Evaluating decision rules for nitrogen fertilization

It is important, both for farmer profit and for the environment, to correctly dose nitrogen fertilizer for crop growth. Fertilizer recommendations are embodied in decision rules, which give a recommended dose of nitrogen (N) as a function of information available at the time the decision is made. In this paper, we first propose a criterion for evaluating decision rules. The proposed criterion is the expectation of the objective function when the decision rule is implemented. The major problem here is the estimation of this criterion. Two estimators are considered, a model-based and a nonparametric estimator. A simulation study shows that, in essentially all cases, the nonparametric estimator is better or no worse than the model-based estimator. The bias in the nonparametric estimator is always very small.     

关于广义Potthoff—Roy估计

本文考察了生长曲线模型的定义形式,并因此建立了相应的广义Potthoff-Roy估计,在最小范数准则下,给出了估计的最佳选择并且讨论了协变量以及改进估计的方法,尤其当设计阵病态时,给出了两类新的岭型Potthoff-Roy估计。     

Estimating the false discovery rate using nonparametric deconvolution

Given a set of microarray data, the problem is to detect differentially expressed genes, using a false discovery rate (FDR) criterion. As opposed to common procedures in the literature, we do not base the selection criterion on statistical significance only, but also on the effect size. Therefore, we select only those genes that are significantly more differentially expressed than some f-fold (e.g., f = 2). This corresponds to use of an interval null domain for the effect size. Based on a simple error model, we discuss a naive estimator for the FDR, interpreted as the probability that the parameter of interest lies in the null-domain (e.g., mu < log(2)(2) = 1) given that the test statistic exceeds a threshold. We improve the naive estimator by using deconvolution. That is, the density of the parameter of interest is recovered from the data. We study performance of the methods using simulations and real data.     

Homoplasy corrected estimation of genetic similarity from AFLP bands,and the effect of the number of bands on the precision of estimation

AFLP is a DNA fingerprinting technique, resulting in binary band presence–absence patterns, called profiles, with known or unknown band positions. We model AFLP as a sampling procedure of fragments, with lengths sampled from a distribution. Bands represent fragments of specific lengths. We focus on estimation of pairwise genetic similarity, defined as average fraction of common fragments, by AFLP. Usual estimators are Dice (D) or Jaccard coefficients. D overestimates genetic similarity, since identical bands in profile pairs may correspond to different fragments (homoplasy). Another complicating factor is the occurrence of different fragments of equal length within a profile, appearing as a single band, which we call collision. The bias of D increases with larger numbers of bands, and lower genetic similarity. We propose two homoplasy- and collision-corrected estimators of genetic similarity. The first is a modification of D, replacing band counts by estimated fragment counts. The second is a maximum likelihood estimator, only applicable if band positions are available. Properties of the estimators are studied by simulation. Standard errors and confidence intervals for the first are obtained by bootstrapping, and for the second by likelihood theory. The estimators are nearly unbiased, and have for most practical cases smaller standard error than D. The likelihood-based estimator generally gives the highest precision. The relationship between fragment counts and precision is studied using simulation. The usual range of band counts (50–100) appears nearly optimal. The methodology is illustrated using data from a phylogenetic study on lettuce.     

Inference of Microbial Recombination Rates from Metagenomic Data

Metagenomic sequencing projects from environments dominated by a small number of species produce genome-wide population samples. We present a two-site composite likelihood estimator of the scaled recombination rate, ρ = 2N_ec, that operates on metagenomic assemblies in which each sequenced fragment derives from a different individual. This new estimator properly accounts for sequencing error, as quantified by per-base quality scores, and missing data, as inferred from the placement of reads in a metagenomic assembly. We apply our estimator to data from a sludge metagenome project to demonstrate how this method will elucidate the rates of exchange of genetic material in natural microbial populations. Surprisingly, for a fixed amount of sequencing, this estimator has lower variance than similar methods that operate on more traditional population genetic samples of comparable size. In addition, we can infer variation in recombination rate across the genome because metagenomic projects sample genetic diversity genome-wide, not just at particular loci. The method itself makes no assumption specific to microbial populations, opening the door for application to any mixed population sample where the number of individuals sampled is much greater than the number of fragments sequenced.     

Closed Form Estimators of Latent Cell Frequencies

One-stage and two-stage closed form estimators of latent cell frequencies in multidimensional contingency tables are derived from the weighted least squares criterion. The first stage estimator is asymptotically equivalent to the conditional maximum likelihood estimator and does not necessarily have minimum asymptotic variance. The second stage estimator does have minimum asymptotic variance relative to any other existing estimator. The closed form estimators are defined for any number of latent cells in contingency tables of any order under exact general linear constraints on the logarithms of the nonlatent and latent cell frequencies.     

