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PubMed2000

Bayesian estimators for conditional hazard functions.

This article introduces a new Bayesian approach to the analysis of right-censored survival data. The hazard rate of interest is modeled as a product of conditionally independent stochastic processes corresponding to (1) a baseline hazard function and (2) a regression function representing the temporal influence of the covariates. These processes jump at times that form a time-homogeneous Poisson process and have a pairwise dependency structure for adjacent values. The two processes are assumed to be conditionally independent given their jump times. Features of the posterior distribution, such as the mean covariate effects and survival probabilities (conditional on the covariate), are evaluated using the Metropolis-Hastings-Green algorithm. We illustrate our methodology by an application to nasopharynx cancer survival data.

Bayes Theorem↗
PubMed2002

Model-checking techniques based on cumulative residuals.

Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.

Adolescent↗
PubMed2002

Testing the relationship between morphological and molecular rates of change along phylogenies.

Molecular evolution has been considered to be essentially a stochastic process, little influenced by the pace of phenotypic change. This assumption was challenged by a study that demonstrated an association between rates of morphological and molecular change estimated for "total-evidence" phylogenies, a finding that led some researchers to challenge molecular date estimates of major evolutionary radiations. Here we show that Omland's (1997) result is probably due to methodological bias, particularly phylogenetic nonindependence, rather than being indicative of an underlying evolutionary phenomenon. We apply three new methods specifically designed to overcome phylogenetic bias to 13 published phylogenetic datasets for vertebrate taxa, each of which includes both morphological characters and DNA sequence data. We find no evidence of an association between rates of molecular and morphological rates of change.

Animals↗
PubMed2004

A likelihood-based method for testing for nonstochastic variation of diversification rates in phylogenies.

Observed variations in rates of taxonomic diversification have been attributed to a range of factors including biological innovations, ecosystem restructuring, and environmental changes. Before inferring causality of any particular factor, however, it is critical to demonstrate that the observed variation in diversity is significantly greater than that expected from natural stochastic processes. Relative tests that assess whether observed asymmetry in species richness between sister taxa in monophyletic pairs is greater than would be expected under a symmetric model have been used widely in studies of rate heterogeneity and are particularly useful for groups in which paleontological data are problematic. Although one such test introduced by Slowinski and Guyer a decade ago has been applied to a wide range of clades and evolutionary questions, the statistical behavior of the test has not been examined extensively, particularly when used with Fisher's procedure for combining probabilities to analyze data from multiple independent taxon pairs. Here, certain pragmatic difficulties with the Slowinski-Guyer test are described, further details of the development of a recently introduced likelihood-based relative rates test are presented, and standard simulation procedures are used to assess the behavior of the two tests in a range of situations to determine: (1) the accuracy of the tests' nominal Type I error rate; (2) the statistical power of the tests; (3) the sensitivity of the tests to inclusion of taxon pairs with few species; (4) the behavior of the tests with datasets comprised of few taxon pairs; and (5) the sensitivity of the tests to certain violations of the null model assumptions. Our results indicate that in most biologically plausible scenarios, the likelihood-based test has superior statistical properties in terms of both Type I error rate and power, and we found no scenario in which the Slowinski-Guyer test was distinctly superior, although the degree of the discrepancy varies among the different scenarios. The Slowinski-Guyer test tends to be much more conservative (i.e., very disinclined to reject the null hypothesis) in datasets with many small pairs. In most situations, the performance of both the likelihood-based test and particularly the Slowinski-Guyer test improve when pairs with few species are excluded from the computation, although this is balanced against a decline in the tests' power and accuracy as fewer pairs are included in the dataset. The performance of both tests is quite poor when they are applied to datasets in which the taxon sizes do not conform to the distribution implied by the usual null model. Thus, results of analyses of taxonomic rate heterogeneity using the Slowinski-Guyer test can be misleading because the test's ability to reject the null hypothesis (equal rates) when true is often inaccurate and its ability to reject the null hypothesis when the alternative (unequal rates) is true is poor, particularly when small taxon pairs are included. Although not always perfect, the likelihood-based test provides a more accurate and powerful alternative as a relative rates test.

