On the asymmetry of biological frequency distributions

Quantifying Distances Between Non-Elliptical Clusters to Enhance the Identification of Meaningful Emotional Reactivity Subtypes

Coordinated emotional responses across psychophysiological and subjective indices is a cornerstone of adaptive emotional functioning. Using clustering to identify cross-diagnostic subgroups with similar emotion response profiles may suggest novel underlying mechanisms and treatments.However, many psychophysiological measures are non-normal even in homogenous samples, and over-reliance on traditional elliptical clustering approaches may inhibit the identification of meaningful subgroups. Finite mixture models that allow for non-elliptical cluster distributions is an emerging methodological field that may overcome this hurdle. Furthermore, succinctly quantifying pairwise cluster separation could enhance the clinical utility of the clustering solutions. However, a comprehensive examination of distance measures in the context of elliptical and non-elliptical model-based clustering is needed to provide practical guidance on the computation, benefits, and disadvantages of existing measures. We summarize several measures that can quantify the multivariate distance between two clusters and suggest practical computational tools. Through a simulation study, we evaluate the measures across three scenarios that allow for clusters to differ in location, scale, skewness, and rotation. We then demonstrate our approaches using psychophysiological and subjective responses to emotional imagery captured through the Transdiagnostic Anxiety Study. Finally, we synthesize findings to provide guidance on how to use distance measures in clustering applications.

Reference intervals of the sex hormonal profile in healthy women: A retrospective single-center study in Peru

The female hormonal profile is of utmost importance for the assessment of the endocrinological functional status and the diagnosis of diseases. The analysis must delimit their normality intervals based on the manufacturer's cut-off points. Due to not all intervals can be evaluated before use, it is imperative to verify the reference intervals to achieve uniformity in the interpretation of results in the female population. We determine the reference intervals of five female sex hormones [Follicle Stimulating hormone (FSH), Estradiol, Luteinizing Hormone (LH), Prolactin, and progesterone] using electrochemiluminescence in the Cobas e411 (Roche). We included female patients >18 years old, between the 3rd and 15th day of the menstrual cycle (follicular phase) and had no previous medical history or recent medication. For reference intervals analysis, we followed the recommendations of the CLSI C28-A3 guideline. The average concentration for FSH, progesterone, LH, prolactin and estradiol were 11.48 ± 21.10 mIU/ml, 8.19 ± 11.90 ng/ml, 10.98 ± 11.55 ng/ml, 25.05 ± 32.74 ng/mL, and 147.08 ± 473.8 pmol/mL, respectively. Eighty per cent of parameters showed a satisfactory transfer for the manufacturer's reference intervals, except for estradiol, which had 85.5% of transferred values. Our results suggest that 4/5 sex hormones were found within the manufacturer's reference intervals and can be quantified in Peruvian women, ensuring the quality of their results. However, it is necessary to determine the estradiol with other reagents and assays since we show errors in the transfer of intervals.

Variable Selection for Skewed Model-Based Clustering: Application to the Identification of Novel Sleep Phenotypes

In sleep research, applying finite mixture models to sleep characteristics captured 8 through multiple data types, including self-reported sleep diary, a wrist monitor capturing movement (actigraphy), and brain waves (polysomnography), may suggest new phenotypes that reflect underlying disease mechanisms. However, a direct mixture model application is challenging because there are many sleep variables from which to choose, and sleep variables are often highly skewed even in homogenous samples. Moreover, previous sleep research findings indicate that some of the most clinically interesting solutions will be those that incorporate all three data types. Thus, we present two novel skewed variable selection algorithms based on the multivariate skew normal (MSN) distribution: one that selects the best set of variables ignoring data type and another that embraces the exploratory nature of clustering and suggests multiple statistically plausible sets of variables that each incorporate all data types. Through a simulation study we empirically compare our approach with other asymmetric and normal dimension reduction strategies for clustering. Finally, we demonstrate our methods using a sample of older adults with and without insomnia. The proposed MSN-based variable selection algorithm appears to be suitable for both MSN and multivariate normal cluster distributions, especially with moderate to large sample sizes.

