Inference of missing SNPs and information quantity measurements for haplotype blocks

MOTIVATION: Missing data in genotyping single nucleotide polymorphism (SNP) spots are common. High-throughput genotyping methods usually have a high rate of missing data. For example, the published human chromosome 21 data by Patil et al. contains about 20% missing SNPs. Inferring missing SNPs using the haplotype block structure is promising but difficult because the haplotype block boundaries are not well defined. Here we propose a global algorithm to overcome this difficulty. RESULTS: First, we propose to use entropy as a measure of haplotype diversity. We show that the entropy measure combined with a dynamic programming algorithm produces better haplotype block partitions than other measures. Second, based on the entropy measure, we propose a two-step iterative partition-inference algorithm for the inference of missing SNPs. At the first step, we apply the dynamic programming algorithm to partition haplotypes into blocks. At the second step, we use an iterative process similar to the expectation-maximization algorithm to infer missing SNPs in each haplotype block so as to minimize the block entropy. The algorithm iterates these two steps until the total block entropy is minimized. We test our algorithm in several experimental data sets. The results show that the global approach significantly improves the accuracy of the inference. AVAILABILITY: Upon request.     

Increase in regularity of fetal heart rate variability with age.

It is generally assumed that fetal heart rate variability increases with gestation, reflecting prenatal development of the autonomic nervous system. We examined standard measures quantifying fetal heart rate variability, as well as a complexity measure, approximate entropy, in 66 fetal magnetocardiograms recorded from 22 healthy pregnant women between the 16th and 42nd week of gestation. In particular, regularity in the fetal RR interval time series was assessed on the basis of symbolic dynamics. The results showed that, beside an overall increase in fetal heart rate variability and complexity during pregnancy, there was also an increase in specific sets of binary patterns with low approximate entropy, i.e., a high degree of regularity. These sets were characterized by short epochs of heart rate acceleration and deceleration, and comparison with surrogate data confirmed that their random occurrence is rare. The results most likely reflect the influence of increasingly differentiated fetal behavioral states and transitions between them in association with fetal development.     

Single exposure to testosterone in adulthood rapidly induces regularity in the growth hormone release process

The neonatal gonadal steroid milieu is known to be important in imprinting the striking sexual dimorphism of growth hormone (GH) secretion; however, the influence of the sex steroids on GH control in adult life and their mechanism/site of action are largely unknown. In the present study, we tested the hypothesis that testosterone (T) subserves the gender-specific regularity of the GH release process in adulthood. The approximate entropy statistic (ApEn) was used to quantify the degree of regularity of GH release patterns over time. Eighteen hours after a single subcutaneous injection of 1 mg T, both sham-operated and ovariectomized (OVX) female adult rats displayed plasma GH profiles that were strikingly similar to the regular male-like ultradian rhythm of GH secretion. The highest ApEn values, denoting greater disorderliness of GH secretion, were observed in the ovary-intact group, and T injection significantly (P < 0.001) reduced this irregularity whether or not the ovaries were present. Serial intravenous injections of GH-releasing hormone (GHRH) caused a similar increase in plasma GH levels in sham-operated females independently of time of administration. In contrast, female rats administered T exhibited a male-like intermittent pattern of GH responsiveness to GHRH, the latter known to be due to the cyclic release of endogenous somatostatin. These results demonstrate that acute exposure to T during adult life can rapidly and profoundly "masculinize" GH pulse-generating circuits in the female rat. Our findings suggest that the enhanced orderliness characteristic of the GH release process in males, compared with females, is regulated by T. We postulate that this T-induced regularity is mediated at the level of the hypothalamus by inducing regularity in somatostatin secretion, which in turn governs overall GH periodicity.     

Accurate estimation of entropy in very short physiological time series: the problem of atrial fibrillation detection in implanted ventricular devices

Entropy estimation is useful but difficult in short time series. For example, automated detection of atrial fibrillation (AF) in very short heart beat interval time series would be useful in patients with cardiac implantable electronic devices that record only from the ventricle. Such devices require efficient algorithms, and the clinical situation demands accuracy. Toward these ends, we optimized the sample entropy measure, which reports the probability that short templates will match with others within the series. We developed general methods for the rational selection of the template length m and the tolerance matching r. The major innovation was to allow r to vary so that sufficient matches are found for confident entropy estimation, with conversion of the final probability to a density by dividing by the matching region volume, 2r(m). The optimized sample entropy estimate and the mean heart beat interval each contributed to accurate detection of AF in as few as 12 heartbeats. The final algorithm, called the coefficient of sample entropy (COSEn), was developed using the canonical MIT-BIH database and validated in a new and much larger set of consecutive Holter monitor recordings from the University of Virginia. In patients over the age of 40 yr old, COSEn has high degrees of accuracy in distinguishing AF from normal sinus rhythm in 12-beat calculations performed hourly. The most common errors are atrial or ventricular ectopy, which increase entropy despite sinus rhythm, and atrial flutter, which can have low or high entropy states depending on dynamics of atrioventricular conduction.     