Biodiversity↗
PubMed1979

A new method for the estimation of cell cycle phases.

A method is described, which is applicable to cell renewal systems with an anatomical structure in which all cell locations may be uniquely mapped. Its use is demonstrated on the rat incisor inner enamel epithelium, which forms a one cell thick column in the sagittally sectioned tooth. Cells born in the apical part of the column migrate toward the distal end of the tooth, where they mature. As the cells migrate along the column, they traverse the various cell cycle phases. The present study has been designed to estimate the probability of a cell being in a given phase; all cells touching the basement membrane were numbered, and the number of cells separating any two cells was taken as a measure of distance. Since generally all cells move in one direction (lateral cell migration may occur), it is possible to solve the problem with the aid of functions describing the renewal counting stochastic process in which cell distance serves as an independent variable. The method predicts labelled cell and mitotic rates which agree with those estimated in the usual way. It was then utilized to estimate the fraction of cells in G2.

Animals↗
PubMed2004

How cryptic is the Scandinavian lynx?

A reanalysis of the existing genotypic data shows that they are compatible with the hypothesis that the present-day Scandinavian lynx represents a recent expansion from a single source. This contradicts earlier conclusions. The difference arises when it is assumed that the expansion and colonization have been stochastic processes and that the populations may not be at a drift-migration equilibrium.

Animal Migration↗
PubMed2006

Population size, female fecundity, and sex ratio variation in gynodioecious Plantago maritima.

Theory predicts that the sex ratio of gynodioecious populations (in which hermaphrodites and females coexist) will be affected by the relative female fitness of females and hermaphrodites, and by founder events and genetic drift in small populations. We documented the sex ratio and size of 104 populations of the gynodioecious, perennial herb Plantago maritima in four archipelagos in eastern Sweden and western Finland (from latitude 53 to 64 degrees N). The sex ratio varied significantly both among and within archipelagos (range 0-70% females, median 6.3% females). The frequency of females was highest in the northernmost archipelago and lowest in the southernmost archipelago. As predicted, females were more frequently missing from small than from large populations, and the variance in sex ratio increased with decreasing population size. The relative fecundity of female plants (mean seed output per female/mean seed output per hermaphrodite) ranged from 0.43 to 2.16 (median 1.01, n = 12 populations). Among the 12 populations sampled for seed production (four in each of three archipelagos), the frequency of females was positively related to relative fecundity of females and negatively related to population size. The results suggest that the local sex ratio is influenced both by the relative fecundity of females and hermaphrodites and by stochastic processes in small populations.

Environment↗
PubMed2005

Goodness-of-fit methods for generalized linear mixed models.

We develop graphical and numerical methods for checking the adequacy of generalized linear mixed models (GLMMs). These methods are based on the cumulative sums of residuals over covariates or predicted values of the response variable. Under the assumed model, the asymptotic distributions of these stochastic processes can be approximated by certain zero-mean Gaussian processes, whose realizations can be generated through Monte Carlo simulation. Each observed process can then be compared, both visually and analytically, to a number of realizations simulated from the null distribution. These comparisons enable one to assess objectively whether the observed residual patterns reflect model misspecification or random variation. The proposed methods are particularly useful for checking the functional form of a covariate or the link function. Extensive simulation studies show that the proposed goodness-of-fit tests have proper sizes and are sensitive to model misspecification. Applications to two medical studies lead to improved models.

Anti-HIV Agents↗
PubMed1997

Specificity, tolerance and developmental regulation of natural killer cells defined by expression of class I-specific Ly49 receptors.

