Multistage index selection in finite populations

Multistage selection with fixed proportions and selection indices based on covariates of the target variable is studied. Assuming a multivariate normal distribution before the selection, expressions are presented for the expectation and the variance of the target variable in the retained subpopulation. As the numerical evaluation for finite populations requires lengthy computations, some approximations using methods for infinite populations are proposed. Numerical illustrations are given for selections in up to three stages.     

A statistical analysis of nucleotide sequences of introns and exons in human genes

DNA sequences of 56 human genes for which information on both exons and introns was available were examined. The variance in G+C content among genes is estimated and shown to be substantial. There is a high correlation in G+C content between exons and introns within the same gene. The dinucleotide frequencies of introns are similar to those of intergenic spacer regions and are in reasonable agreement with predictions from substitution rates estimated from pseudogenes, except that the observed deficiency of TA doublets is not predicted. Duplicated bases also show a frequency greater than the expectation under independence. There is marked variability among genes in the frequency of the doublet CG relative to its expectation under independence. This variation is evolutionarily conserved and is correlated with the G+C content. Pseudogenes behave as if they are in a low -G+C, CG-deficient part of the genome, although the genes from which they arose are variable in these respects.      

Maximum likelihood methods for nonignorable missing responses and covariates in random effects models

This article analyzes quality of life (QOL) data from an Eastern Cooperative Oncology Group (ECOG) melanoma trial that compared treatment with ganglioside vaccination to treatment with high-dose interferon. The analysis of this data set is challenging due to several difficulties, namely, nonignorable missing longitudinal responses and baseline covariates. Hence, we propose a selection model for estimating parameters in the normal random effects model with nonignorable missing responses and covariates. Parameters are estimated via maximum likelihood using the Gibbs sampler and a Monte Carlo expectation maximization (EM) algorithm. Standard errors are calculated using the bootstrap. The method allows for nonmonotone patterns of missing data in both the response variable and the covariates. We model the missing data mechanism and the missing covariate distribution via a sequence of one-dimensional conditional distributions, allowing the missing covariates to be either categorical or continuous, as well as time-varying. We apply the proposed approach to the ECOG quality-of-life data and conduct a small simulation study evaluating the performance of the maximum likelihood estimates. Our results indicate that a patient treated with the vaccine has a higher QOL score on average at a given time point than a patient treated with high-dose interferon.     

Experimental design for estimating integrals by numerical quadrature, with applications to pharmacokinetic studies

Many experimental situations, including bioavailability studies, require the estimation of integrals by numerical quadrature applied to dependent variable observations with measurement error. A strategy is described for selecting values for the independent variable (e.g. time). The strategy minimizes the expectation of the square of the difference between the exact integral and the quadrature approximation. This approach was applied to simulated pharmacokinetic problems, including the estimation of bioavailability. Results indicate that the procedure is potentially useful in reducing the variance of resulting estimates and that it appears to be robust with respect to prior assumptions about model parameter values.     

Estimation of Bayesian confidence intervals for the product of conditional survival probabilities

A model is derived to estimate the survival probability of a time interval when censorings occur. The time interval is divided into partial intervals in order to obtain the conditional survival probabilities, each of which is a parameter of a Binomial distributed random variable. To allow for the dependence between the events in the different intervals these parameters are transformed. Corresponding a priori density functions are formulated regarding both the Bayesian uniform distribution and the special model. The a posteriori density function is derived for the product of the conditional survival probabilities, and formulae for the BAYE sian confidence interval and the expectation are given. Lower and upper bounds for the confidence interval and the expectation are derived. Some examples are given to compare the results with other methods.     

