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Estimating regression models with unknown break-points.

This paper deals with fitting piecewise terms in regression models where one or more break-points are true parameters of the model. For estimation, a simple linearization technique is called for, taking advantage of the linear formulation of the problem. As a result, the method is suitable for any regression model with linear predictor and so current software can be used; threshold modelling as function of explanatory variables is also allowed. Differences between the other procedures available are shown and relative merits discussed. Simulations and two examples are presented to illustrate the method.

Bronchitis↗

An EM algorithm for mapping quantitative resistance loci.

Many disease resistance traits in plants have a polygenic background and the disease phenotypes are modified by environmental factors. As a consequence, the phenotypic values usually show a quantitative variation. The phenotypes of such disease traits, however, are often measured in discrete but ordered categories. These traits are called ordinal traits. In terms of disease resistance, they are called quantitative resistance traits, as opposed to qualitative resistance traits, and are controlled by the quantitative resistance loci (QRL). Classical quantitative trait locus mapping methods are not optimal for ordinal trait analysis because the assumption of normal distribution is violated. Methods for mapping binary trait loci are not suitable either because there are more than two categories in ordinal traits. We developed a maximum likelihood method to map these QRL. The method is implemented via a multicycle expectation-conditional-maximization (ECM) algorithm under the threshold model, where we can estimate both the QRL effects and the thresholds that link the disease liability and the categorical phenotype. The method is verified in simulated data under various combinations of the parameters. An SAS program is available to implement the multicycle ECM algorithm. The program can be downloaded from our website at www.statgen.ucr.edu.

Algorithms↗

Genetic evaluation of mastitis resistance using a first-passage time model for wiener processes for analysis of time to first treatment.

A Wiener process is a Brownian-motion process initiated in a certain state in a state space, and the first passage time is defined as the time of the process to reach a predefined absorbing state where the process stops. Time from 31 d prepartum to first treatment of clinical mastitis (CM) was modeled as first passage times of such Wiener processes. Two processes were used to allow for several risk factors, and for each process, initiation was at some arbitrary time point, in a certain health state with drift toward or away from absorption (disease). The drift parameter of each process was expressed as linear functions of covariates (year of calving and sire). First passage time was defined as the time from process initiation until the first health status process reached zero (absorption). The model was fitted to records for 36,178 first-lactation daughters of 245 Norwegian cattle sires using a Bayesian approach and Markov chain Monte Carlo methods. Genetic evaluation of sires was carried out by calculating the posterior probability of no CM (the value of the survival function) by d 331, i.e., 300 d after first calving. Alternatively, sire evaluation was based on the integrated area under the survival curve. These measures were highly correlated (0.999), which indicates a small degree of crossings of the sire-dependent survival curves. Hence, sire-specific hazards were close to proportional, resulting in a higher rank-correlation to sire evaluations from a survival model with proportional hazards than to the results from a multivariate threshold model.

Animals↗

Genetic models of sex effect in unipolar affective illness.

Family study data on unipolar affective illness are analyzed by multiple threshold models of inheritance that incorporate sex effect. In these models males and females share a common genetic-environmental liability, but the less prevalent sex, i.e., males, has a higher genetic threshold for the disorder. Neither single major locus (SML) nor multifactorial-polygenic (MFP) transmission can account for the sex differences in the morbid risk for unipolar disorder. The implications for genetic research in affective disorders are discussed.

Chromosome Mapping↗

Topics in microbial risk assessment: dynamic flow tree process.

