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Practical Bayesian analysis of a simple logistic regression: predicting corneal transplants.

The Bayesian analysis of a logistic regression model is described using an example of predicting the need for a corneal transplant in keratoconus. Controversy over the use of subjective prior information in Bayesian methods is avoided by a formulation representing negligible prior information. Simple computational procedures are described, and it is argued that the results are more accurate, clearer and make fuller use of the information contained in the data. Analysis of more complex models is considered. In particular, it is argued that classical methods as implemented in the computer package GLIM can be used as approximations to Bayesian methods, particularly at the initial stage of model selection.

Bayes Theorem↗

The prospects for polymorphisms shared between species.

Recent molecular evidence has shown that many MHC polymorphisms are not only shared between species but are in fact identical at the molecular level. Species that share these polymorphisms may be very distantly related and often diverged millions of generations ago. It is now known that this phenomenon is very unlikely to occur if the alleles are selectively neutral. A large number of other studies suggest, however, that this phenomenon of shared polymorphisms is very common and extends to many other loci beyond just the MHC/HLA complexes. These studies also suggest that some polymorphisms may be older than the MHC/HLA polymorphisms. The maintenance of these polymorphisms via overdominant and frequency-dependent selection is discussed. Strong levels of selection are required for overdominance to maintain shared polymorphisms but most studies of effective population size produce long-term estimates that are very small and would not permit the level of overdominant selection required to maintain these polymorphisms. Frequency-dependent selection can maintain them for longer with less 'apparent' equilibrium selection and might permit smaller effective sizes. The variance of allele frequencies is suggested to be one way to distinguish between these two selection models.

Alleles↗

A two-locus model for the inheritance of a familial disease.

A model for the inheritance of a disease involving genes at just two linked loci is presented and discussed. One of the two pairs of opposite double homozygotes is assumed to lead to the disease and death. The other genotypes are assumed to be less fit than the double heterozygote. The cause of this reduced fitness may or may not be due to the disease. Conditions for the existence of a stable equilibrium are presented. The model has a sound biological basis and could be used to explain a wide range of disease frequencies and patterns of inheritance. Mutation is not required to explain why the disease persists in the population. Recurrence risks for sibs and twin concordance rates are derived and the consequences of the relaxation of selection against those with the disease are predicted. The effects of a selection model of the kind described on the amount of linkage disequilibrium in the population and on the estimation of the frequency of recombination are discussed.

Chromosome Mapping↗

Detection of genetic heterogeneity for complex quantitative phenotypes.

Statistically characterizing factors responsible for quantitative phenotype expression (e.g., polygenes, major genes, shared household factors, etc.) through model selection strategies is a difficult task. A great deal of effort has been expended on refining mathematical and computational aspects of various segregation models used to characterize unique expressions of quantitative phenotypes in an effort to make these models easier to implement and evaluate for a given set of data. In this paper a slightly different angle is emphasized: namely, the explicit modeling of the potentially numerous heterogeneous genetic and environmental processes (i.e., segregation patterns, household aggregations, etiologic processes, etc.) that could contribute to the overall variation of a quantitative trait. As such, this paper describes tools for detecting quantitative trait heterogeneity that are meant to answer such questions as "are there pedigrees among a great many that show a pattern consistent with a possibly very specific single locus segregation pattern while the rest show compatibility with a polygenic or purely environmental pattern?" Methods for determining the significance of such heterogeneity are also discussed, as are the results of numerous examples and simulation studies carried out in an effort to validate and further elaborate aspects of the proposed techniques.

Genetic Linkage↗

Numerical simulation of the plantar pressure distribution in the diabetic foot during the push-off stance.