The Cerebellum Predicts the Temporal Consequences of Observed Motor Acts

It is increasingly clear that we extract patterns of temporal regularity between events to optimize information processing. The ability to extract temporal patterns and regularity of events is referred as temporal expectation. Temporal expectation activates the same cerebral network usually engaged in action selection, comprising cerebellum. However, it is unclear whether the cerebellum is directly involved in temporal expectation, when timing information is processed to make predictions on the outcome of a motor act. Healthy volunteers received one session of either active (inhibitory, 1Hz) or sham repetitive transcranial magnetic stimulation covering the right lateral cerebellum prior the execution of a temporal expectation task. Subjects were asked to predict the end of a visually perceived human body motion (right hand handwriting) and of an inanimate object motion (a moving circle reaching a target). Videos representing movements were shown in full; the actual tasks consisted of watching the same videos, but interrupted after a variable interval from its onset by a dark interval of variable duration. During the ‘dark’ interval, subjects were asked to indicate when the movement represented in the video reached its end by clicking on the spacebar of the keyboard. Performance on the timing task was analyzed measuring the absolute value of timing error, the coefficient of variability and the percentage of anticipation responses. The active group exhibited greater absolute timing error compared with the sham group only in the human body motion task. Our findings suggest that the cerebellum is engaged in cognitive and perceptual domains that are strictly connected to motor control.     

The nonidentity of invariable positions in the cytochromes c of different species

This study answers the question: Are the variable and invariable codons of cytochrome c largely the same in all species? A method is presented for estimating the number of invariable (as opposed to unvaried) codons common to two taxa. The two taxa in this study were comprised of four fungi and four metazoans. Given the number of mutations fixed in each taxon, one calculates the number of codons that would be expected to have fixed mutations in both taxa, in one taxon only, in the other taxon only, and in neither taxon. This expectation depends upon the number of invariable codons that are assumed to be common to both taxa. In the present example, the assumption of 41 invariable codons in common leads to estimates that deviate by less than 2% from the values actually observed. This leads to the conclusion that there are 46 positions that are variable in one taxon but invariable in the other, thereby demonstrating that the invariable codons are not largely the same between the fungi and the metazoans.     

The size and form of chromosomes are constant in the nucleus, but highly variable in bacteria, mitochondria and chloroplasts

From cytological examination, the size and form of the chromosomes in the eukaryotic nucleus are invariant across generations, leading to the expectation that constancy of inheritance likely depends on constancy of the chromosomal DNA molecule conveying the constant phenotype. Indeed, except for rare mutations, major phenotypic traits appear largely without change from generation to generation. Thus, when it was discovered that the inheritance of traits for bacteria, mitochondria and chloroplasts was also constant, it was assumed that chromosomes in those locations were also constant. Such has not turned out to be the case, however; those chromosomes are highly variable in structure. I propose, therefore, that only for the nucleus is there a requirement that a chromosome be "finished" (contain only fully replicated genomes) before it may segregate to daughter cells. This requirement does not apply to the variable chromosomes among chloroplasts, mitochondria and bacteria.     

Allelic disequilibrium and allele frequency distribution as a function of social and demographic history.

Allelic disequilibrium between closely linked genes is a common observation in human populations and often gives rise to speculation concerning the role of selective forces. In a previous treatment, we have developed a population model of the expected distribution of rare variants (including private polymorphisms) in Amerindians and have argued that, because of the great expansion of Amerindian numbers with the advent of agriculture, most of these rare variants are of relatively recent origin. Many other populations have similar histories of striking recent expansions. In this treatment, we demonstrate that, in consequence of this fact, a high degree of linkage disequilibrium between two nonhomologous alleles <0.5 cM apart is the "normal" expectation, even in the absence of selection. This expectation is enhanced by the previous subdivision of human populations into relatively isolated tribes characterized by a high level of endogamy and inbreeding. We also demonstrate that the alleles associated with a recessive disease phenotype are expected to exist in a population in very variable frequencies: there is no need to postulate positive selection with respect to the more common disease-associated alleles for such entities as phenylketonuria or cystic fibrosis.     

A Bayesian Decision Procedure for Selecting Prognostic Variables Associated with Survival for Data in which Censoring is Prevalent

A Bayesian procedure is developed for the selection of concomitant variables in survival models. The variables are selected in a step-up procedure according to the criterion of maximum expected likelihood, where the expectation is over the prior parameter space. Prior knowledge of the influence of these covariates on patient prognosis is incorporated into the analysis. The step-up procedure is stopped when the Bayes factor in favor of omitting the variable selected in a particular step exceeds a specified value. The resulting model with the selected variables is fitted using Bayes estimates of the coefficients. This technique is applied to Hodgkin's disease data from a large Cooperative Clinical Trial Group and the results are compared to the results from the classical likelihood selection procedure.     