Microbial risk assessment is emerging as a new discipline in risk assessment. A systematic approach to microbial risk assessment is presented that employs data analysis for developing parsimonious models and accounts formally for the variability and uncertainty of model inputs using analysis of variance and Monte Carlo simulation. The purpose of the paper is to raise and examine issues in conducting microbial risk assessments. The enteric pathogen Escherichia coli O157:H7 was selected as an example for this study due to its significance to public health. The framework for our work is consistent with the risk assessment components described by the National Research Council in 1983 (hazard identification; exposure assessment; dose-response assessment; and risk characterization). Exposure assessment focuses on hamburgers, cooked a range of temperatures from rare to well done, the latter typical for fast food restaurants. Features of the model include predictive microbiology components that account for random stochastic growth and death of organisms in hamburger. For dose-response modeling, Shigella data from human feeding studies were used as a surrogate for E. coli O157:H7. Risks were calculated using a threshold model and an alternative nonthreshold model. The 95% probability intervals for risk of illness for product cooked to a given internal temperature spanned five orders of magnitude for these models. The existence of even a small threshold has a dramatic impact on the estimated risk.

Analysis of Variance↗

Effects of pentachlorophenol-contaminated food organisms on toxicity and bioaccumulation in the frog Xenopus laevis.

Sub-adult African clawed frogs (Xenopus laevis) were fed pentachlorophenol (PCP)-injected mealworms containing 64.8 to 2604 ug of PCP per gram of worm for 27 days. There was no mortality and no significant bioaccumulation of PCP in the frogs. After three weeks, frogs fed 2,604 micrograms/g of PCP ceased eating. The no observed adverse effects level (NOAEL) based on significantly reduced food consumption (PCP-injected mealworms) was 638 micrograms/g. This corresponded to a NOAEL based on PCP intake of about 8 micrograms PCP/g frog/day. A toxicity threshold model estimated that about 800 micrograms/L of waterborne PCP may be a threshold for adverse effects in Xenopus or similar amphibians. Further study is needed to verify threshold estimates.

Animals↗

Genomic prediction and genome-wide association study for liver abscesses in crossbred beef cattle.

Liver abscesses are a concern in feedlot cattle, and little is known about the role of genetics in their development. This study aimed to estimate genetic parameters and to identify single-nucleotide polymorphisms (SNPs) associated with liver abscesses. Crossbred cattle representing 18 breeds in the U.S. Meat Animal Research Center Germplasm Evaluation Program were phenotyped for liver abscesses at slaughter (n&#x2005;=&#x2005;9,044). Seventeen percent of cattle had liver abscesses. These cattle had genotypes that were imputed to sequence variant genotypes. After filtering and quality control, 340,723 SNPs were used in the analysis. Liver abscess prevalence was modeled with a single-step genomic best linear unbiased prediction (ssGBLUP) threshold model using a Bayesian framework. The model included contemporary group (sex, treatment group, and slaughter date), additive genomic, and residual effects. Genomic heritability was 0.039 (95% highest posterior density&#x2005;=&#x2005;0.005, 0.081), which was very small. To assess prediction quality, a 5-fold random cross-validation structure was used. Method Linear Regression was used to assess accuracy, bias, and dispersion by comparing estimated breeding values (EBV) from full and reduced analyses. Cross-validation metrics showed EBV based on genotypes had 0.05 reliability (SD&#x2005;<&#x2005;0.01) with no bias relative to EBV based on genotypes and phenotypes. For the genome-wide association study, SNP effects were back calculated from the EBV solutions from ssGBLUP. No SNPs were associated with liver abscesses at a Benjamini-Hochberg adjusted 0.05 significance level. Although a large dataset was used, this result was because of the low genomic heritability and imprecise EBV used to calculate SNP effects. Based on these results, environmental factors contribute to most of the variation in liver abscesses. Genetic selection to reduce liver abscesses would be slow because of the low genomic heritability, measurement late in life, and inability to measure breeding animals. A faster approach would be finding additional environmental interventions that maintain animal performance.

Animals↗

Determinants involved in the perception of the Necker cube: an application of catastrophe theory.