Moving approximate entropy applied to surface electromyographic signals

The objective of this study was to investigate the surface electromyographic signals using moving approximate entropy from 20 healthy participants’ wrist muscles (flexor carpi ulnaris and flexor carpi radialis). The participants were required to voluntary performed wrist flexion/extension, co-contraction and isometric contraction. A moving data window of 200 values was applied to the data and a moving approximate entropy series was obtained from the analysis. The results demonstrate that there are distinct drops of the approximate entropy values at the start and end of a contraction, and high (less regularity) approximate entropy in the middle. Mean values of approximate entropy of 0.54 and 0.55 were found for the start of a contraction compared to 0.79 and 0.77 during the middle, for the flexor and extensor, respectively. At the end, there are values of 0.46 and 0.5, respectively.     

Analysing protein energy data by a stochastic model for cooperative interactions: comparison and characterization of cooperativity

 In the frame of a Markov chain model for cooperative interactions in proteins, previously introduced by us, we deal here with estimation of unknown parameters from protein energy data. One of these parameters characterizes the cooperativity of a protein; we propose to measure it also by the so-called approximate entropy. By our computations the approximate entropy turns out to be a decreasing function of the cooperativity. We analyse both simulated data of the Markov chain, and protein energy data obtained by molecular dynamics simulation. Moreover, we compare two rubredoxin proteins at different temperatures, according to their degrees of cooperativity. Received: 2 October 2000 / Revised version: 4 April 2001 / Published online: 14 March 2002     

Aging, regularity and variability in maximum isometric moments

This study examined the variability and regularity of maximum isometric moment production of the plantar flexors in young and old subjects. It was hypothesized that in the development of maximum isometric moments there would be greater regularity in the moment profiles for older subjects compared with young subjects, due to the reduced number of motor units present in elderly muscle. Two groups of subjects produced three maximal isometric plantar flexions (young: n=11, mean age 23.8+/-2.8 years, mean mass 81.2+/-10.4 kg, mean height 1.78+/-0.05 m; elderly: n=13, mean age 74.0+/-3.3 years, mean mass 78.5+/-3.4 kg, mean height 1.73+/-0.05 m). The plateau of the moment-time curve was analyzed for each trial. A repeat measures analysis of variance showed the young subjects produced statistically greater peak plantar flexion moments than the elderly subjects, but similar coefficients of variation. Signal regularity was determined by computing the signal's approximate entropy, which demonstrated that the older group had greater regularity in their generation of moment profiles. The hypothesis was accepted, with a potential explanation for this increased regularity in old age being the reduced number of motor units to coordinate.     

Feature Selection for Gene Expression Using Model-Based Entropy

Gene expression data usually contain a large number of genes but a small number of samples. Feature selection for gene expression data aims at finding a set of genes that best discriminate biological samples of different types. Using machine learning techniques, traditional gene selection based on empirical mutual information suffers the data sparseness issue due to the small number of samples. To overcome the sparseness issue, we propose a model-based approach to estimate the entropy of class variables on the model, instead of on the data themselves. Here, we use multivariate normal distributions to fit the data, because multivariate normal distributions have maximum entropy among all real-valued distributions with a specified mean and standard deviation and are widely used to approximate various distributions. Given that the data follow a multivariate normal distribution, since the conditional distribution of class variables given the selected features is a normal distribution, its entropy can be computed with the log-determinant of its covariance matrix. Because of the large number of genes, the computation of all possible log-determinants is not efficient. We propose several algorithms to largely reduce the computational cost. The experiments on seven gene data sets and the comparison with other five approaches show the accuracy of the multivariate Gaussian generative model for feature selection, and the efficiency of our algorithms.     

Perinatal health among 1 million Chinese-Americans

The literature on “missing girls” suggests a net preference for sons both in China and among Chinese immigrants to the West. Perhaps surprisingly, we find that newborn Chinese-American girls are treated more intensively in US hospitals: they are kept longer following delivery, have more medical procedures performed, and have more hospital charges than predicted (by the non-Chinese gender difference). What might explain more aggressive medical treatment? We posit that hospitals are responding to worse health at birth of Chinese-American girls. We document higher rates of low birth weight, congenital anomalies, maternal hypertension, and lower APGAR scores among Chinese American girls – outcomes recorded prior to intensive neonatal medical care and relative to the non-Chinese gender gap. To the best of our knowledge, we are the first to find that son preference may also compromise “survivor” health at birth. On net, compromised newborn health seems to outweigh the benefit of more aggressive neonatal hospital care for girls. Relative to non-Chinese gender differences, death on the first day of life and in the post-neonatal period is more common among Chinese-American girls, i.e. later than sex selection is typically believed to occur.     