Lifestyle Modifications Versus Antihypertensive Medications in Reducing Cardiovascular Events in an Aging Society: A Success Rate-oriented Simulation

Objective It is difficult to compare directly the practical effects of lifestyle modifications and antihypertensive medications on reducing cardiovascular disease (CVD). The purpose of this study was to compare the hypothetical potential of lifestyle modifications with that of antihypertensive medications in reducing CVD in an aging society using a success rate-oriented simulation. Methods We constructed a simulation model for virtual Japanese subpopulations according to sex and age at 10-year intervals from 40 years of age as an example of an aging society. The fractional incidence rate of CVD was calculated as the product of the incidence rate at each systolic blood pressure (SBP) level and the proportion of the SBP frequency distribution in the fractional subpopulations of each SBP. The total incidence rate was calculated by the definite integral of the fractional incidence rate at each SBP level in the sex- and age-specific subpopulations. Results If we consider the effects of lifestyle modifications on metabolic factors and transfer them onto SBP, the reductions in the total incidence rate of CVD were competitive between lifestyle modifications and antihypertensive medications in realistic scenarios. In middle-aged women, the preventive effects of both approaches were limited due to a low incidence rate. In middle-aged men and extremely elderly subjects whose adherence to antihypertensive medications is predicted to be low, lifestyle modifications could be an alternative choice. Conclusion The success rate-oriented simulation suggests that the effectiveness of lifestyle modifications or antihypertensive medications in preventing cardiovascular events largely depends on the baseline incidence rate and sex- and age-specific behavioral factors.

Evidence of Commingling in Human Eating Behavior

This investigation tested whether distributions of certain aspects of eating behavior were consistent with the notion of a "mixture model;" that is, two or more distinct commingled component distributions, consistent with the possibility of major gene action. Undergraduates (n=901) completed self-report trait measures of hunger, disinhibition, and dietary restraint. Variables were residualized for gender and age and transformed to remove skewness. Residualized transformed distributions were tested for departure from unimodality with Hartigan's dip statistic. The distributions of all three aspects of eating behavior were significantly non-unimodal. Next, component multivariate normal distributions were estimated via maximum likelihood. Likelihood ratio tests were employed to compare nested models. A mixture of four distributions with unequal variance-covariance matrices fit significantly better than any more parsimonious model. In sum, these data strongly suggest that the distributions of several measures of eating behavior are composed of four component distributions. This finding is consistent with the possibility of major gene effects for eating behavior.

Genome-wide linkage analysis of chromogranin B expression in the CEPH pedigrees: implications for exocytotic sympathochromaffin secretion in humans

Chromogranin B (CgB), a major member of the chromogranin/secretogranin family of catecholamine storage vesicle secretory proteins, plays both intracellular (vesiculogenic) and extracellular (prohormone) roles in the neuroendocrine system, and its biosynthesis and release are under the control of efferent sympathetic nerve traffic ("stimulus-transcription coupling"). To explore the role of heredity in control of CgB, we conducted a genome-wide linkage analysis of CgB release in 12 extended CEPH (Centre d'Etude du Polymorphisme Humain) pedigrees. Region-specific radioimmunoassays were used to measure five CgB fragments in plasma: CgB1-16, CgB312-331, CgB439-451, CgB568-577, and CgB647-657. Substantial heritability, as measured by h2r, was observed for three of the fragment concentrations, CgB312-331, CgB439-451, and CgB568-577, which yielded h2r estimates ranging from 0.378 (P = 0.002) to 0.910 (P < 0.0000001). Variance-component genome-wide linkage analysis with 654 microsatellite markers at 5 cM spacing identified a major quantitative trait locus for CgB312-331 on chromosome 11q24-q25 with a maximum multipoint LOD score of 5.84. Significant allelic associations between markers in the region and CgB levels were also observed. Although the 2-LOD confidence interval for linkage did not include the CgB locus itself, known trans-activators of the CgB gene promoter, or prohormone cleaving proteases, examination of positional candidate loci within this region yielded novel and plausible physiological candidates for further exploration. Allelic variation in this region may thus influence effects of sympathetic outflow on target organs in humans.