The study is concerned with evaluating interactions at the organic level within the visual perception subsystem of living systems. The reported work focuses on the identification of some of the determinants of multistable perception by experimentally testing a nonlinear dynamical systems (catastrophe) model of the Necker Cube. This technique serves as an advantage over linear threshold models which cannot effectively study multivalued functional relationships. It was proposed that manipulation of two independent control parameters (bias or changing shape by continuously varying perspective lines and selective stimulus shading) was compatible with the subjective dichotomy of bistable perception of the Necker cube. One hundred and twenty naive subjects, categorized by age, sex, and optical aids, were presented with a computer-generated sequence of 63 stimuli (7 shading levels X 9 perspective levels) to which they had to respond as to whether they saw a "hollow" or "solid" image. The work revealed that bias and shading exerted their effects in opposition and that each influenced the other. Both were decisive factors involved in the perception of the cube. These findings are supported by topological and psychological evidence.

Adolescent↗

Origin, cellular expression, and cybrid transmission of mitochondrial CAP-R, PYR-IND, and OLI-R mutant phenotypes.

Chloramphenicol-resistant (CAP-R) mouse and Chinese hamster lines were isolated in a single selection step in drug medium containing pyruvate. Cellular expression of the CAP-R phenotype required pyruvate--or an appropriate substitute--as a nutritional supplement. Subclone lines which were pyruvate independent (PYR-IND) arose in second-step selections at a high frequency. CAP-R PYR-IND Chinese hamster mutants could be directly isolated in single-step selections but at a very low frequency. Subclone lines (OLI-R) which were cross-resistant to oligomycin were isolated in a third selection cycle. The PYR-IND and OLI-R phenotypes were cotransmitted with the CAP-R mtDNA mutation but were expressed at the cellular level only if the number of mutant mitochondrial genomes exceeded a minimum threshold value. Analysis of a mtDNA restriction fragment alteration in one series of mutants supported this model. Threshold limits for cellular expression of mitochondrial mutant phenotypes are likely to be a general phenomenon and will constrain models of the origin and segregation of mtDNA mutations.

Animals↗

A time series analysis of the relationship of ambient temperature and common bacterial enteric infections in two Canadian provinces.

The incidence of enteric infections in the Canadian population varies seasonally, and may be expected to be change in response to global climate changes. To better understand any potential impact of warmer temperature on enteric infections in Canada, we investigated the relationship between ambient temperature and weekly reports of confirmed cases of three pathogens in Canada: Salmonella, pathogenic Escherichia coli and Campylobacter, between 1992 and 2000 in two Canadian provinces. We used generalized linear models (GLMs) and generalized additive models (GAMs) to estimate the effect of seasonal adjustments on the estimated models. We found a strong non-linear association between ambient temperature and the occurrence of all three enteric pathogens in Alberta, Canada, and of Campylobacter in Newfoundland-Labrador. Threshold models were used to quantify the relationship of disease and temperature with thresholds chosen from 0 to -10 degrees C depending on the pathogen modeled. For Alberta, the log relative risk of Salmonella weekly case counts increased by 1.2%, Campylobacter weekly case counts increased by 2.2%, and E. coli weekly case counts increased by 6.0% for every degree increase in weekly mean temperature. For Newfoundland-Labrador the log relative risk increased by 4.5% for Campylobacter for every degree increase in weekly mean temperature.

Alberta↗

Intracellular nonlinear frequency response measurements in the cockroach tactile spine neuron.

The threshold of the cockroach tactile neuron increases strongly with depolarization by a process involving at least two time constants. This effect is probably responsible for the rapid and complete adaptation of the neuron's response to step inputs. A technique for intracellular recording and stimulation of the neuron has recently been established and this allows direct observation of the dynamic response of the neuronal encoder. A white noise stimulus was used to modulate the membrane potential of the neuron. The first-order frequency response function between membrane potential and action potential discharge could be explained by a variable threshold model with two time constants. Second-order frequency response functions could be accounted for by a Wiener cascade model. The dynamic nonlinear behavior of the encoder can therefore be explained by a unidirectional threshold which increases linearly and dynamically with membrane potential.

Acoustic Stimulation↗

Na-K ATPase activity in murine glucocorticoid induced polycystic kidney disease in vivo.