Bayesian Nonparametric Estimation of the Probability of Discovering New Species

We consider the problem of evaluating the probability of discoveringa certain number of new species in a new sample of populationunits, conditional on the number of species recorded in a basicsample. We use a Bayesian nonparametric approach. The differentspecies proportions are assumed to be random and the observationsfrom the population exchangeable. We provide a Bayesian estimator,under quadratic loss, for the probability of discovering newspecies which can be compared with well-known frequentist estimators.The results we obtain are illustrated through a numerical exampleand an application to a genomic dataset concerning the discoveryof new genes by sequencing additional single-read sequencesof cdna fragments.     

Regularized estimation in the accelerated failure time model with high-dimensional covariates

We consider two regularization approaches, the LASSO and the threshold-gradient-directed regularization, for estimation and variable selection in the accelerated failure time model with multiple covariates based on Stute's weighted least squares method. The Stute estimator uses Kaplan-Meier weights to account for censoring in the least squares criterion. The weighted least squares objective function makes the adaptation of this approach to multiple covariate settings computationally feasible. We use V-fold cross-validation and a modified Akaike's Information Criterion for tuning parameter selection, and a bootstrap approach for variance estimation. The proposed method is evaluated using simulations and demonstrated on a real data example.     

Bootstrap choice of estimators in parametric and semiparametric families: an extension of EIC

Ishiguro, Sakamoto, and Kitagawa (1997, Annals of the Institute of Statistical Mathematics 49, 411-434) proposed EIC as an extension of Akaike criterion (AIC); the idea leading to EIC is to correct the bias of the log-likelihood, considered as an estimator of the Kullback-Leibler information, using bootstrap. We develop this criterion for its use in multivariate semiparametric situations, and argue that it can be used for choosing among parametric and semiparametric estimators. A simulation study based on aregression model shows that EIC is better than its competitors although likelihood cross-validation performs nearly as well except for small sample size. Its use is illustrated by estimating the mean evolution of viral RNA levels in a group of infants infected by HIV.     

Exploratory analysis of longitudinal trials with staggered intervention times

Longitudinal trials involving surgical interventions commonly have subject-specific intervention times, due to constraints on the availability of surgeons and operating theatres. Moreover, the intervention often effects a discontinuous change in the mean response. We propose a nonparametric estimator for the mean response profile of longitudinal data with staggered intervention times and a discontinuity at the times of intervention, as an exploratory tool to assist the formulation of a suitable parametric model. We use an adaptation of the standard generalized additive model algorithm for estimation, with smoothing constants chosen by a cross-validation criterion. We illustrate the method using longitudinal data from a trial to assess the effect of lung resection surgery in the treatment of emphysema patients.     

Haplotype reconstruction for diploid populations

The inference of haplotype pairs directly from unphased genotype data is a key step in the analysis of genetic variation in relation to disease and pharmacogenetically relevant traits. Most popular methods such as Phase and PL do require either the coalescence assumption or the assumption of linkage between the single-nucleotide polymorphisms (SNPs). We have now developed novel approaches that are independent of these assumptions. First, we introduce a new optimization criterion in combination with a block-wise evolutionary Monte Carlo algorithm. Based on this criterion, the 'haplotype likelihood', we develop two kinds of estimators, the maximum haplotype-likelihood (MHL) estimator and its empirical Bayesian (EB) version. Using both real and simulated data sets, we demonstrate that our proposed estimators allow substantial improvements over both the expectation-maximization (EM) algorithm and Clark's procedure in terms of capacity/scalability and error rate. Thus, hundreds and more ambiguous loci and potentially very large sample sizes can be processed. Moreover, applying our proposed EB estimator can result in significant reductions of error rate in the case of unlinked or only weakly linked SNPs.     

Sample size formulae for two-stage randomized trials with survival outcomes

Two-stage randomized trials are growing in importance in developing adaptive treatment strategies, i.e. treatment policies or dynamic treatment regimes. Usually, the first stage involves randomization to one of the several initial treatments. The second stage of treatment begins when an early nonresponse criterion or response criterion is met. In the second-stage, nonresponding subjects are re-randomized among second-stage treatments. Sample size calculations for planning these two-stage randomized trials with failure time outcomes are challenging because the variances of common test statistics depend in a complex manner on the joint distribution of time to the early nonresponse criterion or response criterion and the primary failure time outcome. We produce simple, albeit conservative, sample size formulae by using upper bounds on the variances. The resulting formulae only require the working assumptions needed to size a standard single-stage randomized trial and, in common settings, are only mildly conservative. These sample size formulae are based on either a weighted Kaplan-Meier estimator of survival probabilities at a fixed time-point or a weighted version of the log-rank test.     

