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PubMed1998

Clinical significance not statistical significance: a simple Bayesian alternative to p values.

OBJECTIVES: To take the common "Bayesian" interpretation of conventional confidence intervals to its logical conclusion, and hence to derive a simple, intuitive way to interpret the results of public health and clinical studies. DESIGN AND SETTING: The theoretical basis and practicalities of the approach advocated is at first explained and then its use is illustrated by referring to the interpretation of a real historical cohort study. The study considered compared survival on haemodialysis (HD) with that on continuous ambulatory peritoneal dialysis (CAPD) in 389 patients dialysed for end stage renal disease in Leicestershire between 1974 and 1985. Careful interpretation of the study was essential. This was because although it had relatively low statistical power, it represented all of the data that were available at the time and it had to inform a critical clinical policy decision: whether or not to continue putting the majority of new patients onto CAPD. MEASUREMENTS AND ANALYSIS: Conventional confidence intervals are often interpreted using subjective probability. For example, 95% confidence intervals are commonly understood to represent a range of values within which one may be 95% certain that the true value of whatever one is estimating really lies. Such an interpretation is fundamentally incorrect within the framework of conventional, frequency-based, statistics. However, it is valid as a statement of Bayesian posterior probability, provided that the prior distribution that represents pre-existing beliefs is uniform, which means flat, on the scale of the main outcome variable. This means that there is a limited equivalence between conventional and Bayesian statistics, which can be used to draw simple Bayesian style statistical inferences from a standard analysis. The advantage of such an approach is that it permits intuitive inferential statements to be made that cannot be made within a conventional framework and this can help to ensure that logical decisions are taken on the basis of study results. In the particular practical example described, this approach is applied in the context of an analysis based upon proportional hazards (Cox) regression. MAIN RESULTS AND CONCLUSIONS: The approach proposed expresses conclusions in a manner that is believed to be a helpful adjunct to more conventional inferential statements. It is of greatest value in those situations in which statistical significance may bear little relation to clinical significance and a conventional analysis using p values is liable to be misleading. Perhaps most importantly, this includes circumstances in which an important public health or clinical decision must be based upon a study that has unavoidably low statistical power. However, it is also useful in situations in which a decision must be based upon a large study that indicates that an effect that is highly statistically significant seems too small to be of practical relevance. In the illustrative example described, the approach helped in making a decision regarding the use of CAPD in Leicestershire during the latter half of the 1980s.

Bayes Theorem↗

PubMed1988

Euthanasia, letting die and the pause.

There is a marked disparity between medical intuitions and philosophical argument about euthanasia. In this paper I argue that the following objections can be raised. First, medical intuitions are against it and this is an area in which judgement and sensitivity are required in that death is a unique and complex process and the patient has many needs including the need to know that others have not discounted his or her worth. Also, part of the moral constitution of a good doctor is a devotion to the protection and preservation of life whatever reasons are produced to dissuade her. Finally, we do not know what the final events of a person's life might hold.

Ethical Analysis↗

PubMed2001

Analysing health outcomes.

If we cross-classify the absolutist-consequentialist distinction with an intuitive-analytical one we can see that economists probably attract the hostility of those in the other three cells as a result of being analytical consequentialists, as much as because of their concern with "costs". Suggesting that some sources of utility (either "outcome" or "process" in origin) are to be regarded as rights cannot, says the analytical consequentialist, overcome the fact that fulfilling and respecting rights is a resource-consuming activity, one that will inevitably have consequences, in resource-constrained situations, for the fulfillment of the rights of others. Within the analytical consequentialist framework QALY-type measures of health outcome have the unique advantage of allowing technical and allocative efficiency to be addressed simultaneously, while differential weighting of QALYs accruing to different groups means that efficiency and equity can be merged into the necessary single maximand. But what if such key concepts of the analytical consequentialist are not part of the discursive equipment of others? Are they to be disqualified from using them on this ground? Is it ethical for intuition to be privileged in ethical discourse, or is the analyst entitled to "equal opportunities" in the face of "analysisism", the cognitive equivalent of "racism" and "sexism"?

Cost-Benefit Analysis↗

PubMed2004

Statistical and visual morph movie analysis of crystallographic mutant selection bias in protein mutation resource data.