The prevalence and severity of polycystic kidney disease (PKD) induced by glucocorticoids in mice can be predicted by a mathematical "threshold" model. We studied the relationship between Na-K ATPase activity and cyst formation in C3H (low threshold for PKD) and DBA mice (high threshold). There was no difference in Na-K ATPase induction by 200 mg/kg methyl prednisolone acetate (MPA) (C3H; 97.4 nmol NADH/min/mg protein: DBA; 94.2 nmol NADH/min/mg protein). C3H mice demonstrated greater cyst formation than DBA animals as measured by area (20.1% relative area vs 13.9%, p < 0.05) or by calculated volume (7.4% relative volume vs 2.3%, p < 0.001). Significant relationships were seen between Na-K ATPase activity and logarithmically transformed area data in C3H animals and with cyst volume in both strains. Na-K ATPase activity is related to cyst formation in glucocorticoid induced PKD, but the level of Na-K ATPase activity is not a determinant of the threshold for glucocorticoid induced PKD.

Animals↗

Mapping quantitative trait loci for complex binary diseases using line crosses.

A composite interval gene mapping procedure for complex binary disease traits is proposed in this paper. The binary trait of interest is assumed to be controlled by an underlying liability that is normally distributed. The liability is treated as a typical quantitative character and thus described by the usual quantitative genetics model. Translation from the liability into a binary (disease) phenotype is through the physiological threshold model. Logistic regression analysis is employed to estimate the effects and locations of putative quantitative trait loci (our terminology for a single quantitative trait locus is QTL while multiple loci are referred to as QTLs). Simulation studies show that properties of this mapping procedure mimic those of the composite interval mapping for normally distributed data. Potential utilization of the QTL mapping procedure for resolving alternative genetic models (e.g., single- or two-trait-locus model) is discussed.

Chromosome Mapping↗

At issue: are traditional societies schizophrenogenic?

Schizophrenia is apparently less common in traditional than in nontraditional societies, and the course of illness in these cultural settings may also be more benign. Viral, political, economic, social labeling, and other explanations have been offered over the years for these differences. In contrast to those ideas that suggest the presence of a schizophrenogenic stress in urbanized, Westernized populations, I propose that traditional societies are actually schizophrenogenic compared with nontraditional societies. Assuming a multifactorial threshold model for the development of schizophrenia, traditional societies may be characterized by a lower threshold for developing schizophrenia in at-risk individuals. In the short term, this leads to a greater proportion of all clinical cases being of a less severe variety; in the long term, genes predisposing individuals to develop schizophrenia are exposed to the effects of negative selection, ultimately resulting in a relatively lower level of overt schizophrenia in these populations. The greater social demands placed on individual actors in traditional societies and the lack of variability in social network size may contribute to the (relatively) schizophrenogenic environment.

Cross-Cultural Comparison↗

Sex differences in the hyperkinetic syndrome of childhood.

Among a clinic sample of 6525 subjects, 61 males and 18 females with an ICD-9 diagnosis of the hyperkinetic syndrome of childhood were identified. Hyperactive girls had a lower IQ and significantly higher rates of language disorders and neurological disorders, suggesting a possible neurological basis for hyperactivity in females. In contrast, there was a population of male hyperactives with less evidence of brain dysfunction and a normal IQ, evidence compatible with the model of greater male constitutional variability. There was little evidence for the polygenetic multiple threshold model of sex inheritance.

Child↗

Precautionary principles: a jurisdiction-free framework for decision-making under risk.