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.     

Two Estimators of Mean Frequency in Products of Multinormal Probability Models

Two estimators, one additive the other multiplicative, are considered for mean frequencies in a complete three-way table. Using the mean square error criterion it is shown that preference for the additive estimator can be as high 7/8 in tables with row-column independence and in homogeneous tables. Extension to other estimators are discussed.     

A General Framework for Longitudinal Data through Marked Point Processes

This paper reviews a general framework for the modelling of longitudinal data with random measurement times based on marked point processes and presents a worked example. We construct a quite general regression models for longitudinal data, which may in particular include censoring that only depend on the past and outside random variation, and dependencies between measurement times and measurements. The modelling also generalises statistical counting process models. We review a non-parametric Nadarya-Watson kernel estimator of the regression function, and a parametric analysis that is based on a conditional least squares (CLS) criterion. The parametric analysis presented, is a conditional version of the generalised estimation equations of LIANG and ZEGER (1986). We conclude that the usual nonparametric and parametric regression modelling can be applied to this general set-up, with some modifications. The presented framework provides an easily implemented and powerful tool for model building for repeated measurements.     

Variable selection for logistic regression using a prediction-focused information criterion

In biostatistical practice, it is common to use information criteria as a guide for model selection. We propose new versions of the focused information criterion (FIC) for variable selection in logistic regression. The FIC gives, depending on the quantity to be estimated, possibly different sets of selected variables. The standard version of the FIC measures the mean squared error of the estimator of the quantity of interest in the selected model. In this article, we propose more general versions of the FIC, allowing other risk measures such as the one based on L(p) error. When prediction of an event is important, as is often the case in medical applications, we construct an FIC using the error rate as a natural risk measure. The advantages of using an information criterion which depends on both the quantity of interest and the selected risk measure are illustrated by means of a simulation study and application to a study on diabetic retinopathy.     

An estimator of number of species from quadrat sampling

We consider the problem of estimating the number of distinct species S in a study area from the recorded presence or absence of species in each of a sample of quadrats. A generalized jackknife estimator of S is derived, along with an estimate of its variance. It is compared with the jackknife estimator for S proposed by Heltshe and Forrester and the empirical Bayes estimator of Mingoti and Meeden. We show that the empirical Bayes estimator has the form of a generalized jackknife estimator under a specific model for species distribution. We compare the new estimators of S to the empirical Bayes estimator via simulation. We characterize circumstances under which each is superior.     

A Note on Comparing Stochastically Restricted Linear Estimators in a Regression Model

In his recent paper Liski (1989) derived conditions for superiority of the minimum dispersion estimator over another with respect to the covariance matrix when the parameter vector of a regression model is subject to competing stochastic restrictions. The aim of this note is to provide another necessary and sufficient condition which admits an easier interpretation of superiority related to the covariance matrix criterion.     

一维响应变量时最高无毒副作用剂量水平的识别

在毒性试验中,将暴露在某一剂量水平下的处理组与接受相当于零剂量处理的对照组相比,随着药物剂量的增加,感兴趣的变量通常会呈现一种递增的趋势。考虑不会导致风险显著增加的最高剂量,本文使用AIC(Akaike information criterion)方法得到该剂量水平的强相合估计,并且通过两组数据及模拟的结果来说明AIC方法的优良性.     

Influence of physical and chemical factors during foraging and culture of the symbiont fungus in Atta sexdens rubropilosa （Hymenoptera： Formicidae）

The aim of this paper is to investigate the influence of physical and chemical factors on transport and use of substrate for Atta sexdens rubropilosa workers. Three types of rectangular fragments were used to study the physical influence factors： filter paper with paraffin, filter paper without paraffin and polyester film. To study the chemical factors, some fragments were impregnated with organic extract of orange albedo, others were soaked with soybean oil and for the remaining ones nothing was applied. The fonowing parameters were evaluated： （i） attractiveness of substrate for transport and number of loading workers per treatment; （ii） foraged material incorporation; （iii） rejection by numbers of fragments deposited in the garbage or beside the fungus garden. All the polyester film fragments carried out to the fungus garden were subsequently rejected. We verified that chemical factors of the substrate were more quickly detected by the workers, whereas physical factors were used as a criterion in the decision-making to reject or accept the substrate collected.