Natural killer cells in the mouse express class I MHC-specific inhibitory receptors of the Ly49 protein family. The receptors mediate inhibition of the lysis of tumor cells and normal cells, and mediate the specificity of bone-marrow graft rejection by NK cells in vivo. The function of these receptors may be to confer upon NK cells the capacity to distinguish normal self cells from cells that have down-regulated expression of some or all self-class I molecules. Ly49 receptors discriminate between different class I molecules, and are distributed in expression to overlapping subsets of NK cells. The receptors appear to interact with class I-MHC residues and associated N-glycans, with little or no discrimination of the class I-bound peptide. The Ly49 receptor repertoire may be initially generated by a stochastic process that distributes receptors randomly to different cells and treats the two alleles of a given Ly49 gene independently. However, class I-MHC-dependent "education" processes shape the functional repertoire. The education processes silence potentially auto-aggressive NK cells, probably by ensuring that each NK cell expresses at least one self-specific Ly49 receptor. In addition, NK cell clones that express multiple self-specific Ly49 receptors are disfavored by the education processes, perhaps to confer greater discrimination on to individual NK cells.

Animals↗
PubMed2001

Different patterns in molecular evolution of the Triticeae.

A huge part of the genomes of most Triticeae species is formed by different families of repetitive DNA sequences. In this paper the phylogenetic distribution of two major classes of the repeats, retrotransposons and tandemly organized DNA sequences, are considered and compared with the evolution of gene-rich regions and generally accepted Triticeae phylogenetic relationships. In Hordeum, LTR-containing retrotransposons are dispersed along the chromosomes and are consistent with the existing picture of the phylogeny of Hordeum. Another retrotransposon class, LINEs, have evolved independently from LTR-retrotransposons. Different retrotransposon classes appear to have competed for genome space during the evolution of Hordeum. Another class of repeats, tandemly organized DNA sequences, tends to cluster at the functionally important regions of chromosomes, centromeres and telomeres. The distribution of a number of tandem DNA families in Triticeae is not congruent with generally accepted phylogenetic relationships. While natural selection is the dominant factor determining the structure of genic regions we suggest that the contribution of random events is important in the evolution of repetitive DNA sequences. The interplay of stochastic processes, molecular drive, and selection determines the structure of chromosomal regions, notably at centromeres and telomeres, stabilizing and differentiating species-specific karyotypes. Thus, the evolution of these regions may occur largely independently of the evolution of gene-rich regions.

Blotting, Southern↗
PubMed1999

Stem cells, pre-progenitor cells and lineage-committed cells: are our dogmas correct?

Recent developments warrant careful reexamination of several of the central dogmas of hematopoiesis. The bioassays previously used may have predetermined which subsets of hematopoietic stem cells are regarded as having long-term repopulating activity and thus have produced misleading data. Lineage commitment in multipotential cells has been regarded as an immutable stochastic process but may be a process that can be modified by extrinsic signaling. Finally, loss of self-renewal activity has been regarded as progressive and irreversible but this response to signaling can be blocked by cytokine-inducible modulating proteins.

Animals↗
PubMed2001

Assessing serial irregularity and its implications for health.

Approximate entropy (ApEn) is a recently formulated family of parameters and statistics quantifying regularity (orderliness) in serial data, with developments within theoretical mathematics as well as numerous applications to multiple biological contexts. We discuss the motivation for ApEn development, from the study of inappropriate application of dynamical systems (complexity) algorithms to general time-series settings. ApEn is scale invariant and model independent, evaluates both dominant and subordinant patterns in data, and discriminates series for which clear feature recognition is difficult. ApEn is applicable to systems with at least 50 data points and to broad classes of models: it can be applied to discriminate both general classes of correlated stochastic processes, as well as noisy deterministic systems. Moreover, ApEn is complementary to spectral and autocorrelation analyses, providing effective discriminatory capability in instances in which the aforementioned measures exhibit minimal distinctions. Representative ApEn applications to human aging studies, based on both heart rate and endocrinologic (hormonal secretory) time series, are featured. Heart rate (HR) studies include gender- and age-related changes in HR dynamics in older subjects, and analyses of "near-SIDS" infants. Endocrinologic applications establish clear quantitative changes in joint LH-testosterone secretory dynamics in older versus younger men (a "partial male menopause"), via cross-ApEn, a related two-variable asynchrony formulation; a disruption in LH-FSH-NPT (penile tumescence) synchrony in older subjects; and changes in LH-FSH secretory dynamics across menopause. The capability of ApEn to assess relatively subtle disruptions, typically found earlier in the history of a subject than mean and variance changes, holds the potential for enhanced preventative and earlier interventionist strategies.