Structural studies of the effects of non-silent mutations on protein conformational change are an important key in deciphering the language that relates protein amino acid primary structure to tertiary structure. Elsewhere, we presented the Protein Mutant Resource (PMR) database, a set of online tools that systematically identified groups of related mutant structures in the Protein DataBank (PDB), accurately inferred mutant classifications in the Gene Ontology using an innovative, statistically rigorous data-mining algorithm with more general applicability, and illustrated the relationship of these mutant structures via an intuitive user interface. Here, we perform a comprehensive statistical analysis of the effect of PMR mutations on protein tertiary structure. We find that, although the PMR does contain spectacular examples of conformational change, in general there is a counter-intuitive inverse relationship between conformational change (measured as C-alpha displacement or RMS of the core structure) and the number of mutations in a structure. That is, point mutations by structural biologists present in the PDB contrast naturally evolved mutations. We compare the frequency of mutations in the PMR/PDB datasets against the accepted PAM250 natural amino acid mutation frequency to confirm these observations. We generated morph movies from PMR structure pairs using technology previously developed for the Macromolecular Motions Database (http://molmovdb.org), allowing bioinformaticians, geneticists, protein engineers, and rational drug designers to analyze visually the mechanisms of protein conformational change and distinguish between conformational change due to motions (e.g., ligand binding) and mutations. The PMR morph movies and statistics can be freely viewed from the PMR website, http://pmr.sdsc.edu.

Amino Acid Sequence↗

PubMed2004

Toward an integrative science of the person.

To build a science of the person, the most basic question was, and remains, how can one identify and understand the psychological invariance that distinctively characterizes an individual and that underlies the variations in the thoughts, feelings, and actions that occur across contexts and over time? This question proved particularly difficult because of the discrepancies that soon emerged between the expressions of consistency that were expected and those that were found. The resulting dilemma became known as the classic "personality paradox": How can we reconcile our intuitions-and theories-about the invariance and stability of personality with the equally compelling empirical evidence for the variability of the person's behavior across diverse situations? Which is right: the intuitions or the research findings? In this chapter I review and discuss some of the advances made to answer this question since it was posed. These findings have allowed a resolution of the paradox, and provide the outlines for a conception of the underlying structure and dynamics of personality that seems to better account for the data.

Humans↗

PubMed2001

Telesurgical laparoscopic radical prostatectomy. Initial experience.

INTRODUCTION: Telepresence surgery offers theoretically to overcome two main problems of laparoscopic surgery, i.e. the limitation to only four degrees of freedom and the lack of stereovision. Since 1998, telesurgical minimally invasive procedures have been performed with the da Vinci system mainly for cardiac bypass surgery. Clinical experience in urology is still very limited. We want to present our initial experience using the device for robot-assisted laparoscopic radical prostatectomy. MATERIAL AND METHODS: The Intuitive surgical system consists of two main components: the surgeon's viewing and control console with 3D imaging and the surgical arm unit that positions and maneuvers detachable surgical instruments. These instruments introduced via two 8-mm trocars allow movements in all 6 degrees of freedom due to the EndoWrist technology. The surgeon performs the procedure seated at the console holding specially designed instruments. Highly specialized computer software and mechanics transfer the surgeon's hand movements exactly to the microsurgical movements of the manipulators at the operative site. We have used a semilunar-shaped 5-trocar arrangement with the robot's arms at the lateral trocars and two assistant trocars medially. A sixth trocar was used in the right suprapubic area for retraction of the gland. The left assistant used different instruments such as bipolar forceps, Ultracision, Endoclip, whereas the right assistant mainly used the suction-irrigation device. Except the first case, the Intuitive System was attached after exposure of Retzius' space. RESULTS: We have treated 6 patients (2 pT2, 4 pT3, median Gleason score 6). The OR time averaged 315 (242-480) min including pelvic lymph node dissection. No intraoperative complications occurred, 1 patient required transfusions. There were no positive margins, median catheter time was 5 days. 3 patients were completely continent after 1 month. CONCLUSION: Telerobotic laparoscopic surgery offers several advantages over all presently available techniques, such as all six degrees of freedom, dexterity enhancement, tremor filtering, and stereovision. There is a learning curve with the device, mainly because of the magnification, the 3D image and the lack of tactile feedback. However, only after a short period of time, the experienced surgeon is able to get familiar with the device. However, there are still concerns with respect to the high investment and running costs of the device as well as regarding the necessity of further developments of instruments for urological procedures.

Aged↗

PubMed1992

A universal system for interactive image-directed neurosurgery.

