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PubMed1981

The role of modeling methods in medical diagnosis.

Modeling methods in medical diagnosis are concerned with medical information processing as it pertains to utilizing biological modeling methods to facilitate patient care. Major considerations in this particular area are (1) the classification problem related to the establishment of disease entities-the taxonomy problem, and (2) the diagnosis of diseases. Available are properties, criteria, signs, symptoms, and manifestations of diseases that have been cumulated and categorized by clinicians and researchers. The problem is to optimally utilize the information content of a sign or set of signs in the practice of patient care as pertaining to the medical diagnosis problem. Some mathematical approaches implemented to facilitate such analyses include cluster analysis, discriminant analysis, Bayesian methods, computer approaches, game theory, information theory, stochastic representations, stepwise procedures, decision analysis, and pattern recognition techniques. Each of these has been studied in depth by numerous researchers advocating computer applications in medicine. Here we discuss the scope and limitations of utilizing modeling methods as a viable approach to interpreting vast amounts of biological data collected on a single patient during an encounter. We consider the following: (1) limitations associated with modeling methodologies; (2) levels of responsibilities, ranging over logging, summarizing, reporting, monitoring, and therapy selection; and (3) operational strategies and considerations as they affect hardware logistics, the actual algorithm utilized, and implementation of these sophisticated analysis systems.

Decision Theory↗
PubMed2005

Fluctuation-dissipation theorem and models of learning.

Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian learners perform on different data and argue that it is difficult to determine which learning-theoretic computation is performed by a particular organism using just its performance in learning a stationary target (learning curve). Based on the fluctuation-dissipation relation in statistical physics, we then discuss a different experimental setup that might be able to solve the problem.

Animals↗
PubMed2001

Estimating the Bayesian loss function. A conjoint analysis approach.

Current health economic literature does not provide clear guidelines on how uncertainty around cost-effectiveness estimates should be incorporated into economic decision models. Bayesian analysis is a promising alternative to classical statistics for incorporating uncertainty in economic analysis. Estimating a loss function that relates outcomes to societal welfare is a key component of Bayesian decision analysis. Health economists commonly compute the loss function based on the quality-adjusted life-years associated with each outcome. However, if welfare economics is adopted as the theoretical foundation of the analysis, a loss function based in cost-benefit analysis (CBA) may be more appropriate. CBA has not found wide use in health economics due to practical issues associated with estimating such a loss function. In this paper, we present a method based in conjoint analysis for estimating the CBA loss function that can be applied in practice. We illustrate the use of the methodology using data from a pilot study.

Acute Disease↗
PubMed1997

Constructing probabilistic models.

Bayesian networks have become one of the most popular probabilistic techniques in AI, largely due to the development of several efficient inference algorithms. In this paper we describe a heuristic method for constructing Bayesian networks. Our construction method relies on the relationship between Bayesian networks and decomposable models, a special kind of graphical model. We explain this relationship and then show how it can be used to facilitate model construction. Finally, we describe an implemented computer program that illustrates these ideas.

Algorithms↗
PubMed2004

Parametric shape modeling using deformable superellipses for prostate segmentation.

Automatic prostate segmentation in ultrasound images is a challenging task due to speckle noise, missing boundary segments, and complex prostate anatomy. One popular approach has been the use of deformable models. For such techniques, prior knowledge of the prostate shape plays an important role in automating model initialization and constraining model evolution. In this paper, we have modeled the prostate shape using deformable superellipses. This model was fitted to 594 manual prostate contours outlined by five experts. We found that the superellipse with simple parametric deformations can efficiently model the prostate shape with the Hausdorff distance error (model versus manual outline) of 1.32 +/- 0.62 mm and mean absolute distance error of 0.54 +/- 0.20 mm. The variability between the manual outlinings and their corresponding fitted deformable superellipses was significantly less than the variability between human experts with p-value being less than 0.0001. Based on this deformable superellipse model, we have developed an efficient and robust Bayesian segmentation algorithm. This algorithm was applied to 125 prostate ultrasound images collected from 16 patients. The mean error between the computer-generated boundaries and the manual outlinings was 1.36 +/- 0.58 mm, which is significantly less than the manual interobserver distances. The algorithm was also shown to be fairly insensitive to the choice of the initial curve.