Bayesian segregation analysis of production traits in two strains of laying chickens

A bayesian marker-free segregation analysis was applied to search for evidence of segregating genes affecting production traits in two strains of laying hens under long-term selection. The study used data from 6 generations of Leghorn (H77) and New Hampshire (N88) breeding nuclei. Estimation of marginal posterior means of variance components and parameters of a single autosomal locus was performed by use of the Gibbs sampler. The results showed evidence for a mixed major gene: -polygenic inheritance of BW and age at sexual maturity (ASM) in both strains. Single genes affecting BW and ASM explained one-third of the genetic variance. For ASM large overdominance effect at single locus was estimated. Initial egg production (IEP) and average egg weight (EW) showed a polygenic model of inheritance. The polygenic heritability estimates for BW, ASM, IEP, and EW were 0.32, 0.25, 0.23, and 0.08 in Strain H77 and 0.25, 0.24, 0.11, and 0.38 in Strain N88, respectively.

Testing the robustness of the likelihood-ratio test in a variance-component quantitative-trait loci-mapping procedure

Detection of linkage to genes for quantitative traits remains a challenging task. Recently, variance components (VC) techniques have emerged as among the more powerful of available methods. As often implemented, such techniques require assumptions about the phenotypic distribution. Usually, multivariate normality is assumed. However, several factors may lead to markedly nonnormal phenotypic data, including (a) the presence of a major gene (not necessarily linked to the markers under study), (b) some types of gene x environment interaction, (c) use of a dichotomous phenotype (i.e., affected vs. unaffected), (d) nonnormality of the population within-genotype (residual) distribution, and (e) selective (extreme) sampling. Using simulation, we have investigated, for sib-pair studies, the robustness of the likelihood-ratio test for a VC quantitative-trait locus-detection procedure to violations of normality that are due to these factors. Results showed (a) that some types of nonnormality, such as leptokurtosis, produced type I error rates in excess of the nominal, or alpha, levels whereas others did not; and (b) that the degree of type I error-rate inflation appears to be directly related to the residual sibling correlation. Potential solutions to this problem are discussed. Investigators contemplating use of this VC procedure are encouraged to provide evidence that their trait data are normally distributed, to employ a procedure that allows for nonnormal data, or to consider implementation of permutation tests.

Blood pressure and the global burden of cardiovascular disease

Cardiovascular disease is responsible for a large and increasing proportion of death and disability worldwide. Half of this burden occurs in Asia. This study assessed the possible effects of population-wide (2% lower DBP for all) and targeted (7% lower DBP for those with usual DBP > or = 95 mmHg) BP interventions in Asia, using data from surveys of blood pressure levels, the Global Burden of Disease Project, Eastern Asian cohort studies and randomised trials of blood pressure lowering. Overall each of the two interventions would be expected to avert about one million deaths per year throughout Asia in 2020. These benefits would be approximately additive. About half a million deaths might be averted annually by each intervention in China alone, with about four-fifths of this benefit due to averted stroke. The relative benefits of these two strategies are similar to estimates made for US and UK populations. However, the absolute benefits are many times greater due to the size of the predicted CVD burden in Asia.

Multiple phenotype modeling in gene-mapping studies of quantitative traits: power advantages

Genomewide searches for loci influencing complex human traits and diseases such as diabetes, hypertension, and obesity are often plagued by low power and interpretive difficulties. Attempts to remedy these difficulties have typically relied on, and have promoted the use of, novel subject-ascertainment schemes, larger sample sizes, a greater density of DNA markers, and more-sophisticated statistical modeling and analysis strategies. Many of these remedies can be costly to implement. We investigate the utility of a simple statistical model for the mapping of quantitative-trait loci that incorporates multiple phenotypic or diagnostic endpoints into a gene-mapping analysis. The approach considers finding a linear combination of multiple phenotypic values that maximizes the evidence for linkage to a locus. Our results suggest that substantial increases in the power to map loci can be obtained with the proposed technique, although the increase in power obtained is a function of the size and direction of the residual correlation among the phenotypes used in the analysis. Extensive simulation studies are described that justify these claims, for cases in which two phenotypic measures are analyzed. This approach can be easily extended to cover more-complex situations and may provide a basis for more insightful genetic-analysis paradigms.

Analyzing intensive care unit length of stay data: problems and possible solutions

OBJECTIVES

To explore methods of evaluating the length of stay patterns of intensive care unit (ICU) patients. It was hypothesized that the mean does not adequately describe the typical length of stay (central tendency) because distribution patterns are often markedly skewed by patients with extended stays. Therefore, other descriptors are needed. In addition, ways are needed to identify outliers-patients with stays longer or shorter than the bulk of the data.