Stereotactic methods confer great accuracy to intracranial target localization, but require strict adherence to a complex program of mechanical and computational maneuvers. A computerized, articulated, localizing 'arm' has been developed that frees the neurosurgeon of these constraints and provides a completely intuitive, 'user-friendly' interface. This universal system is independent of whatever localizing fiducial system is selected. The arm may be sterilized for intracranial use. A variety of intraoperative end effectors may be selected. The patient's CT/MR/PET scans are loaded into computer memory and a three-dimensional shaded surface wireframe diagram of the patient's head is displayed simultaneously with up to 3 independent sets of cross-referenced CT/MR/PET scan images on the intraoperative video screen. The arm's endpoint location and the directional vector are shown as cursors on the relevant scan slices, and change continuously as the surgeon moves the arm. Because the information is continuously updated, an unlimited number of targets and trajectories may be displayed throughout the operation. The arm has an ultimate design accuracy for end-point localization to within 0.1 mm throughout a target volume of 40 x 40 x 40 cm. The tested application accuracy of the first prototype model is 0.31 mm. In clinical use during 30 surgeries, its real-world application accuracy is 0.9 mm. This system provides stereotactic accuracy and universally compatible, intuitive, interactive operation.

Biopsy↗

PubMed2025

Heterogeneity Analysis of Associations Involving the Large-Scale Online MindCrowd Survey Memory Test.

INTRODUCTION: Alzheimer's disease and related disorders (ADRDs), as well as general age-related cognitive decline, are known to be multifactorial with heterogeneous etiologies. Identifying and accommodating heterogeneity in any one ADRD-related data set can be pursued using different analytical techniques, each with different assumptions or purposes. For example, whereas a great deal of research has explored clustering individuals or variables that exhibit greater similarity in some way, little research has explored evidence for heterogeneity in the relationships between relevant outcomes, such as performance on a memory test, and risk factors such as environmental exposures, behaviors, or genetic factors among individuals. METHODS: We explored evidence of heterogeneity in the relationships between ability on a memory test, specifically the paired associate learning (PAL) test, and multiple social and demographic risk factors using the large MindCrowd study database (n > 90,000 individuals). We focused on mixtures of regression models but compared models assuming many interaction effects among independent variables as well as random effects. RESULTS: We ultimately find substantial evidence for heterogeneity and offer an intuitive explanation for it involving individual motivation for participating in the MindCrowd study. Basically, we argue that our mixture of regression model analysis results suggest that a smaller group of individuals (∼16%) likely participated in the MindCrowd study out of a concern for their cognitive abilities as they exhibit stronger and statistically significant negative associations between age, number of medications they are on, some ancestries, and the number correct on the PAL test. They also exhibit stronger positive associations between education and PAL test results in a dose-dependent manner suggesting that a "cognitive reserve" associated with greater education could benefit them. Analysis models assuming interaction terms and random effects suggested that other forms of heterogeneity in the relationships between variables exist in the data set, but their results do not carry with them the same intuitive explanation that the results of the mixture model analyses do. CONCLUSION: We find evidence for heterogeneity in the relationships between social and demographic variables and PAL test results in the large MindCrowd study database. This heterogeneity is likely due to individuals with and without concerns for their cognitive abilities participating in the study. We also find other types of evidence in the data set. Our results should motivate caution in the use of large epidemiological study or survey-oriented data sets to build predictive models of clinical or subclinical pathologies without exploring or accommodating heterogeneity. Our results also suggest that one should include questions about motivation to participate in large epidemiological studies since different motivations may impact important relationships between independent and dependent variables.

Humans↗

PubMedDate not supplied

A time-tradeoff method for cost-effectiveness models applied to radiology.

PURPOSE: The wait tradeoff (WTO) is a simple time-tradeoff method designed for temporary health states that uses a realistic and intuitive interface for the patient/subject. This method was tested by assessing patients' preferences for magnetic resonance angiography (MRA) versus x-ray angiography (XRA). MATERIALS AND METHODS: The WTO was tested by telephone interview in 38 patients with atherosclerotic peripheral vascular disease, all having previously undergone both MRA and XRA. At indifference point, patients were ambivalent about having MRA or XRA and immediate treatment, versus having a waiting period for test results and treatment after a hypothetical "ideal test" that entailed no pain or risk. RESULTS: The patients were willing to wait a mean of 42.1 days after the ideal test for results and treatment, as opposed to XRA. They were willing to wait only 16.1 days as opposed to MRA. This difference in waiting times was significant (p = 0.0001) and indicates a clear preference for MRA, in agreement with known literature. CONCLUSION: The WTO method assesses preferences for these radiologic tests in an intuitive fashion that does not invoke artificial or irrelevant health states. This approach may also prove useful for other testing situations or short-term treatments being evaluated for cost-effectiveness.