The primary objective of conservative care for the diabetic foot is to protect the foot from excessive pressures. Pressure reduction and redistribution may be achieved by designing and fabricating orthotic devices based on foot structure, tissue mechanics, and external loads on the diabetic foot. The purpose of this paper is to describe the process used for the development of patient-specific mathematical models of the second and third rays of the foot, their solution by the finite element method, and their sensitivity to model parameters and assumptions. We hypothesized that the least complex model to capture the pressure distribution in the region of the metatarsal heads would include the bony structure segmented as toe, metatarsal and support, with cartilage between the bones, plantar fascia and soft tissue. To check the hypothesis, several models were constructed with different levels of details. The process of numerical simulation is comprised of three constituent parts: model definition, numerical solution and prediction. In this paper the main considerations relating model selection and computation of approximate solutions by the finite element method are considered. The fit of forefoot plantar pressures estimated using the FEA models and those explicitly tested were good as evidenced by high Pearson correlations (r=0.70-0.98) and small bias and dispersion. We concluded that incorporating bone support, metatarsal and toes with linear material properties, tendon and fascia with linear material properties, soft tissue with nonlinear material properties, is sufficient for the determination of the pressure distribution in the metatarsal head region in the push-off position, both barefoot and with shoe and total contact insert. Patient-specific examples are presented.

Biomechanical Phenomena↗

Dicarboxylic degradation products of nonylphenol polyethoxylates. Determination and structural elucidation in water samples by solid-phase extraction and gas chromatography-mass spectrometry after methylation.

A reliable method combining solid-phase extraction, derivatization and gas chromatography-chemical ionization mass spectrometry (GC-CI-MS) was developed for the measurement, in river and sewage effluent water, of four select model compounds of dicarboxylic metabolites (dm-CA(5-8)P1EC) and other dicarboxylic metabolites (CA(5-8)P1ECs) of nonylphenol polyethoxylates. These selected isomers were referred as dm-CA(5-8)P1ECs because they have an alpha,alpha-dimethyl configuration (expressed as "dm"), five to eight C atoms and a carboxyl group in the alkyl chain, and an ethoxy acetic acid group. The derivatization of terminal carboxyl groups was successful with (trimethylsilyl)diazomethane. The best extraction conditions were obtained using an Oasis HLB cartridge as a sorbent bed and 4 ml of MTBE/methanol (9:1, v/v) elution mixture. The method detection limits of 0.03-0.07 microg/l for dm-CA(5-8)P1ECs were attained in 500 ml pure water. The recovery was then evaluated for pure water, river and sewage effluent water samples. The high recoveries of typically >89% for each isomer indicated the high performance of the method. Although dm-CA(5-8)P1ECs were not detected in the collected water samples, 21 isomers of CA(5-8)P1ECs were identified by CI-MS and the tentative structures of six out of them were elucidated, mainly limited to the branch at alpha-C atom, by studying the EI-mass spectra. The relative concentrations of individual CA(5-8)P1EC metabolites were calculated based on dm-CA(5-8)P1ECs. The results showed that the main degradation on the nonyl chain occurred via the elimination of two carbon-units and the concentrations in Japan were much lower than those in Taiwan and Italy.

Chemical Fractionation↗

Computational fluid dynamics modeling of impeller designs for the HeartQuest left ventricular assist device.

To finalize the design of the next generation of the HeartQuest left ventricular assist device, a suitable impeller had to be designed and tested. The new prototype was based on calculations and test results of previous designs, but required several changes to decrease the size. For most pump designs, this is a simple matter of altering impeller geometry and rotational speed to achieve the desired pressure rise and flow rate. However, this particular pump was limited by housing geometry and the magnetic bearings that support the impeller. Without much freedom in the overall impeller size, the only parameters open to the designers were the blade profiles and the rotating speed. Rather than build several candidates and test them in a rig at enormous cost, computational models of several designs were tested and analyzed. This not only saved money, but also sped up the development time for the project. The computer models were developed in TASCflow, a computational fluid dynamics software package from AEA Technologies. This paper analyzes the data from several of the selected models, paying close attention to pumping performance and general trends from specific design changes.

Heart-Assist Devices↗

Physical Appearance Anxiety and Eating Disorders Symptomatology: A Systematic Review and Meta-Analysis.

