Distribution-free Estimation of a Monotonic pth Quantile Function

When analyzing biological data sets, a frequent problem is to estimate the pth quantile of a distribution, when that quantile is assumed to depend on a covariate; in the present paper the dependence of the quantile on the covariate is assumed to be monotonic. Some properties of an isotonic pth quantile regression, considered as an estimator of an increasing pth quantile function, are presented.     

Quantile Inference with Multivariate Failure Time Data

Quantiles, especially the medians, of survival times are often used as summary statistics to compare the survival experiences between different groups. Quantiles are robust against outliers and preferred over the mean. Multivariate failure time data often arise in biomedical research. For example, in clinical trials, each patient in the study may experience multiple events which may be of the same type or distinct types, while in family studies of genetic diseases or litter matched mice studies, failure times for subjects in the same cluster may be correlated. In this article, we propose nonparametric procedures for the estimation of quantiles with multivariate failure time data. We show that the proposed estimators asymptotically follow a multivariate normal distribution. The asymptotic variance‐covariance matrix of the estimated quantiles is estimated based on the kernel smoothing and bootstrap techniques. Simulation results show that the proposed estimators perform well in finite samples. The methods are illustrated with the burn‐wound infection data and the Diabetic Retinopathy Study (DRS) data.     

Quantile regression for left-truncated semicompeting risks data

Semicompeting risks is often encountered in biomedical studies where a terminating event censors a nonterminating event but not vice versa. In practice, left truncation on the terminating event may arise and can greatly complicate the regression analysis on the nonterminating event. In this work, we propose a quantile regression method for left-truncated semicompeting risks data, which provides meaningful interpretations as well as the flexibility to accommodate varying covariate effects. We develop estimation and inference procedures that can be easily implemented by existing statistical software. Asymptotic properties of the resulting estimators are established including uniform consistency and weak convergence. The finite-sample performance of the proposed method is evaluated via simulation studies. An application to a registry dataset provides an illustration of our proposals.     

Choice of topology estimators in Bayesian phylogenetic analysis

Wheeler WC and Pickett KM (2008. Topology-Bayes versus clade-Bayesin phylogenetic analysis. Mol Biol Evol. 25:447–453.)discuss two ways of summarizing the posterior probability distributionof a Bayesian phylogenetic analysis, which they refer to as"topology-Bayes" and "clade-Bayes." They claim that the clade-Bayesapproach leads to problems such as "exaggerated clade support,inconsistently biased priors, and the impossibility of topologyhypothesis testing," which are not problems for the topology-Bayesapproach. However, their argument for topology-Bayes over clade-Bayesis based on errors in the interpretation of summary statisticsassociated with Bayesian phylogenetic analysis. Although thereis a well-documented difference between the maximum posteriorprobability topology and the majority-rule consensus topology(the established terms for topology-Bayes and clade-Bayes summaries,respectively), both have a place in phylogenetic analysis. Choiceof summarization strategy should be driven by choice of parametersthat need to be estimated versus those to be marginalized giventhe evolutionary questions being asked or hypotheses being tested.     

Adaptive Quantile Estimation and its Application in Analysis of Biological Signals

Quantiles and their estimations are the basis for solving numerous problems of statistics. The paper presents adaptive recursive estimation methods for this statistical parameter. Its specifical properties are investigated and the possibilities of applications in computer assisted analysis of biological signals are demonstrated even satisfying real time requirements.     

Comparison and Evaluation of Three Methods of Estimation of the Johnson Sb Distribution

Thre methods of estimating the parameters of the Johnson S₆ distribution were tested by simulation. The maximum likelihood method, the method based on percentiles of a sample and the method based on moments of a transformed random variable were taken into consideration. Many sets of samples were generated differing in sizes and in the actual values of parameters, whereupon the parameters were estimated by the three methods. It was proved that if the sample is small or the skewness of the distribution is considerable, the maximum likelihood estimates can assume preposterous values. The method based on moments is recommended due to its simplicity and to the fact that the estimates, though usually biased, never assume absurd values.     

基于分位数回归模型的卫生总费用影响因素研究

目的:利用分位数回归模型对近十年来陕西省卫生总费用增长的影响因素进行研究,从而为卫生行政部门配置卫生总费用以及制定卫生政策提供依据。方法:首先根据已往文献研究以及陕西地区实际情况,挑选出2003-2014年间可能影响陕西省卫生总费用的因素,然后利用逐步回归法检验自变量间的共线性,并对解释变量进行筛选,最后利用R软件对陕西省卫生总费用及其影响因素建立分位数回归模型,确定影响卫生总费用的因素。结果:陕西省国内生产总值(GDP)在10%-90%分位点上的系数检验结果均有统计学意义,且所有分位点的回归系数均为正值。结论:国内生产总值是影响陕西省卫生总费用的主要因素,其与卫生总费用的变化呈正相关,国内生产总值的增长促进了陕西省卫生总费用的增长。     

Naturalism, evidence and creationism: The case of Phillip Johnson

Phillip Johnson claims that Creationism is a better explanation of the existence and characteristics of biological species than is evolutionary theory. He argues that the only reason biologists do not recognize that Creationist's negative arguments against Darwinism have proven this is that they are wedded to a biased ideological philosophy —Naturalism — which dogmatically denies the possibility of an intervening creative god. However, Johnson fails to distinguish Ontological Naturalism from Methodological Naturalism. Science makes use of the latter and I show how it is not dogmatic but follows from sound requirements for empirical evidential testing. Furthermore, Johnson has no serious alternative type of positive evidence to offer for Creationism, and purely negative argumentation, despite his attempt to legitimate it, will not suffice.     

The Binary Regression Quantile Plot: Assessing the Importance of Predictors in Binary Regression Visually

We present a graphical measure of assessing the explanatory power of regression models with a binary response. The binary regression quantile plot and an area defined by it are used for the visual comparison and ordering of nested binary response regression models. The plot shows how well various models explain the data. Two data sets are analyzed and the area representing the fit of a model is shown to agree with the usual likelihood ratio test.     

Consistency of estimators of the population-scaled recombination rate

We consider (approximate) likelihood methods for estimating the population-scaled recombination rate from population genetic data. We show that the dependence between the data from two regions of a chromosome decays inversely with the amount of recombination between the two regions. We use this result to show that the maximum likelihood estimator (mle) for the recombination rate, based on the composite likelihood of Fearnhead and Donnelly, is consistent. We also consider inference based on the pairwise likelihood of Hudson. We consider two approximations to this likelihood, and prove that the mle based on one of these approximations is consistent, while the mle based on the other approximation (which is used by McVean, Awadalla and Fearnhead) is not.