Algorithms↗
PubMed2026

The Spatial and Temporal Repeatability of Genomic Responses to Natural Selection as Demonstrated in Stickleback Populations Experiencing Highly Dynamic Environments.

The evolution of genotypic parallelism under shared environmental conditions provides strong evidence for the role of natural selection. However, analyses typically examine genomic signatures of selection long after the putative selection event and only assess the repeatability of responses across spatial population replicates. This impedes our ability to attribute a particular response to a given selection pressure and to distinguish non-parallel responses caused by stochastic processes from those caused by local selection. As such, the consistency of natural selection over space and time is unknown, and the role of persistent local selection pressures is unclear. Here, we leveraged the natural bar-built estuary system of Santa Cruz, California, to examine the repeatability of seasonal genomic change in threespine stickleback (Gasterosteus aculeatus) over space and time. By comparing allele-frequency shifts that are shared across locations (spatial repeatability) with those that are shared across years within locations (temporal repeatability), we identified both spatially shared and local components of putative selection. We found that repeated seasonal outlier responses occurred more often than expected under a neutral null model. Although repeatability declined as the number of estuaries sharing an outlier increased, enrichment above neutral expectations increased with broader spatial sharing, particularly for outliers repeated across both years. While the precise outlier SNPs varied across years, estuary-specific patterns of responses were broadly consistent, suggesting an important role for local conditions. Together, our findings show that temporal sampling can reveal components of putative selection that would be missed from spatial comparisons alone. More broadly, they highlight the importance of examining repeatability over both space and time to understand the parallel and non-parallel components of adaptive genomic change.

Animals↗
PubMed1972

Quantal independence and uniformity of presynaptic release kinetics at the frog neuromuscular junction.

1. Amplitude and latency fluctuations of the end-plate potential at the frog neuromuscular junction were studied simultaneously at low temperatures, using intracellular or focal extracellular recording techniques and average quantal contents between 0.5 and 3.2. At the release rates studied, the evoked release of one quantum has in most cases no significant effect on the probability of subsequent quantal release to the same stimulus, confirming the mutual independence of quantal releases in this preparation.3. An equation derived from Poisson's law was applied to a histogram of the latencies of the first quantum released on each of a series of trials, to predict the average quantal content of end-plate responses originating at various times after nerve stimulation. The shape of the predicted time distribution of quantal contents usually agreed closely with that of the experimentally observed time distribution of end-plate response amplitudes. This agreement demonstrates that both the amplitude and the latency fluctuations of the end-plate response result from one presynaptic stochastic process that is uniform in magnitude and time course after each stimulus.4. Analysis of extracellular records from synaptic regions with a history of extensive activity often suggested the existence of depressive interaction among quantal releases, perhaps caused by depletion of the supply of releasable quanta.

Animals↗
PubMed1977

The effect of calcium ions and temperature on the binomial parameters that control acetylcholine release by a nerve impulse at amphibian neuromuscular synapses.