The present study aimed to assess the link between physical appearance anxiety (PAA) and eating disorder (ED) symptomatology by a meta-analysis of existing literature. Eligible studies were searched across six electronic databases up until November 20, 2025. Pooled effect sizes (r) were calculated using random-effects models. Potential variables that influence effect heterogeneity were analyzed by univariable and multivariable meta-regressions. Influence analyses and a three-parameter selection model (3PSM) were used to assess robustness of the results and publication bias. Twenty-seven effect sizes from 21 studies (N = 5261) were obtained. The results indicated a strong association (i.e., r = 0.559) between the two variables under consideration, which was notably stronger (i) among females compared to males; and (ii) for overall eating disorder symptoms rather than bulimic symptoms. The results of this study advocate for further investigation into the effectiveness of addressing anxiety responses related to personal body traits, particularly among females, within the context of preventing and treating eating disorders.

Humans↗

A model for plant lighting system selection.

A decision model is presented that compares lighting systems for a plant growth scenario and chooses the most appropriate system from a given set of possible choices. The model utilizes a Multiple Attribute Utility Theory approach, and incorporates expert input and performance simulations to calculate a utility value for each lighting system being considered. The system with the highest utility is deemed the most appropriate system. The model was applied to a greenhouse scenario, and analyses were conducted to test the model's output for validity. Parameter variation indicates that the model performed as expected. Analysis of model output indicates that differences in utility among the candidate lighting systems were sufficiently large to give confidence that the model's order of selection was valid.

Decision Making, Computer-Assisted↗

Modeling Philadelphia chromosome positive leukemias.

The Ph chromosome has been genetically linked to CML and ALL. Its chimeric fusion gene product, BCR-ABL, can generate leukemia in mice. This review will discuss selected model systems developed to study BCR-ABL induced leukemia and focuses on what we have learned about the human disease from these models. Five main experimental approaches will be discussed including: (i) Reconstitution of mice with bone marrow cells retrovirally transduced with BCR-ABL; (ii) Transgenic mice expressing BCR-ABL; (iii) Knock-in mice with BCR-ABL expression driven from the endogenous bcr locus; (iv) Development of CML-like disease in mice with loss of function mutations in heterologous genes; and (v) ES in vitro hematopoietic differentiation coupled with regulated BCR-ABL expression.

Animals↗

Striatal neuroadaptation and rescue of locomotor deficit by L-dopa in aphakia mice, a model of Parkinson's disease.

Preferential neurodegeneration of dopaminergic neurons in the ventral substantia nigra of the midbrain is a hallmark of Parkinson's disease. The homeobox transcription factor Pitx3 is similarly and selectively expressed in the same neurons. Pitx3 deficiency in a natural mouse mutant, the aphakia mouse, was correlated with the loss of these neurons and with a deficit in locomotor activity. We now report that the locomotor deficit of aphakia mice is established by 40 days of age and that it can be rescued by injection of l-dopa. We further show that downstream striatal correlates of the midbrain neuronal losses in aphakia mice, as assessed by dopamine transporter binding and expression of dopamine receptors, enkephalin, dynorphin and neurotensin, are highly similar to neuroadaptive responses observed following rapid neurodegeneration induced by neurotoxin administration in adult animals or following the progressive neurodegenerative processes as seen in Parkinson patients. Taken collectively, these data support the idea that the aphakia mice represent a selective model of dopaminergic deficiency that closely resembles the midbrain and striatal neuropathology associated with Parkinson's disease, and this suggests that these mice are a good model to assess therapies for Parkinson's disease as well as to understand the susceptibility of these neurons to neurodegeneration.

Adaptation, Physiological↗

Molecular determinants of receptor affinity and selectivity of the natural delta-opioid agonist, dermenkephalin.

