushu, Clade 3 from western Shikoku and Kyushu, and Clade 4 from Chubu-Kinki and central-eastern Shikoku. Of these, Clades 1 and 2, and Clades 3 and 4, respectively, correspond to Groups A and B previously recognized from the analyses of allozyme data in this species, but monophyly of these groups was not strongly supported. Unlike the previous results, the western and eastern samples from Shikoku did not form a clade, and were grouped with Kyushu-B in Clade 3 and Chubu-Kinki in Clade 4, respectively. The reason for this conflict between mtDNA and allozyme results is unknown, but might be related to retention of ancestral mtDNA polymorphism in Shikoku populations. Nearly simultaneous divergence of as many as four lineages in wide-ranging H. naevius is inferred for the late Miocene-Pliocene history of this taxon.

Animals↗

Issues in applied statistics for public health bioterrorism surveillance using multiple data streams: research needs.

The objective of this report is to provide a basis to inform decisions about priorities for developing statistical research initiatives in the field of public health surveillance for emerging threats. Rapid information system advances have created a vast opportunity of secondary data sources for information to enhance the situational and health status awareness of populations. While the field of medical informatics and initiatives to standardize healthcare-seeking encounter records continue accelerating, it is necessary to adapt analytic and statistical methodologies to mature in sync with sibling information science technologies. One major right-of-passage for statistical inference is to advance the optimal application of analytic methodologies for using multiple data streams in detecting and characterizing public health population events of importance. This report first describes the problem in general and the data context, then delineates more specifically the practical nature of the problem and the related issues. Approaches currently applied to data with time-series, statistical process control and traditional inference concepts are described with examples in the section on Statistics and the Role of the Analytic Surveillance Data Monitor. These are the techniques that are providing substance to surveillance professionals and enabling use of multiple data streams. The next section describes use of a more complex approach that takes temporal as well as spatial dimensions into consideration for detection and situational awareness regarding event distributions. The space-time statistic has successfully been used to detect and track public health events of interest. Important research questions which are summarized at the end of this report are described in more detail with respect to the methodological application in the respective sections. This was thought to help elucidate the research requirements as summarized later in the report. Following the description of the space-time scan statistical application; this report extends to a less traditional area of promise given what has been observed in recent application of analytic methods. Bayesian networks (BNs) represent a conceptual step with advantages of flexibility for the public health surveillance community. Progression from traditional to the more extending statistical concepts in the context of the dynamic status quo of responsibility and challenge, leads to a conclusion consisting of categorical research needs. The report is structured by design to inform judgment about how to build on practical systems to achieve better analytic outcomes for public health surveillance. There are references to research issues throughout the sections with a summarization at the end, which also includes items previously unmentioned in the report.

Algorithms↗

Comparison of the diagnostic accuracy of lymphatic endothelium markers: Bayesian approach.

Tumor lymphatic density is evaluated by means of specific lymphatic endothelium markers, and is a potential predictor of clinically meaningful outcomes. There are many claims on the postulated superiority of some of these markers to identify lymphatics, always in the absence of quantitative data. We therefore compared the diagnostic accuracy of the antibody against podoplanin and the commercially available D2-40, employing Bayesian statistics to account for the absence of a gold standard. We used the pan-endothelial marker CD34 to identify 23,542 distinct blood and lymphatic vessels in sections from 30 formalin-fixed, paraffin-embedded archival tissue blocks of head and neck squamous cell carcinoma specimens. We stained two adjacent sections with podoplanin and D2-40 and identified the continuum of each stained vessel in the sections with a comprehensive method. Overall, 1,864 vessels were stained with both markers, 119 only with podoplanin and 391 only with D2-40. Significantly more vessels with intraluminal red blood cells were stained with D2-40 compared to podoplanin (McNemar's P<0.0001). Both antibodies had extremely high specificity (99.7% (95% credible interval (CrI): 99.5-99.9%) and 98.8% (95% CrI: 98.3-99.5%) for podoplanin and D2-40, respectively) and very high sensitivity (92.6% (95% CrI: 86.1-97.9%) and 97.3% (95% CrI: 94.9-99.2%) for podoplanin and D2-40, respectively). Inferences were qualitatively similar when we took into account in the analyses the possibility that the two tests (antibodies) may be correlated. We calculated that 96.3% (95% CrI: 94.2-98.6%) of the vessels stained with podoplanin and 88.9% (95% CrI: 83.9-95.7%) of the vessels stained with D2-40 were truly lymphatics. These numbers were in agreement with the observed number of stained vessels without intraluminal red blood cells. Our results suggest that both antibodies are excellent lymphatic endothelium markers and that there may be little reason to prefer either of them in most settings.

Antibodies, Monoclonal↗