1. A study has been made of the effects of changing the external calcium concentration, [Ca](o), and the temperature on both the number of quanta available for release by the nerve impulse (n) as well as the increase in release probability of a quantum p(t) during the release period (from 0 to T) following a nerve impulse at synapses in amphibian striated muscle.2. When [Ca](o) was increased in the low range from 0.25 to 0.4 mM at 18 degrees C, the average quantal content of the e.p.p. (m) increased as the fourth power of [Ca](o) and this was primarily due to a third power dependence of n on [Ca](o); the dissociation constants and power dependence of n on calcium determined in the [Ca](o) range from 0.25 to 1.0 mM were successfully used to predict the changes in size of the e.p.p. in the very high [Ca](o) range from 1 to 10 mM. When the temperature was increased from 7 to 18 degrees C in a [Ca](o) of 0.6 mM or 0.35 mM, n increased with a Q(10) of 2.5.3. When [Ca](o) was increased in the range from 0.25 to 1.0 mM at 18 degrees C, the probability that a quantum initially available for release is released during the release period (p(T)) was very sensitive to [Ca](o), increasing as the third power of [Ca](o) and with a dissociation constant of 0.13 mM. When the temperature was increased from 7 to 18 degrees C in a [Ca](o) of 0.6 mM or 0.35 mM, p(T) decreased.4. The histograms of latencies of individual quanta following a nerve impulse was very temperature dependent: the time to peak of the histograms (i.e. the interval in which most quanta fell) had a Q(10) of over 4 as did the time constant of decline of the histograms in the temperature range from 7 to 18 degrees C.5. The average number of quanta released up to time t during the release period following a nerve impulse, namely np(t), was well described by a stochastic process in which p(t) was determined by two reactions; one of these reactions released available quanta from the nerve terminal whilst the other made some of the available quanta unavailable for release by the nerve impulse.

Acetylcholine↗
PubMedDate not supplied

Model of the spatial-frequency-dependent detective quantum efficiency of phosphor screens.

We have developed a theoretical model to predict the modulation transfer function (MTF), the shape of the x-ray quantum noise power spectrum (NPS), and the spatial-frequency-dependent detective quantum efficiency (DQE) of an x-ray phosphor screen. The transfer of energy through the screen is modelled as a series of cascaded stochastic processes assuming that the screen consists of many thin phosphor layers. In this way, the model is able to account for the possibility of secondary-quantum noise and the difference in shape between MTF2 and the x-ray quantum NPS. Modelling a Kodak Min-R screen we were able to predict both the number of light quanta emitted per absorbed x-ray and MTF(f) to better than +/- 5%, and the scintillation efficiency to within 10% of experimentally measured values. The shape of the x-ray quantum NPS is predicted to within +/- 5% for spatial frequencies less than about 6 mm-1 and to within +/- 20% for higher frequencies.

Mathematics↗
PubMed2003

Reduced models for the medium-frequency dynamics of stochastic systems.

In this paper, a frequency domain vibration analysis procedure of a randomly parametered structural system is described for the medium-frequency range. In this frequency range, both traditional modal analysis and statistical energy analysis (SEA) procedures well-suited for low- and high-frequency vibration analysis respectively, lead to computational and conceptual difficulties. The uncertainty in the structural system can be attributed to various reasons such as the coupling of the primary structure with a variety of secondary systems for which conventional modeling is not practical. The methodology presented in the paper consists of coupling probabilistic reduction methods with dynamical reduction methods. In particular, the Karhunen-Loeve and Polynomial Chaos decompositions of stochastic processes are coupled with an operator decomposition scheme based on the spectrum of an energy operator adapted to the frequency band of interest.

Journal Article↗
PubMed2003

A substructure approach for the midfrequency vibration of stochastic systems.

A novel substructure coupling technique based on the proper orthogonal decomposition method is presented for the midfrequency range vibration of linear dynamical systems with parameter uncertainty. For a given frequency band, the methodology permits the derivation of an adaptive basis for each subsystem and the construction of a reduced-order model of the global structure. The formulation is directed toward the efficient probabilistic characterization of model-based predictions in the framework of a stochastic finite element method. The efficiency of the substructure method has been contrasted both from the viewpoint of adopting free-free and fixed-fixed substructure proper orthogonal modes in order to arrive at a reduced subsystem model. The distinction as well as similarity of the present methodology with the component mode synthesis is also pointed out The proper orthogonal modes are obtained from both frequency- and time-domain approaches, and their suitability is discussed in relation to the behavior of a specific system. The substructure approach elegantly integrates with a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes.

Journal Article↗