Clinical studies of lactoferrin in children

Much has been learned in recent years about the mechanisms by which breastfeeding improves child health and survival. However, there has been little progress in using these insights to improve pediatric care. The aim of this study was to review all clinical studies of lactoferrin (LF) in children in an effort to determine which interventions may improve pediatric care or require further research. We conducted a systematic and critical review of published literature and found 19 clinical studies that have used human or bovine LF for different outcomes: iron metabolisms and anemia (6 studies), fecal flora (5 studies), enteric infections (3 studies), common pediatric illnesses (1 study), immunomodulation (3 studies), and neonatal sepsis (1 study). Although the efficacies have varied in each trial, the main finding of all published studies is the safety of the intervention. Protection against enteric infections and neonatal sepsis are the most likely biologically relevant activities of LF in children. Future studies on neonatal sepsis should answer critically important questions. If the data from these sepsis studies are proven to be correct, it will profoundly affect the treatment of low birth weight neonates and will aid in the reduction of child mortality worldwide.     

An exploration of fixed and random effects selection for longitudinal binary outcomes in the presence of nonignorable dropout

We explore a Bayesian approach to selection of variables that represent fixed and random effects in modeling of longitudinal binary outcomes with missing data caused by dropouts. We show via analytic results for a simple example that nonignorable missing data lead to biased parameter estimates. This bias results in selection of wrong effects asymptotically, which we can confirm via simulations for more complex settings. By jointly modeling the longitudinal binary data with the dropout process that possibly leads to nonignorable missing data, we are able to correct the bias in estimation and selection. Mixture priors with a point mass at zero are used to facilitate variable selection. We illustrate the proposed approach using a clinical trial for acute ischemic stroke.     

Bayesian analysis for generalized linear models with nonignorably missing covariates

We propose Bayesian methods for estimating parameters in generalized linear models (GLMs) with nonignorably missing covariate data. We show that when improper uniform priors are used for the regression coefficients, phi, of the multinomial selection model for the missing data mechanism, the resulting joint posterior will always be improper if (i) all missing covariates are discrete and an intercept is included in the selection model for the missing data mechanism, or (ii) at least one of the covariates is continuous and unbounded. This impropriety will result regardless of whether proper or improper priors are specified for the regression parameters, beta, of the GLM or the parameters, alpha, of the covariate distribution. To overcome this problem, we propose a novel class of proper priors for the regression coefficients, phi, in the selection model for the missing data mechanism. These priors are robust and computationally attractive in the sense that inferences about beta are not sensitive to the choice of the hyperparameters of the prior for phi and they facilitate a Gibbs sampling scheme that leads to accelerated convergence. In addition, we extend the model assessment criterion of Chen, Dey, and Ibrahim (2004a, Biometrika 91, 45-63), called the weighted L measure, to GLMs and missing data problems as well as extend the deviance information criterion (DIC) of Spiegelhalter et al. (2002, Journal of the Royal Statistical Society B 64, 583-639) for assessing whether the missing data mechanism is ignorable or nonignorable. A novel Markov chain Monte Carlo sampling algorithm is also developed for carrying out posterior computation. Several simulations are given to investigate the performance of the proposed Bayesian criteria as well as the sensitivity of the prior specification. Real datasets from a melanoma cancer clinical trial and a liver cancer study are presented to further illustrate the proposed methods.     

Dynamic Approximate Entropy Electroanatomic Maps Detect Rotors in a Simulated Atrial Fibrillation Model