Algorithms↗
PubMed2003

Bayesian inference on order-constrained parameters in generalized linear models.

In biomedical studies, there is often interest in assessing the association between one or more ordered categorical predictors and an outcome variable, adjusting for covariates. For a k-level predictor, one typically uses either a k-1 degree of freedom (df) test or a single df trend test, which requires scores for the different levels of the predictor. In the absence of knowledge of a parametric form for the response function, one can incorporate monotonicity constraints to improve the efficiency of tests of association. This article proposes a general Bayesian approach for inference on order-constrained parameters in generalized linear models. Instead of choosing a prior distribution with support on the constrained space, which can result in major computational difficulties, we propose to map draws from an unconstrained posterior density using an isotonic regression transformation. This approach allows flat regions over which increases in the level of a predictor have no effect. Bayes factors for assessing ordered trends can be computed based on the output from a Gibbs sampling algorithm. Results from a simulation study are presented and the approach is applied to data from a time-to-pregnancy study.

Adult↗
PubMed2005

The estimation of distributions and the minimum relative entropy principle.

Estimation of Distribution Algorithms (EDA) have been proposed as an extension of genetic algorithms. In this paper we explain the relationship of EDA to algorithms developed in statistics, artificial intelligence, and statistical physics. The major design issues are discussed within a general interdisciplinary framework. It is shown that maximum entropy approximations play a crucial role. All proposed algorithms try to minimize the Kullback-Leibler divergence KLD between the unknown distribution p(x) and a class q(x) of approximations. However, the Kullback-Leibler divergence is not symmetric. Approximations which suppose that the function to be optimized is additively decomposed (ADF) minimize KLD(q||p), the methods which learn the approximate model from data minimize KLD(p||q). This minimization is identical to maximizing the log-likelihood. In the paper three classes of algorithms are discussed. FDA uses the ADF to compute an approximate factorization of the unknown distribution. The factors are marginal distributions, whose values are computed from samples. The second class is represented by the Bethe-Kikuchi approach which has recently been rediscovered in statistical physics. Here the values of the marginals are computed from a difficult constrained minimization problem. The third class learns the factorization from the data. We analyze our learning algorithm LFDA in detail. It is shown that learning is faced with two problems: first, to detect the important dependencies between the variables, and second, to create an acyclic Bayesian network of bounded clique size.

Algorithms↗
PubMed2005

Bayesian latent variable models for mixed discrete outcomes.

In studies of complex health conditions, mixtures of discrete outcomes (event time, count, binary, ordered categorical) are commonly collected. For example, studies of skin tumorigenesis record latency time prior to the first tumor, increases in the number of tumors at each week, and the occurrence of internal tumors at the time of death. Motivated by this application, we propose a general underlying Poisson variable framework for mixed discrete outcomes, accommodating dependency through an additive gamma frailty model for the Poisson means. The model has log-linear, complementary log-log, and proportional hazards forms for count, binary and discrete event time outcomes, respectively. Simple closed form expressions can be derived for the marginal expectations, variances, and correlations. Following a Bayesian approach to inference, conditionally-conjugate prior distributions are chosen that facilitate posterior computation via an MCMC algorithm. The methods are illustrated using data from a Tg.AC mouse bioassay study.

Acrylates↗
PubMed2026

Comparing ARG Inference Methods Under Transmission of Reproductive Success: Tree Imbalance Matters.

Inferring coalescent trees from genomic data has become a major subject in population genetics, particularly with the recent advances in tree sequence reconstruction methods. However, it remains unclear how well these methods perform for imbalanced genealogies. Such imbalances can arise from processes such as cultural transmission of reproductive success (CTRS) or positive selection. Using simulated genomic data, we benchmarked three major software packages, SINGER, Relate, and tsinfer, by comparing the imbalance of reconstructed trees by these methods with that of the true simulated trees, for three indices that quantify this imbalance. The three methods performed well under scenarios yielding balanced trees. However, their accuracy declined as imbalance increased. Performances also varied with mutation rate, recombination rate, and sample size. This study opens possibilities for applying these methods to infer CTRS or positive selection in large-scale genomic datasets, using simulation-based inference such as approximate Bayesian computation.