Processing of the polyprotein precursor pro-dermorphin generates two distantly related D-amino acid-containing peptides, dermorphin and dermenkephalin, which are among the most selective high affinity agonists described, respectively, for the mu- and delta-opioid receptors. Dermenkephalin, Tyr-D-Met-Phe-His-Leu-Met-Asp-NH2, is a linear, potentially flexible peptide devoid of structural homology with either enkephalins, endorphins, or dynorphins and, as such, represents a useful tool for identifying determinants of high affinity and selective binding of opioids to the delta-receptor. A series of selected dermenkephalin analogs and homologs was investigated for affinity at the mu- and delta-sites in the brain. Whereas dermenkephalin has high affinity and specificity for the delta-opioid receptors, its tetrapeptide amino end, dermenkephalin-[1-4]-NH2 binds almost exclusively at the mu-receptors. Dermorphin, Tyr-D-Ala-Phe-Gly-Tyr-Pro-Ser-NH2, is only marginally more selective for the u-sites than is dermenkephalin-[1-4]-NH2. Using dermorphin-dermenkephalin peptide hybrids and C-terminal deletion analogs of dermenkephalin, we showed the critical role that the C-terminal residues Met6 and Asp7 play in specifying correct addressing of dermenkephalin toward delta-receptors. The potent mu-deteminant located within the amino end of dermenkephalin is over-whelmed by the powerful delta-directing ability of the carboxy end. The negatively charged side chain of Asp7 makes a significant contribution to the delta-addressing ability of the C-terminal region, a finding consistent with Schwyzer's membrane selection model (Schwyzer, R. (1986) Biochemistry 25, 6335-6342). The Leu residue in position 5 and D-configuration about the alpha-carbon of Met2 were found to be of crucial importance for high affinity binding to delta-receptors. Whereas the Met residue in position 6 in dermenkephalin could safely be oxidized or replaced with D-Met, oxidation of Met2 led to deleterious effects, this analog being 1/100 as potent as dermenkephalin at delta-sites. Overall, the data collected demonstrate that highest levels of selectivity and affinity for the delta-opioid receptors can be achieved with small-sized, potentially flexible, linear peptides and further support the model according to which, in addition to optimum accommodation at the receptor, selection for delta-receptors is reduced by the effective positive charge of the molecule. Dermenkephalin may provide a starting point for the design of agonists and antagonists with nearly total specificity for the delta-sites. Such pharmacological agents could be used to explore the ill-defined physiological role and behavioral actions conveyed by delta-opioid receptors.

Amino Acid Sequence↗

Tree-structured prediction for censored survival data and the Cox model.

Prediction trees for the analysis of survival data are discussed. It is shown that trees are useful not only in summarizing the prognostic information contained in a set of covariates (prognostic classification), but also in detecting and displaying treatment-covariates interactions (subgroup analysis). The RECPAM approach to tree-growing is outlined; prognostic classification and subgroup analysis are then formulated within the RECPAM framework and on the basis of the Cox proportional hazards models with a priori strata. Two examples of data analysis are presented. The issue of cross-validation is discussed in relation to computationally cheaper model selection criteria.

Algorithms↗

A paradox of temporal perception revealed by a stimulus oscillating in colour and orientation.

Psychophysical experiments with stimuli oscillating concurrently in colour and orientation revealed an apparently paradoxical dissociation between the perceived simultaneity of stimulus changes and the perceptual pairing of the events demarked by those changes. When subjects were required to report whether changes in colour and orientation were simultaneous, judgements were generally accurate within +/-10 ms. When subjects were required to report which colour was paired predominantly with which orientation, judgements showed a systematic temporal bias of up to 50 ms in favour of colour. This dissociation between different temporal judgements concerning the same stimulus sequence is not predicted by any of the current models of binding in conscious vision. We propose an account of these data based on the temporal response properties of colour- and orientation-selective model neurons such that the perceived pairing of visual attributes is modelled as the cross-correlation of time-varying neural response profiles and thus reflects both neuronal latencies and the rate of rapid adaptation rather than simply the temporal pattern of responses to stimulus transitions.

Color↗

Altered positive selection due to corecognition of floppy peptide/MHC II conformers supports an integrative model of thymic selection.