Fundamental principles of precaution are legal maxims that ask for preventive actions, perhaps as contingent interim measures while relevant information about causality and harm remains unavailable, to minimize the societal impact of potentially severe or irreversible outcomes. Such principles do not explain how to make choices or how to identify what is protective when incomplete and inconsistent scientific evidence of causation characterizes the potential hazards. Rather, they entrust lower jurisdictions, such as agencies or authorities, to make current decisions while recognizing that future information can contradict the scientific basis that supported the initial decision. After reviewing and synthesizing national and international legal aspects of precautionary principles, this paper addresses the key question: How can society manage potentially severe, irreversible or serious environmental outcomes when variability, uncertainty, and limited causal knowledge characterize their decision-making? A decision-analytic solution is outlined that focuses on risky decisions and accounts for prior states of information and scientific beliefs that can be updated as subsequent information becomes available. As a practical and established approach to causal reasoning and decision-making under risk, inherent to precautionary decision-making, these (Bayesian) methods help decision-makers and stakeholders because they formally account for probabilistic outcomes, new information, and are consistent and replicable. Rational choice of an action from among various alternatives--defined as a choice that makes preferred consequences more likely--requires accounting for costs, benefits and the change in risks associated with each candidate action. Decisions under any form of the precautionary principle reviewed must account for the contingent nature of scientific information, creating a link to the decision-analytic principle of expected value of information (VOI), to show the relevance of new information, relative to the initial (and smaller) set of data on which the decision was based. We exemplify this seemingly simple situation using risk management of BSE. As an integral aspect of causal analysis under risk, the methods developed in this paper permit the addition of non-linear, hormetic dose-response models to the current set of regulatory defaults such as the linear, non-threshold models. This increase in the number of defaults is an important improvement because most of the variants of the precautionary principle require cost-benefit balancing. Specifically, increasing the set of causal defaults accounts for beneficial effects at very low doses. We also show and conclude that quantitative risk assessment dominates qualitative risk assessment, supporting the extension of the set of default causal models.

Decision Making↗

Undesired phenotypic and genetic trend for stillbirth in Danish Holsteins.

The primary aim of this study was to evaluate the phenotypic and genetic trends for stillbirth in Danish Holsteins. Trends of calving difficulty and calf size were also evaluated. The second aim was to compare predicted transmitting abilities (PTA) of sires for stillbirth using a linear and a threshold model. Direct and maternal genetic effects were modeled by fitting correlated additive genetic effects of the sire and the maternal grandsire (MGS). For both the calf and the dam, covariates of breed proportions of Holstein-Friesian (HF) and the heterozygosity between HF and the original Danish Black and White (ODBW) were included. Records from 1.8 million first-calving Danish Holstein cows calving from 1985 to 2002 were used. In this period, the overall frequency of stillbirth increased from 0.071 to 0.090. An unfavorable genetic trend of stillbirth was found for both the direct and maternal effect. The background for the genetic trends was an intense use of HF sires as sires of sons, which increased the proportion of HF genes to 94% in the Danish Holstein calves born in 2002. The effect of the imported HF genes was higher direct effects of calf size, calving difficulty, and stillbirth compared with the ODBW genes. The maternal effect of stillbirth was poorer for HF than for ODBW even though HF had a better maternal calving performance than ODBW. The threshold and the linear models showed almost similar predictions of transmitting abilities of sires.

Animals↗

Seed reserve-dependent growth responses to temperature and water potential in carrot (Daucus carota L.).

Both temperature and soil moisture vary greatly in the surface layers of the soil through which seedlings grow following germination. The work presented studied the impact of these environmental variables on post-germination carrot growth to nominal seedling emergence. The rapid pre-crook downward growth of both the hypocotyl and root was consistent with their requirement for establishment in soil drying from the surface. At all temperatures, both hypocotyl and root growth rates decreased as water stress increased and there was a very distinct temperature optimum that tended to occur at lower temperatures as water stress increased. A model based on the thermodynamics of reversible protein denaturation was adapted to include the effects of water potential in order to describe these growth rate responses. In general, the percentage of seedlings that reached the crook stage (start of upward hypocotyl growth) decreased at the extremes of the temperature range used and was progressively reduced by increasing water stress. A model was developed to describe this response based on the idea that each seedling within a population has lower and upper temperature thresholds and a water potential threshold which define the conditions within which it is able to grow. This threshold modelling approach which applies growth rates within a distribution of temperature and water potential thresholds could be used to simulate seedling growth by dividing time into suitable units.

Daucus carota↗