Fitting distributions to microbial contamination data collected with an unequal probability sampling design

Aims

The fitting of statistical distributions to microbial sampling data is a common application in quantitative microbiology and risk assessment applications. An underlying assumption of most fitting techniques is that data are collected with simple random sampling, which is often times not the case. This study develops a weighted maximum likelihood estimation framework that is appropriate for microbiological samples that are collected with unequal probabilities of selection.

Methods and Results

A weighted maximum likelihood estimation framework is proposed for microbiological samples that are collected with unequal probabilities of selection. Two examples, based on the collection of food samples during processing, are provided to demonstrate the method and highlight the magnitude of biases in the maximum likelihood estimator when data are inappropriately treated as a simple random sample.

Conclusions

Failure to properly weight samples to account for how data are collected can introduce substantial biases into inferences drawn from the data.

Significance and Impact of the Study

The proposed methodology will reduce or eliminate an important source of bias in inferences drawn from the analysis of microbial data. This will also make comparisons between studies and the combination of results from different studies more reliable, which is important for risk assessment applications.     

Blinded sample size recalculation in multicentre trials with normally distributed outcome

The internal pilot study design enables to estimate nuisance parameters required for sample size calculation on the basis of data accumulated in an ongoing trial. By this, misspecifications made when determining the sample size in the planning phase can be corrected employing updated knowledge. According to regulatory guidelines, blindness of all personnel involved in the trial has to be preserved and the specified type I error rate has to be controlled when the internal pilot study design is applied. Especially in the late phase of drug development, most clinical studies are run in more than one centre. In these multicentre trials, one may have to deal with an unequal distribution of the patient numbers among the centres. Depending on the type of the analysis (weighted or unweighted), unequal centre sample sizes may lead to a substantial loss of power. Like the variance, the magnitude of imbalance is difficult to predict in the planning phase. We propose a blinded sample size recalculation procedure for the internal pilot study design in multicentre trials with normally distributed outcome and two balanced treatment groups that are analysed applying the weighted or the unweighted approach. The method addresses both uncertainty with respect to the variance of the endpoint and the extent of disparity of the centre sample sizes. The actual type I error rate as well as the expected power and sample size of the procedure is investigated in simulation studies. For the weighted analysis as well as for the unweighted analysis, the maximal type I error rate was not or only minimally exceeded. Furthermore, application of the proposed procedure led to an expected power that achieves the specified value in many cases and is throughout very close to it.     

Doubled haploids for estimating genetic variances and a scheme for population improvement in self-pollinating crops

Summary An analysis is derived for a diallel experiment in which each cross is represented by a number of homozygous Unes developed by the doubled haploid method. Both additive and additive x additive genetic variances can be estimated with this analysis. A population-improvement scheme involving the doubled haploid or single seed descent methods is also proposed.     

作物杂种后代基因型值和杂种优势的预测方法

本文提出了利用作物亲本和F_1预测杂种后代基因型值和杂种优势的统计分析方法.该方法运用加性-显性遗传模型,分析双列杂交试验资料,用MINQUE(1)法估算方差分量以及预测遗传效应值.由加性和显性效应预测值可进一步预测F_1,F_2,BC_1,BC_2,等不同世代的基因型值,在预测F_1群体平均优势和群体超亲优势的基础上,可以推导出其它各世代的杂种优势.提出了预测杂种后代保持超亲优势世代数的简单公式,根据杂交组合F_1群体平均优势和双亲相对遗传差异,便可预测该组合能在生产上直接利用的世代数.以棉花六个品种完全双列杂交试验资料为例,分析了各组合F_1和F_2的基因型值、超亲优势和保持5％超亲优势的世代数.     