There is evidence that rotors could be drivers that maintain atrial fibrillation. Complex fractionated atrial electrograms have been located in rotor tip areas. However, the concept of electrogram fractionation, defined using time intervals, is still controversial as a tool for locating target sites for ablation. We hypothesize that the fractionation phenomenon is better described using non-linear dynamic measures, such as approximate entropy, and that this tool could be used for locating the rotor tip. The aim of this work has been to determine the relationship between approximate entropy and fractionated electrograms, and to develop a new tool for rotor mapping based on fractionation levels. Two episodes of chronic atrial fibrillation were simulated in a 3D human atrial model, in which rotors were observed. Dynamic approximate entropy maps were calculated using unipolar electrogram signals generated over the whole surface of the 3D atrial model. In addition, we optimized the approximate entropy calculation using two real multi-center databases of fractionated electrogram signals, labeled in 4 levels of fractionation. We found that the values of approximate entropy and the levels of fractionation are positively correlated. This allows the dynamic approximate entropy maps to localize the tips from stable and meandering rotors. Furthermore, we assessed the optimized approximate entropy using bipolar electrograms generated over a vicinity enclosing a rotor, achieving rotor detection. Our results suggest that high approximate entropy values are able to detect a high level of fractionation and to locate rotor tips in simulated atrial fibrillation episodes. We suggest that dynamic approximate entropy maps could become a tool for atrial fibrillation rotor mapping.     

Quantifying trait selection driving community assembly: a test in herbaceous plant communities under contrasted land use regimes

Plant traits are particularly important in determining plant community structure. However, how can one identify which traits are the most important in driving community assembly? Here we propose a method 1) to quantify the direction and strength of trait selection during community assembly and 2) to obtain parsimonious lists of traits that can predict species relative abundances in plant communities. We tested our method using floristic data from 32 plots experiencing different treatments (fertilisation and grazing) in southern France. Twelve functional traits were measured on 68 species. We determined the direction and strength of selection on these 12 traits using a metric derived from a maximum entropy model (i.e. lambda). We then determined our parsimonious list of traits using a backward selection of traits based on these lambda values (for all treatments and in each treatment separately). We finally compared our method to two other methods: one based on iterative RLQ and the other based on an entropy‐based forward selection of traits. We found major differences in the direction and strength of selection across the 12 traits and treatments. From the 12 traits, plant vegetative and reproductive heights, leaf dry matter content leaf nitrogen content, specific leaf area, and leaf phosphorus content were particularly important for predicting species relative abundances when considering all treatments together. Our method yielded results similar to those produced by the entropy‐based approach but differed from those produced by the iterative RLQ, whose selected traits could not significantly predict species relative abundances. Together these results suggest that the assembly of these communities is primarily driven by a small number of key functional traits. We argue that our method provides an objective way of determining a parsimonious list of traits that together accurately predict community structure and which, despite its complementarities with entropy‐based method, offers significant advantages.     

The diagnostic and prognostic role of MiRNA 15b and MiRNA 378a in neonatal sepsis

Background and objectivesSepsis is one of the major factors for both term and preterm babies with morbidity and mortality. On the basis of recent clinical trials, altered circulating micro-RNAs (miRNAs) may serve as possible biomarkers in sepsis for diagnosis and prognosis. The aim of this research is to assess the diagnostic and prognostic biomarkers of miRNA 15b and miRNA 378a for neonatal sepsis.Subjects & methodsThis study was carried out 25 neonates with sepsis admitted to neonatal ICU of Menoufia University Hospital and 25 healthy controls from February 2019 to May 2020. The relative quantification (RQ) of miRNA-15b and miRNA-378a expression was assessed using real time PCR technique. Results: Our results demonstrated that patients with sepsis had significantly higher level of MiRNA-15b than the healthy volunteers. On the other hand, patients with sepsis had significantly lower level of MiRNA-378a than the healthy volunteers. The ROC curve showed that the serum MiRNA-15b was a significant discriminator of sepsis with a combined sensitivity and specificity of 76% and 88% with cutoff point of 3.24. In addition, serum MiRNA-378a was a significant discriminator of sepsis with a combined sensitivity and specificity of 60% and 88% with cutoff point of 0.361. The miRNA-15b expression significantly correlated positive with respiratory rate (r =0.415,p =0.039), WBCs (r = 0.408, p =0.043), and CRP (r =0.407, p=0.043). Likewise, miRNA-378a expression significantly correlated negative with respiratory rate (r =-0.415p =0.024), WBCs (r =- 0.442, p =0.027), and CRP (r =- 0.459, p=0.021).ConclusionBoth MiRNA 15b and 378a are promising biomarker for neonatal sepsis.     