DESIGN

Review of retrospective data.

SETTING

University hospital surgical ICU.

PATIENTS

Representative data included all (4,499) patients admitted over a 6-yr period. Each was assigned to a diagnostic group that represented either a frequently performed surgical procedure (e.g., thymectomy) or in cases where there was no predominant procedure, a surgical discipline (e.g., otolaryngology).

INTERVENTIONS

None.

MEASUREMENTS AND MAIN RESULTS

The frequency distributions were usually skewed to the right and included two populations of interest: The portion with the majority of observations ("body"), which described "typical" behavior, and the "tail", which provided information on outliers. The average of the mean lengths of stay of all diagnostic groups was higher than the average of the medians (3.9 +/- 1.8 [SD] vs. 2.7 +/- 1.1 days, p < .001) and modes (2.1 +/- 1.2 days, p < .001), reflecting the rightward skewness of the length of stay frequency distributions. The median +/- 1 day included 75 +/- 13% of the patients, thus confirming that the median was the most useful descriptor of central tendency. Various methods were used to identify outliers. Histograms of the frequency distributions were examined and outliers visually identified. Conventional outlier analysis labeled as outliers patients staying greater than two standard deviations from the mean stay. This method underestimated the number of outliers when the distributions were skewed to the right. Another method involved designating a specific length of stay (e.g., 7 or 10 days) or percentage of patients as the outlier threshold. Each method designated different numbers of patients as outliers.

CONCLUSIONS

When analyzing length of stay data it is important to visually examine the frequency distribution because it is often skewed to the right. This skewness renders traditional parameters such as the mean and standard deviation less useful for describing the typical length of stay. Instead, the median, mode, and harmonic mean should be used. When reporting length of stay, some indication of the characteristics of the data should be presented. A graph of the frequency distribution rapidly allows the reader to determine its shape. A simple method is to report the mean, median, and range.

Mixture distributions in human genetics research

The use of mixture distributions in genetics research dates back to at least the late 1800s when Karl Pearson applied them in an analysis of crab morphometry. Pearson's use of normal mixture distributions to model the mixing of different species of crab (or 'families' of crab as he referred to them) within a defined geographic area motivated further use of mixture distributions in genetics research settings, and ultimately led to their development and recognition as intuitive modelling devices for the effects of underlying genes on quantitative phenotypic (i.e. trait) expression. In addition, mixture distributions are now used routinely to model or accommodate the genetic heterogeneity thought to underlie many human diseases. Specific applications of mixture distribution models in contemporary human genetics research are, in fact, too numerous to count. Despite this long, consistent and arguably illustrious history of use, little mention of mixture distributions in genetics research is made in many recent reviews on mixture models. This review attempts to rectify this by providing insight into the role that mixture distributions play in contemporary human genetics research. Tables providing examples from the literature that describe applications of mixture models in human genetics research are offered as a way of acquainting the interested reader with relevant studies. In addition, some of the more problematic aspects of the use of mixture models in genetics research are outlined and addressed.

Complex segregation analysis provides evidence for a major gene acting on serum triglyceride levels in 55 British families with familial combined hyperlipidemia

Familial combined hyperlipidemia (FCHL) was first described as an autosomal dominant inherited trait with primary action on triglyceride levels and secondary effects on cholesterol metabolism. This conclusion has since been questioned by several groups despite subsequent supportive biochemical and metabolic studies. To reexplore the genetics of FCHL, we assembled 55 families from the United Kingdom comprising 559 persons ascertained through probands with both hypercholesterolemia and hypertriglyceridemia. The results of univariate complex segregation analysis were consistent with a major gene acting on triglyceride and explaining two thirds of the genetic variability and 20% of the phenotypic variance in triglyceride levels. Univariate analysis did not identify a major genetic component acting on cholesterol levels. Bivariate segregation analysis rejected a major gene model. We also reexamined the original FCHL pedigrees collected by Goldstein et al and obtained results similar to those in the UK families. The prospects for mapping putative major genes determining triglyceride levels in FCHL patients by linkage analysis are discussed.

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.