Models, Genetic↗
PubMed1997

Efficient temporal probabilistic reasoning via context-sensitive model construction.

We present a language for representing context-sensitive temporal probabilistic knowledge. Context constraints allow inference to be focused on only the relevant portions of the probabilistic knowledge. We provide a declarative semantics for our language. We present a sound and complete algorithm for computing posterior probabilities of temporal queries, as well as an efficient implementation of the algorithm. Throughout we illustrate the approach with the problem of reasoning about the effects of medications and interventions on the state of a patient in cardiac arrest. We empirically evaluate the efficiency of our system by comparing its inference times on problems in this domain with those of standard Bayesian network representations of the problems.

Algorithms↗
PubMed2002

A Bayesian approach to the transmission/disequilibrium test for binary traits.

The transmission/disequilibrium test (TDT) for binary traits is a powerful method for detecting linkage between a marker locus and a trait locus in the presence of allelic association. The TDT uses information on the parent-to-offspring transmission status of the associated allele at the marker locus to assess linkage or association in the presence of the other, using one affected offspring from each set of parents. For testing for linkage in the presence of association, more than one offspring per family can be used. However, without incorporating the correlation structure among offspring, it is not possible to correctly assess the association in the presence of linkage. In this presentation, we propose a Bayesian TDT method as a complementary alternative to the classical approach. In the hypothesis testing setup, given two competing hypotheses, the Bayes factor can be used to weigh the evidence in favor of one of them, thus allowing us to decide between the two hypotheses using established criteria. We compare the proposed Bayesian TDT with a competing frequentist-testing method with respect to power and type I error validity. If we know the mode of inheritance of the disease, then the joint and marginal posterior distributions for the recombination fraction (theta) and disequilibrium coefficient (delta) can be obtained via standard MCMC methods, which lead naturally to Bayesian credible intervals for both parameters.

Alleles↗
PubMed1997

Advances in statistical methods to map quantitative trait loci in outbred populations.

Statistical methods to map quantitative trait loci (QTL) in outbred populations are reviewed, extensions and applications to human and plant genetic data are indicated, and areas for further research are identified. Simple and computationally inexpensive methods include (multiple) linear regression of phenotype on marker genotypes and regression of squared phenotypic differences among relative pairs on estimated proportions of identity-by-descent at a locus. These methods are less suited for genetic parameter estimation in outbred populations but allow the determination of test statistic distributions via simulation or data permutation; however, further inferences including confidence intervals of QTL location require the use of Monte Carlo or bootstrap sampling techniques. A method which is intermediate in computational requirements is residual maximum likelihood (REML) with a covariance matrix of random QTL effects conditional on information from multiple linked markers. Testing for the number of QTLs on a chromosome is difficult in a classical framework. The computationally most demanding methods are maximum likelihood and Bayesian analysis, which take account of the distribution of multilocus marker-QTL genotypes on a pedigree and permit investigators to fit different models of variation at the QTL. The Bayesian analysis includes the number of QTLs on a chromosome as an unknown.

Bayes Theorem↗
PubMed2006

Computational modeling of the Plasmodium falciparum interactome reveals protein function on a genome-wide scale.

Many thousands of proteins encoded by the genome of Plasmodium falciparum, the causal organism of the deadliest form of human malaria, are of unknown function. It is of utmost importance that these proteins be characterized if we are to develop combative strategies against malaria based on the biology of the parasite. In an attempt to infer protein function on a genome-wide scale, we computationally modeled the P. falciparum interactome, elucidating local and global functional relationships between gene products. The resulting interaction network, reconstructed by integrating in silico and experimental functional genomics data within a Bayesian framework, covers approximately 68% of the parasite genome and provides functional inferences for more than 2000 uncharacterized proteins, based on their associations. Network reconstruction involved the use of a novel strategy, where we incorporated continuously updated, uniform reference priors in our Bayesian model. This method for generating interaction maps is thus also well suited for application to other genomes, where pre-existing interactome knowledge is sparse. Additionally, we superimposed this map on genomes of three apicomplexan pathogens--Plasmodium yoelii, Toxoplasma gondii, and Cryptosporidium parvum--describing relationships between these organisms based on retained functional linkages. This comparison provided a glimpse of the highly evolved nature of P. falciparum; for instance, a deficit of nearly 26% in terms of predicted interactions is observed against P. yoelii, because of missing ortholog partners in pairs of functionally linked proteins.