Adjusting for publication bias in meta-analysis via inverse probability weighting using clinical trial registries

Publication bias is a major concern in conducting systematic reviews and meta-analyses. Various sensitivity analysis or bias-correction methods have been developed based on selection models, and they have some advantages over the widely used trim-and-fill bias-correction method. However, likelihood methods based on selection models may have difficulty in obtaining precise estimates and reasonable confidence intervals, or require a rather complicated sensitivity analysis process. Herein, we develop a simple publication bias adjustment method by utilizing the information on conducted but still unpublished trials from clinical trial registries. We introduce an estimating equation for parameter estimation in the selection function by regarding the publication bias issue as a missing data problem under the missing not at random assumption. With the estimated selection function, we introduce the inverse probability weighting (IPW) method to estimate the overall mean across studies. Furthermore, the IPW versions of heterogeneity measures such as the between-study variance and the I² measure are proposed. We propose methods to construct confidence intervals based on asymptotic normal approximation as well as on parametric bootstrap. Through numerical experiments, we observed that the estimators successfully eliminated bias, and the confidence intervals had empirical coverage probabilities close to the nominal level. On the other hand, the confidence interval based on asymptotic normal approximation is much wider in some scenarios than the bootstrap confidence interval. Therefore, the latter is recommended for practical use.     

不同坡位对GPS项圈定位性能的影响

GPS项圈已广泛应用于大中型野生动物的野外定位监测,支持野生动物生态学研究和保护管理规划.但由于地形等因素影响,GPS项圈返回的数据可能有定位误差和定位数据缺失偏歧.因此,在进行生境选择等相关生态学研究之前,应对GPS项圈的定位性能进行评估.本研究于2019年11月至2020年10月,在云南大理苍山5个测试点各静态放置...     

QUANTITATIVE GENETIC MODELING AND INFERENCE IN THE PRESENCE OF NONIGNORABLE MISSING DATA

Natural selection is typically exerted at some specific life stages. If natural selection takes place before a trait can be measured, using conventional models can cause wrong inference about population parameters. When the missing data process relates to the trait of interest, a valid inference requires explicit modeling of the missing process. We propose a joint modeling approach, a shared parameter model, to account for nonrandom missing data. It consists of an animal model for the phenotypic data and a logistic model for the missing process, linked by the additive genetic effects. A Bayesian approach is taken and inference is made using integrated nested Laplace approximations. From a simulation study we find that wrongly assuming that missing data are missing at random can result in severely biased estimates of additive genetic variance. Using real data from a wild population of Swiss barn owls Tyto alba, our model indicates that the missing individuals would display large black spots; and we conclude that genes affecting this trait are already under selection before it is expressed. Our model is a tool to correctly estimate the magnitude of both natural selection and additive genetic variance.     

Intrinsic mode entropy based on multivariate empirical mode decomposition and its application to neural data analysis

Entropy, a measure of the regularity of a time series, has long been used to quantify the complexity of brain dynamics. Given the multiple spatiotemporal scales inherent in the brain, traditional entropy analysis based on a single scale is not adequate to accurately describe the underlying nonlinear dynamics. Intrinsic mode entropy (IMEn) is a recent development with appealing properties to estimate entropy over multiple time scales. It is a multiscale entropy measure that computes sample entropy (SampEn) over different scales of intrinsic mode functions extracted by empirical mode decomposition (EMD) method. However, it suffers from both mode-misalignment and mode-mixing problems when applied to multivariate time series data. In this paper, we address these two problems by employing the recently introduced multivariate empirical mode decomposition (MEMD). First, we extend the MEMD to multi-channel multi-trial neural data to ensure the IMEn matched at different scales. Second, for the discriminant analysis of IMEn, we propose to improve the discriminative ability by including variance that has not been used before in entropy analysis. Finally, we apply the proposed approach to the multi-electrode local field potentials (LFPs) simultaneously collected from visual cortical areas of macaque monkeys while performing a generalized flash suppression task. The results have shown that the entropy of LFP is indeed scale-dependent and is closely related to the perceptual conditions. The discriminative results of the perceptual conditions, revealed by support vector machine, show that the accuracy based on IMEn and variance reaches 83.05%, higher than that only by IMEn (76.27%). These results suggest that our approach is sensitive to capture the complex dynamics of neural data.     

Physiological time-series analysis using approximate entropy and sample entropy

Entropy, as it relates to dynamical systems, is the rate of information production. Methods for estimation of the entropy of a system represented by a time series are not, however, well suited to analysis of the short and noisy data sets encountered in cardiovascular and other biological studies. Pincus introduced approximate entropy (ApEn), a set of measures of system complexity closely related to entropy, which is easily applied to clinical cardiovascular and other time series. ApEn statistics, however, lead to inconsistent results. We have developed a new and related complexity measure, sample entropy (SampEn), and have compared ApEn and SampEn by using them to analyze sets of random numbers with known probabilistic character. We have also evaluated cross-ApEn and cross-SampEn, which use cardiovascular data sets to measure the similarity of two distinct time series. SampEn agreed with theory much more closely than ApEn over a broad range of conditions. The improved accuracy of SampEn statistics should make them useful in the study of experimental clinical cardiovascular and other biological time series.