Spreadsheet Method for Evaluation of Biochemical Reaction Rate Coefficients and Their Uncertainties by Weighted Nonlinear Least-Squares Analysis of the Integrated Monod Equation

A convenient method for evaluation of biochemical reaction rate coefficients and their uncertainties is described. The motivation for developing this method was the complexity of existing statistical methods for analysis of biochemical rate equations, as well as the shortcomings of linear approaches, such as Lineweaver-Burk plots. The nonlinear least-squares method provides accurate estimates of the rate coefficients and their uncertainties from experimental data. Linearized methods that involve inversion of data are unreliable since several important assumptions of linear regression are violated. Furthermore, when linearized methods are used, there is no basis for calculation of the uncertainties in the rate coefficients. Uncertainty estimates are crucial to studies involving comparisons of rates for different organisms or environmental conditions. The spreadsheet method uses weighted least-squares analysis to determine the best-fit values of the rate coefficients for the integrated Monod equation. Although the integrated Monod equation is an implicit expression of substrate concentration, weighted least-squares analysis can be employed to calculate approximate differences in substrate concentration between model predictions and data. An iterative search routine in a spreadsheet program is utilized to search for the best-fit values of the coefficients by minimizing the sum of squared weighted errors. The uncertainties in the best-fit values of the rate coefficients are calculated by an approximate method that can also be implemented in a spreadsheet. The uncertainty method can be used to calculate single-parameter (coefficient) confidence intervals, degrees of correlation between parameters, and joint confidence regions for two or more parameters. Example sets of calculations are presented for acetate utilization by a methanogenic mixed culture and trichloroethylene cometabolism by a methane-oxidizing mixed culture. An additional advantage of application of this method to the integrated Monod equation compared with application of linearized methods is the economy of obtaining rate coefficients from a single batch experiment or a few batch experiments rather than having to obtain large numbers of initial rate measurements. However, when initial rate measurements are used, this method can still be used with greater reliability than linearized approaches.     

A nonlinear regression program for small computers

A BASIC computer program for performing weighted nonlinear regression is described and a listing of the program is given. The program, which is small and simple to use, has been designed to be run by users with little knowledge of mathematics or computers. Robust methods of analysis are described which may be applied to data in which experimental errors are not normally distributed, and the program incorporates one such method. It is shown that the program is useful for the analysis of data conforming to the Michaelis-Menten equation, a single exponential, and to binding equations, and other applications are discussed.     

作物品种间杂种优势遗传分析的新方法

本文提出了分析双列杂交试验资料的两个遗传模型。第一个模型包括加性、显性和母体效应;第二个模型只包括简单的加性和显性效应。还介绍了分析杂种优势、估算遗传方差分量以及预测遗传效应值的相应统计分析方法。用所介绍的遗传模型和分析方法以及常用的Griffing配合力分析方法,分析了棉花6个品种双列杂交的产量性状,并进一步比较了不同方法的分析结果。采用本文所介绍的遗传模型和分析方法,可以克服用Griffing的配合力模型及其方法分析杂种优势和配合力遗传表现所存在的局限性。     

A group additivity model for analyzing absorption spectra of organic compounds: applications to partial structural analysis and molecular weight determinations of polymers, nucleotides, and peptides.

A new method for the analysis of organic structural groups from absorption spectra is described. The method is based on the integrated intensity of absorption. It requires only micrograms of analyzed compound, which may be fully recovered after analysis from its solution. The method can be used for different kinds of structural and/or kinetic studies. For example, the reaction kinetics and tautomeric equilibria can be easily studied by this method. The method can also be used for the determination of molecular weight and quantitative composition of polymers, nucleotides, and/or peptides. Hydrolysis or derivatization of the studied compounds is not necessary. On the basis of this method, automatic molecular weight, nucleotide, and peptide analyzers can be constructed.     

The use of regression methods to study genotype-environment interactions: extending Griffing's model for diallel cross experiments and testing an empirical grouping method.

A model combining features of Griffing's diallel cross analysis with regression analysis for genotype-environment interactions is introduced using carp data of Moav et al. (1975) as an example. An analysis of variance based on this model provides information on the combining abilities of genetic effects and the interactions of these effects with environments from which inferences can readily be made on heterosis and heterosis-environment interactions. Applying the empirical grouping method of Lin and Thompson (1975) to these data (ignoring their diallel cross structure) established groups which were remarkably consistent with their members' crossing backgrounds.     