Variable selection for zero‐inflated and overdispersed data with application to health care demand in Germany

In health services and outcome research, count outcomes are frequently encountered and often have a large proportion of zeros. The zero‐inflated negative binomial (ZINB) regression model has important applications for this type of data. With many possible candidate risk factors, this paper proposes new variable selection methods for the ZINB model. We consider maximum likelihood function plus a penalty including the least absolute shrinkage and selection operator (LASSO), smoothly clipped absolute deviation (SCAD), and minimax concave penalty (MCP). An EM (expectation‐maximization) algorithm is proposed for estimating the model parameters and conducting variable selection simultaneously. This algorithm consists of estimating penalized weighted negative binomial models and penalized logistic models via the coordinated descent algorithm. Furthermore, statistical properties including the standard error formulae are provided. A simulation study shows that the new algorithm not only has more accurate or at least comparable estimation, but also is more robust than the traditional stepwise variable selection. The proposed methods are applied to analyze the health care demand in Germany using the open‐source R package mpath .     

Testing equality of survival functions based on both paired and unpaired censored data

We introduce two test procedures for comparing two survival distributions on the basis of randomly right-censored data consisting of both paired and unpaired observations. Our procedures are based on generalizations of a pooled rank test statistic previously proposed for uncensored data. One generalization adapts the Prentice-Wilcoxon score, while the other adapts the Akritas score. The use of these particular scoring systems in pooled rank tests with randomly right-censored paired data has been advocated by several researchers. Our test procedures utilize the permutation distributions of the test statistics based on a novel manner of permuting the scores. Permutation versions of tests for right-censored paired data and for two independent right-censored samples that use the proposed scoring systems are obtained as special cases of our test procedures. Simulation results show that our test procedures have high power for detecting scale and location shifts in exponential and log-logistic distributions for the survival times. We also demonstrate the advantages of our test procedures in terms of utilizing randomly occurring unpaired observations that are discarded in test procedures for paired data. The tests are applied to skin graft data previously reported elsewhere.     

A new u-statistic with superior design sensitivity in matched observational studies

Summary In an observational or nonrandomized study of treatment effects, a sensitivity analysis indicates the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naïve analysis that presumes adjustments for observed covariates suffice to remove all bias. The power of sensitivity analysis is the probability that it will reject a false hypothesis about treatment effects allowing for a departure from random assignment of a specified magnitude; in particular, if this specified magnitude is “no departure” then this is the same as the power of a randomization test in a randomized experiment. A new family of u‐statistics is proposed that includes Wilcoxon's signed rank statistic but also includes other statistics with substantially higher power when a sensitivity analysis is performed in an observational study. Wilcoxon's statistic has high power to detect small effects in large randomized experiments—that is, it often has good Pitman efficiency—but small effects are invariably sensitive to small unobserved biases. Members of this family of u‐statistics that emphasize medium to large effects can have substantially higher power in a sensitivity analysis. For example, in one situation with 250 pair differences that are Normal with expectation 1/2 and variance 1, the power of a sensitivity analysis that uses Wilcoxon's statistic is 0.08 while the power of another member of the family of u‐statistics is 0.66. The topic is examined by performing a sensitivity analysis in three observational studies, using an asymptotic measure called the design sensitivity, and by simulating power in finite samples. The three examples are drawn from epidemiology, clinical medicine, and genetic toxicology.     

Multiply imputing missing values arising by design in transplant survival data

In this article, we address a missing data problem that occurs in transplant survival studies. Recipients of organ transplants are followed up from transplantation and their survival times recorded, together with various explanatory variables. Due to differences in data collection procedures in different centers or over time, a particular explanatory variable (or set of variables) may only be recorded for certain recipients, which results in this variable being missing for a substantial number of records in the data. The variable may also turn out to be an important predictor of survival and so it is important to handle this missing-by-design problem appropriately. Consensus in the literature is to handle this problem with complete case analysis, as the missing data are assumed to arise under an appropriate missing at random mechanism that gives consistent estimates here. Specifically, the missing values can reasonably be assumed not to be related to the survival time. In this article, we investigate the potential for multiple imputation to handle this problem in a relevant study on survival after kidney transplantation, and show that it comprehensively outperforms complete case analysis on a range of measures. This is a particularly important finding in the medical context as imputing large amounts of missing data is often viewed with scepticism.     