Thymocytes bearing the E alpha 52-68/I-A(b) complex-specific 1H3.1 alpha beta T cell antigen receptor are positively selected in Ab-Ep [Ab-Ep transgenic, invariant chain (Ii)(-/-), I-A beta(b-/-)] mice, where I-A(b) molecules present only E alpha 52-68. Although Ii reintroduction led to deletion, I-A beta(b) reintroduction disrupted positive selection. T cell antigen receptor transgenic Ab-Ep I-A beta(b+) mice had a large thymus with an increased absolute number of CD4(+)CD8(+) cells and no overt signs of deletion. Unlike Ab-Ep Ii(+) antigen-presenting cells, Ab-Ep I-A beta(b+) antigen-presenting cells did not activate 1H3.1 T cells. However, their capacity to present E alpha 52-68 was intact. Thus, positive selection of 1H3.1 thymocytes on the tight compact E alpha 52-68/I-A(b) complex is neutralized by the corecognition of loose compact self-peptide/I-A(b) conformers that do not interfere with the cognate activation of mature 1H3.1 T cells. The data support the notion that the integration of distinct signals generated by the simultaneous recognition of multiple self-peptide/MHC complexes directs intrathymic selection of T cells.

Animals↗

The question of nonlinearity in the dose-response relation between particulate matter air pollution and mortality: can Akaike's Information Criterion be trusted to take the right turn?

The shape of the dose-response relation between particulate matter air pollution and mortality is crucial for public health assessment, and departures of this relation from linearity could have important regulatory consequences. A number of investigators have studied the shape of the particulate matter-mortality dose-response relation and concluded that the relation could be adequately described by a linear model. Some of these researchers examined the hypothesis of linearity by comparing Akaike's Information Criterion (AIC) values obtained under linear, piecewise linear, and spline alternative models. However, at the current time, the efficacy of the AIC in this context has not been assessed. The authors investigated AIC as a means of comparing competing dose-response models, using data from Cook County, Illinois, for the period 1987-2000. They found that if nonlinearities exist, the AIC is not always successful in detecting them. In a number of the scenarios considered, AIC was equivocal, picking the correct simulated dose-response model about half of the time. These findings suggest that further research into the shape of the dose-response relation using alternative model selection criteria may be warranted.

Aged↗

A Bayesian approach to reconstructing genetic regulatory networks with hidden factors.

MOTIVATION: We have used state-space models (SSMs) to reverse engineer transcriptional networks from highly replicated gene expression profiling time series data obtained from a well-established model of T cell activation. SSMs are a class of dynamic Bayesian networks in which the observed measurements depend on some hidden state variables that evolve according to Markovian dynamics. These hidden variables can capture effects that cannot be directly measured in a gene expression profiling experiment, for example: genes that have not been included in the microarray, levels of regulatory proteins, the effects of mRNA and protein degradation, etc. RESULTS: We have approached the problem of inferring the model structure of these state-space models using both classical and Bayesian methods. In our previous work, a bootstrap procedure was used to derive classical confidence intervals for parameters representing 'gene-gene' interactions over time. In this article, variational approximations are used to perform the analogous model selection task in the Bayesian context. Certain interactions are present in both the classical and the Bayesian analyses of these regulatory networks. The resulting models place JunB and JunD at the centre of the mechanisms that control apoptosis and proliferation. These mechanisms are key for clonal expansion and for controlling the long term behavior (e.g. programmed cell death) of these cells. AVAILABILITY: Supplementary data is available at http://public.kgi.edu/wild/index.htm and Matlab source code for variational Bayesian learning of SSMs is available at http://www.cse.ebuffalo.edu/faculty/mbeal/software.html.

Bayes Theorem↗

A process-oriented approach. Selecting a nursing model for psychiatric nursing.

The nursing literature is replete with articles and books that describe nursing conceptual frameworks and models and encourage their use in clinical, education, and research activities. Although much information exists on the content of nursing models, less has been written about how a model is to be chosen and the process that may facilitate the choice of a model. This article reviews potential benefits and limitations of nursing models and conceptual frameworks and describes a three-phase process for selecting a model for psychiatric nursing practice.

Choice Behavior↗