Animals↗
PubMed2005

A probabilistic model of face mapping with local transformations and its application to person recognition.

This paper proposes a new measure of "distance" between faces. This measure involves the estimation of the set of possible transformations between face images of the same person. The global transformation, which is assumed to be too complex for direct modeling, is approximated by a patchwork of local transformations, under a constraint imposing consistency between neighboring local transformations. The proposed system of local transformations and neighboring constraints is embedded within the probabilistic framework of a two-dimensional hidden Markov model. More specifically, we model two types of intraclass variabilities involving variations in facial expressions and illumination, respectively. The performance of the resulting method is assessed on a large data set consisting of four face databases. In particular, it is shown to outperform a leading approach to face recognition, namely, the Bayesian intra/extrapersonal classifier.

Algorithms↗
PubMed2005

Accuracy of identification of grating contrast by human observers: Bayesian models of V1 contrast processing show correspondence between discrimination and identification performance.

This paper presents the results of a contrast identification study, where accuracy in identification is quantified as mutual information between stimulus contrast and observer's response. The stimulus was a set of 2-8 gratings, spanning the range of visible contrasts. Gratings from the set were presented individually for 500 ms, and the observer had to respond by giving the number label corresponding to the contrast of the grating presented. Mutual information increased with set size up to a maximum of around 2.35 bits, i.e., only 5 clearly identifiable contrasts. Set sizes greater than 5 showed a plateau or decline in performance. These data were well fit by Bayesian models of V1 contrast coding, with the parameters obtained by fitting the contrast discrimination results of Chirimuuta and Tolhurst [Chirimuuta, M., & Tolhurst, D. J. (2005). Does a Bayesian model of V1 contrast coding offer a neurophysiological account of human contrast discrimination? Vision Research].

Adult↗
PubMed1994

A bayesian approach to Arrhenius prediction of shelf-life.

The use of a bayesian method for estimating the shelf-life of pharmaceutical formulations is evaluated and compared with classical linear regression. Using three real data sets, the greater flexibility provided by the bayesian approach is demonstrated. In particular, the bayesian approach enabled the consideration of cases when the error distribution is non-normal. However much more computation is required with the bayesian method.

Bayes Theorem↗
PubMed2004

Bayesian models for the analysis of genetic structure when populations are correlated.

MOTIVATION: Population allele frequencies are correlated when populations have a shared history or when they exchange genes. Unfortunately, most models for allele frequency and inference about population structure ignore this correlation. Recent analytical results show that among populations, correlations can be very high, which could affect estimates of population genetic structure. In this study, we propose a mixture beta model to characterize the allele frequency distribution among populations. This formulation incorporates the correlation among populations as well as extending the model to data with different clusters of populations. RESULTS: Using simulated data, we show that in general, the mixture model provides a good approximation of the among-population allele frequency distribution and a good estimate of correlation among populations. Results from fitting the mixture model to a dataset of genotypes at 377 autosomal microsatellite loci from human populations indicate high correlation among populations, which may not be appropriate to neglect. Traditional measures of population structure tend to overestimate the amount of genetic differentiation when correlation is neglected. Inference is performed in a Bayesian framework. CONTACT: fur@ohsu.edu.

Bayes Theorem↗
PubMed2003

A comparison of bayesian methods for haplotype reconstruction from population genotype data.

In this report, we compare and contrast three previously published Bayesian methods for inferring haplotypes from genotype data in a population sample. We review the methods, emphasizing the differences between them in terms of both the models ("priors") they use and the computational strategies they employ. We introduce a new algorithm that combines the modeling strategy of one method with the computational strategies of another. In comparisons using real and simulated data, this new algorithm outperforms all three existing methods. The new algorithm is included in the software package PHASE, version 2.0, available online (http://www.stat.washington.edu/stephens/software.html).

Algorithms↗