Adult↗

PubMedDate not supplied

How do expert labor nurses view their role?

OBJECTIVE: To examine how expert perinatal nurses in a nurse-managed labor model view their role in caring for mothers during labor and birth. DESIGN: Focus group methodology. Data were analyzed using inductive coding methods to gain understanding from the perspective of those providing the care. SETTING: Labor and birth units in four large Midwestern medical centers. PARTICIPANTS: Fifty-four expert labor nurses. INCLUSION CRITERIA: 5 years experience in nursing care during labor and birth in institutions where nurse-managed labor was the predominant practice model. RESULTS: Four common themes related to nursing roles were identified. These included knowing the labor process and the intuitive nature of nursing care provided by expert labor nurses based on years of experience, knowing the woman and letting her body guide labor, advocacy for laboring woman, and the autonomous nature of the nurse-managed labor model. CONCLUSIONS: Expert labor nurses developed a keen sense of intuitive knowledge based on their years of experience. They reported using hands-on high-touch supportive care techniques with the potential to affect labor and birth outcomes. Autonomy is perceived as a key component of practice within the nurse-managed labor model.

Anecdotes as Topic↗

PubMed2005

Non-linear mapping for exploratory data analysis in functional genomics.

BACKGROUND: Several supervised and unsupervised learning tools are available to classify functional genomics data. However, relatively less attention has been given to exploratory, visualisation-driven approaches. Such approaches should satisfy the following factors: Support for intuitive cluster visualisation, user-friendly and robust application, computational efficiency and generation of biologically meaningful outcomes. This research assesses a relaxation method for non-linear mapping that addresses these concerns. Its applications to gene expression and protein-protein interaction data analyses are investigated. RESULTS: Publicly available expression data originating from leukaemia, round blue-cell tumours and Parkinson disease studies were analysed. The method distinguished relevant clusters and critical analysis areas. The system does not require assumptions about the inherent class structure of the data, its mapping process is controlled by only one parameter and the resulting transformations offer intuitive, meaningful visual displays. Comparisons with traditional mapping models are presented. As a way of promoting potential, alternative applications of the methodology presented, an example of exploratory data analysis of interactome networks is illustrated. Data from the C. elegans interactome were analysed. Results suggest that this method might represent an effective solution for detecting key network hubs and for clustering biologically meaningful groups of proteins. CONCLUSION: A relaxation method for non-linear mapping provided the basis for visualisation-driven analyses using different types of data. This study indicates that such a system may represent a user-friendly and robust approach to exploratory data analysis. It may allow users to gain better insights into the underlying data structure, detect potential outliers and assess assumptions about the cluster composition of the data.

Algorithms↗

PubMed2005

Providing visualisation support for the analysis of anatomy ontology data.

BACKGROUND: Improvements in technology have been accompanied by the generation of large amounts of complex data. This same technology must be harnessed effectively if the knowledge stored within the data is to be retrieved. Storing data in ontologies aids its management; ontologies serve as controlled vocabularies that promote data exchange and re-use, improving analysis. The Edinburgh Mouse Atlas Project stores the developmental stages of the mouse embryo in anatomy ontologies. This project is looking at the use of visual data overviews for intuitive analysis of the ontology data. RESULTS: A prototype has been developed that visualises the ontologies using directed acyclic graphs in two dimensions, with the ability to study detail in regions of interest in isolation or within the context of the overview. This is followed by the development of a technique that layers individual anatomy ontologies in three-dimensional space, so that relationships across multiple data sets may be mapped using physical links drawn along the third axis. CONCLUSION: Usability evaluations of the applications confirmed advantages in visual analysis of complex data. This project will look next at data input from multiple sources, and continue to develop the techniques presented to provide intuitive identification of relationships that span multiple ontologies.

Anatomy↗

PubMed2006

Djinn Lite: a tool for customised gene transcript modelling, annotation-data enrichment and exploration.