Inference from Stratified Samples: Study Design,Bias and Graphical Model Representations

Stratification is a widely used strategy in empirical research to improve efficiency of the sampling design. One concern of stratification is that ignoring it on analysis may bias the relationship between variables. A weighted analysis can only be carried out when sampling weights are known. When these are unknown, valid inference on the relationship between variables then depends on the ignorability of the design, which may be difficult to establish. Here, graphical representations of multivariate dependencies and independencies are used to find necessary conditions for ignorability of stratified sampling designs for inference on conditional and marginal relationships between variables.     

The Use of Combining Ability Analysis to Identify Elite Parents for Artemisia annua F1 Hybrid Production

Artemisia annua is an important medicinal crop used for the production of the anti-malarial compound artemisinin. In order to assist in the production of affordable high quality artemisinin we have carried out an A. annua breeding programme aimed at improving artemisinin concentration and biomass. Here we report on a combining ability analysis of a diallel cross to identify robust parental lines for hybrid breeding. The parental lines were selected based on a range of phenotypic traits to encourage heterosis. The general combining ability (GCA) values for the diallel parental lines correlated to the positive alleles of quantitative trait loci (QTL) in the same parents indicating the presence of beneficial alleles that contribute to parental performance. Hybrids generated from crossing specific parental lines with good GCA were identified as having an increase in both artemisinin concentration and biomass when grown either in glasshouse or experimental field trials and compared to controls. This study demonstrates that combining ability as determined by a diallel cross can be used to identify elite parents for the production of improved A. annua hybrids. Furthermore, the selection of material for breeding using this approach was found to be consistent with our QTL-based molecular breeding approach.     

动物杂交试验的正反交循环设计法

为了提高配合力等参数估测的有效性、准确性和经济性。本文从动物自身的和试验的具体特点出发,提出了一种适于(1)客观条件仅允许试验部分组合、(2)试验目的仅为确定杂交育种的种群选配方案、(3)完全双列杂交试验分地分批进行等三种情况的新杂交试验设计法——正反交循环法,并且探讨了由这种设计法所设计的试验,即正反交循环杂交试验的最小二乘分析。     

Analysis of Partial Diallel Crosses in Incomplete Blocks

With a large number of lines in a diallel cross experiment, the number of crosses becomes unmanageable to be accommodated in homogeneous blocks. To overcome this problem, a sample of crosses, known as partial diallel cross (PDC) is often used. The selection of a PDC is based on the criterion of high efficiency for the estimation of general combining ability (gca) effects. Even with a moderately large number of crosses, the use of incomplete blocks is necessary to obtain homogeneous experimental units. The analysis of data from a general PDC grown in general incomplete block designs is being described. An iterative scheme is being developed for obtaining a generalized inverse of the information matrix used in estimating gca effects. Properties such as connectedness and efficiency of mating designs embedded in environment designs are being examined. The paper also examines the universal optimality of some designs in a class of designs. An illustration of the numerical procedure is also presented.     

Principles for Griffing's combining ability analysis

Griffing's diallel analysis is used in plant improvement programs to identify superior parents for crossing and for characterizing general, specific, and reciprocal effects. Eight different model/method combinations are commonly used in the analysis. The accuracy of the analysis is improved by using the appropriate model and method. In many instances, Model One with Method Three or Four is the most appropriate for obtaining unbiased estimates of combining abilities and gene action. The effective use of Griffing's analysis and the influence of several factors on this analysis are discussed. A personal computer program on this analysis is also made available to interested readers.     

Prevalence and origin of de novo duplications in Charcot-Marie-Tooth disease type 1A: first report of a de novo duplication with a maternal origin.