Screen technical noise in single cell RNA sequencing data

We proposed a data cleaning pipeline for single cell (SC) RNA-seq data, where we first screen genes (gene-wise screening) followed by screening cell libraries (library-wise screening). Gene-wise screening is based on the expectation that for a gene with a low technical noise, a gene's count in a library will tend to increase with the increase of library size, which was tested using negative binomial regression of gene count (as dependent variable) against library size (as independent variable). Library-wise screening is based on the expectation that across-library correlations for housekeeping (HK) genes is expected to be higher than the correlations for non-housekeeping (NHK) genes in those libraries with low technical noise. We removed those libraries, whose mean pairwise correlation for HK genes is NOT significantly higher than that for NHK genes. We successfully applied the pipeline to two large SC RNA-seq datasets. The pipeline was also developed into an R package.     

Probability distributions of ancestries and genealogical distances on stochastically generated rooted binary trees

The stationary birth-only, or Yule-Furry, process for rooted binary trees has been analysed with a view to developing explicit expressions for two fundamental statistical distributions: the probability that a randomly selected leaf is preceded by N nodes, or “ancestors”, and the probability that two randomly selected leaves are separated by N nodes. For continuous-time Yule processes, the first of these distributions is presented in closed analytical form as a function of time, with time being measured with respect to the moment of “birth” of the common ancestor (which is essentially inaccessible to phylogenetic analysis), or with respect to the instant at which the first bifurcation occurred.The second distribution is shown to follow in an iterative manner from a hierarchy of second-order ordinary differential equations.For Yule trees of a given number n of tips, expressions have been derived for the mean and variance for each of these distributions as functions of n, as well as for the distributions themselves.In addition, it is shown how the methods developed to obtain these distributions can be employed to find, with minor effort, expressions for the expectation values of two statistics on Yule trees, the Sackin index (sum over all root-to-leaf distances), and the sum over all leaf-to-leaf distances.     

Nonparametric mixed effects models for unequally sampled noisy curves

We propose a method of analyzing collections of related curves in which the individual curves are modeled as spline functions with random coefficients. The method is applicable when the individual curves are sampled at variable and irregularly spaced points. This produces a low-rank, low-frequency approximation to the covariance structure, which can be estimated naturally by the EM algorithm. Smooth curves for individual trajectories are constructed as best linear unbiased predictor (BLUP) estimates, combining data from that individual and the entire collection. This framework leads naturally to methods for examining the effects of covariates on the shapes of the curves. We use model selection techniques--Akaike information criterion (AIC), Bayesian information criterion (BIC), and cross-validation--to select the number of breakpoints for the spline approximation. We believe that the methodology we propose provides a simple, flexible, and computationally efficient means of functional data analysis.     

Latent variable models for longitudinal data with multiple continuous outcomes

Multiple outcomes are often used to properly characterize an effect of interest. This paper proposes a latent variable model for the situation where repeated measures over time are obtained on each outcome. These outcomes are assumed to measure an underlying quantity of main interest from different perspectives. We relate the observed outcomes using regression models to a latent variable, which is then modeled as a function of covariates by a separate regression model. Random effects are used to model the correlation due to repeated measures of the observed outcomes and the latent variable. An EM algorithm is developed to obtain maximum likelihood estimates of model parameters. Unit-specific predictions of the latent variables are also calculated. This method is illustrated using data from a national panel study on changes in methadone treatment practices.     

甘草酸提取的分形维数研究

本文从非线性动力学角度探索了甘草酸浸提过程的混沌性态,提出了浸出物甘草酸质量由扩散项和噪声项两部分组成的模型假设,估算关联维数和甘草酸的浸出均值,对天然植物有效成分的提取及数据资源挖掘具有重要的作用。