BACKGROUND: There is an ever increasing rate of data made available on genetic variation, transcriptomes and proteomes. Similarly, a growing variety of bioinformatic programs are becoming available from many diverse sources, designed to identify a myriad of sequence patterns considered to have potential biological importance within inter-genic regions, genes, transcripts, and proteins. However, biologists require easy to use, uncomplicated tools to integrate this information, visualise and print gene annotations. Integrating this information usually requires considerable informatics skills, and comprehensive knowledge of the data format to make full use of this information. Tools are needed to explore gene model variants by allowing users the ability to create alternative transcript models using novel combinations of exons not necessarily represented in current database deposits of mRNA/cDNA sequences. RESULTS: Djinn Lite is designed to be an intuitive program for storing and visually exploring of custom annotations relating to a eukaryotic gene sequence and its modelled gene products. In particular, it is helpful in developing hypothesis regarding alternate splicing of transcripts by allowing the construction of model transcripts and inspection of their resulting translations. It facilitates the ability to view a gene and its gene products in one synchronised graphical view, allowing one to drill down into sequence related data. Colour highlighting of selected sequences and added annotations further supports exploration, visualisation of sequence regions and motifs known or predicted to be biologically significant. CONCLUSION: Gene annotating remains an ongoing and challenging task that will continue as gene structures, gene transcription repertoires, disease loci, protein products and their interactions become more precisely defined. Djinn Lite offers an accessible interface to help accumulate, enrich, and individualize sequence annotations relating to a gene, its transcripts and translations. The mechanism of transcript definition and creation, and subsequent navigation and exploration of features, are very intuitive and demand only a short learning curve. Ultimately, Djinn Lite can form the basis for providing valuable clues to plan new experiments, providing storage of sequences and annotations for dedication to customised projects. The application is appropriate for Windows 98-ME-2000-XP-2003 operating systems.

Alternative Splicing↗

PubMed2003

Evidence-based medicine in primary care: qualitative study of family physicians.

BACKGROUND: The objectives of this study were: a) to examine physician attitudes to and experience of the practice of evidence-based medicine (EBM) in primary care; b) to investigate the influence of patient preferences on clinical decision-making; and c) to explore the role of intuition in family practice. METHOD: Qualitative analysis of semi-structured interviews of 15 family physicians purposively selected from respondents to a national survey on EBM mailed to a random sample of Canadian family physicians. RESULTS: Participants mainly welcomed the promotion of EBM in the primary care setting. A significant number of barriers and limitations to the implementation of EBM were identified. EBM is perceived by some physicians as a devaluation of the 'art of medicine' and a threat to their professional/clinical autonomy. Issues regarding the trustworthiness and credibility of evidence were of great concern, especially with respect to the influence of the pharmaceutical industry. Attempts to become more evidence-based often result in the experience of conflicts. Patient factors exert a powerful influence on clinical decision-making and can serve as trumps to research evidence. A widespread belief that intuition plays a vital role in primary care reinforced views that research evidence must be considered alongside other factors such as patient preferences and the clinical judgement and experience of the physician. DISCUSSION: Primary care physicians are increasingly keen to consider research evidence in clinical decision-making, but there are significant concerns about the current model of EBM. Our findings support the proposed revisions to EBM wherein greater emphasis is placed on clinical expertise and patient preferences, both of which remain powerful influences on physician behaviour.

Access to Information↗

PubMed2006

Design principles of molecular networks revealed by global comparisons and composite motifs.

BACKGROUND: Molecular networks are of current interest, particularly with the publication of many large-scale datasets. Previous analyses have focused on topologic structures of individual networks. RESULTS: Here, we present a global comparison of four basic molecular networks: regulatory, co-expression, interaction, and metabolic. In terms of overall topologic correlation--whether nearby proteins in one network are close in another--we find that the four are quite similar. However, focusing on the occurrence of local features, we introduce the concept of composite hubs, namely hubs shared by more than one network. We find that the three 'action' networks (metabolic, co-expression, and interaction) share the same scaffolding of hubs, whereas the regulatory network uses distinctly different regulator hubs. Finally, we examine the inter-relationship between the regulatory network and the three action networks, focusing on three composite motifs--triangles, trusses, and bridges--involving different degrees of regulation of gene pairs. Our analysis shows that interaction and co-expression networks have short-range relationships, with directly interacting and co-expressed proteins sharing regulators. However, the metabolic network contains many long-distance relationships: far-away enzymes in a pathway often have time-delayed expression relationships, which are well coordinated by bridges connecting their regulators. CONCLUSION: We demonstrate how basic molecular networks are distinct yet connected and well coordinated. Many of our conclusions can be mapped onto structured social networks, providing intuitive comparisons. In particular, the long-distance regulation in metabolic networks agrees with its counterpart in social networks (namely, assembly lines). Conversely, the segregation of regulator hubs from other hubs diverges from social intuitions (as managers often are centers of interactions).

Amino Acid Motifs↗

PubMed2002

The analysis of repeated multivariate binary quality of life data: a hierarchical model approach.

Many quality of life measuring instruments consist of a number of questions that are answered on ordinal scales. Often these responses are then totalled to give a summary score for each quality of life domain within the instrument. This, however, may lose valuable information about individual aspects of patient quality of life and also can have little intuitive meaning. Here we present an alternative analysis, in which dichotomized individual items of the questionnaire are analyzed. We first show how a hierarchical logistic regression model for repeated binary data can be extended to the multivariate case. We then use such a model for analyzing the prevalence of six symptoms in a palliative treatment trial in non-small-cell lung cancer. The analysis provides information about the correlations between symptoms, both between and within person. If appropriate, it also permits the estimation of a treatment effect common to all symptoms. Methods for model checking are discussed. We conclude that this methodology can provide a more intuitive and informative analysis of quality of life data than that obtained by considering summary scores.

Carcinoma, Non-Small-Cell Lung↗

PubMed2006

How much stress do researchers inflict on their study animals? A case study using a scincid lizard, Eulamprus heatwolei.

Research on live vertebrates is regulated by ethics committees, who prohibit ;excessively stressful' procedures. That judgment is based on intuition - a notoriously unreliable criterion when dealing with animals phylogenetically distant from humans. To objectively evaluate the stress imposed by research practices, we measured plasma corticosterone levels in lizards (Eulamprus heatwolei Wells & Wellington, Scincidae). Some procedures (handling and measuring, toe-clipping for identification, exposure to predator scent) did not induce significant increases in corticosterone levels, suggesting that these stimuli generated relatively little stress. However, other stimuli (testing locomotor speed, microchip implantation, blood sampling, an unfamiliar enclosure, tail autotomy, exposure to a heterospecific lizard) were more stressful, with corticosterone levels increasing only transiently in some treatments (<2 h for tail autotomy), but persisting much longer in others (14 days for microchip implantation). Overall, our data suggest that the levels of stress induced by routine laboratory procedures are no greater than those often experienced by lizards in nature; but that intuition provides a poor basis for evaluating the levels of stress induced by research. For example, toe-clipping is often criticized and sometimes banned; but our data suggest that this method is actually less stressful than the technique frequently recommended to replace it on ethical grounds (microchip implantation). Toe-clipping also was less stressful than superficially trivial manipulations such as housing the animal in an unfamiliar enclosure. More generally, we urge researchers to seek objective information on the effects of their activities on research subjects, rather than relying upon subjectivity and anthropomorphism in making these evaluations.

Acclimatization↗

PubMed2026

A Bayesian framework for multivariate differential analysis.

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a hierarchical formulation with moderated-variance estimators for each analyte directly injected into the t-statistic. While standard hypothesis testing strategies are recognised for their low computational cost, allowing for quick extraction of the most differential among thousands of elements, they generally overlook key aspects such as handling missing values, inter-element correlations, and uncertainty quantification. The present paper proposes a fully Bayesian framework for differential analysis, leveraging a conjugate hierarchical formulation for both the mean and the variance. Inference is performed by computing the posterior distribution of compared experimental conditions and sampling from the distribution of differences. This approach provides well-calibrated uncertainty quantification at a similar computational cost as hypothesis testing by leveraging closed-form equations. Furthermore, a natural extension enables multivariate differential analysis that accounts for possible inter-element correlations. We also demonstrate that, in this Bayesian treatment, missing at random data should generally be ignored in univariate settings, and further derive a tailored approximation that handles multiple imputation for the multivariate setting. We argue that probabilistic statements in terms of effect size and associated uncertainty are better suited to practical decision-making. Therefore, we finally propose simple and intuitive inference criteria, such as the overlap coefficient, which express group similarity as a probability rather than traditional, and often misleading, p-values. The performance of this approach is evaluated through an extensive empirical study using both synthetic and controlled real-world proteomics datasets. Overall, we believe that this Bayesian framework for (multivariate) differential analysis provides a valuable and intuitive counterpart to standard methods at a comparable computational cost.

Bayes Theorem↗