Charcot-Marie-Tooth disease (CMT) is the most common inherited peripheral neuropathy. Sporadic cases of CMT have been described since the earliest reports of the disease. The most frequent form of the disorder, CMT1A, is associated with a 1.5-Mb DNA duplication on chromosome 17p11.2, which segregates with the disease. In order to investigate the prevalence of de novo CMT1A duplications, this study examined 118 duplication-positive CMT1A families. In 10 of these families it was demonstrated that the disease had arisen as the result of a de novo mutation. By taking into account the ascertainment of families, it can be estimated that > or = 10% of autosomal dominant CMT1 families are due to de novo duplications. The CMT1A duplication is thought to be the product of unequal crossing over between parental chromosome 17 homologues during meiosis. Polymorphic markers from within the duplicated region were used to determine the parental origin of these de novo duplications in eight informative families. Seven were of paternal and one of maternal origin. This study represents the first report of a de novo duplication with a maternal origin and indicates that it is not a phenomenon associated solely with male meioses. Recombination fractions for the region duplicated in CMT1A are larger in females than in males. That suggests that oogenesis may be afforded greater protection from misalignment during synapsis, and/or that there may be lower activity of those factors or mechanisms that lead to unequal crossing over at the CMT1A locus.     

Weighted compromise trees: a method to summarize competing phylogenetic hypotheses

A new consensus method for summarizing competing phylogenetic hypotheses, weighted compromise, is described. The method corrects for a bias inherent in majority‐rule consensus/compromise trees when the source trees exhibit non‐independence due to ambiguity in terminal clades. Suggestions are given for its employment in parsimony analyses and tree resampling strategies such as bootstrapping and jackknifing. An R function is described that can be used with the programming language R to produce the consensus.     

Additive and Non-additive Genetic Correlations. I. Properties of Sampling Distributions

The sampling distributions of additive and non-additive genetic correlations estimated from a diallel experiment were determined through a computer simulation study. The properties of the sampling distributions were investigated in terms of the effect of varying the magnitude of the relevant variance components and the true correlation coefficient (Q), as well as the size of the diallel experiment. It was found that there was a high incidence of Q falling outside the range ?1 ≦Q≦1 when Q was close to 1 or -1, and the variance components were small. The degrees of freedom of the correlation components were shown to affect the variability of Q, and it was shown that a diallel experiment, that is to be used for a correlation analysis, should not be smaller than a 12 × 12 half diallel. Use of the Z transformation as a means of testing the significance of Q has been verified in this study and improvements on the degrees of freedom used for the transformation have been discussed.     

Evaluation of the normal equations for the analysis of diallels

Summary Analysis of diallel experiments usually requires specialised computer programs. A simple relationship between the normal equations for a diallel and the normal equations for a hypothetical model in which the general combining ability factor is viewed as two separate distinct simple factors may be useful in adapting general statistical analysis packages to the desired analysis.     

A general Bayesian approach to analyzing diallel crosses of inbred strains

The classic diallel takes a set of parents and produces offspring from all possible mating pairs. Phenotype values among the offspring can then be related back to their respective parentage. When the parents are diploid, sexed, and inbred, the diallel can characterize aggregate effects of genetic background on a phenotype, revealing effects of strain dosage, heterosis, parent of origin, epistasis, and sex-specific versions thereof. However, its analysis is traditionally intricate, unforgiving of unplanned missing information, and highly sensitive to imbalance, making the diallel unapproachable to many geneticists. Nonetheless, imbalanced and incomplete diallels arise frequently, albeit unintentionally, as by-products of larger-scale experiments that collect F(1) data, for example, pilot studies or multiparent breeding efforts such as the Collaborative Cross or the Arabidopsis MAGIC lines. We present a general Bayesian model for analyzing diallel data on dioecious diploid inbred strains that cleanly decomposes the observed patterns of variation into biologically intuitive components, simultaneously models and accommodates outliers, and provides shrinkage estimates of effects that automatically incorporate uncertainty due to imbalance, missing data, and small sample size. We further present a model selection procedure for weighing evidence for or against the inclusion of those components in a predictive model. We evaluate our method through simulation and apply it to incomplete diallel data on the founders and F(1)'s of the Collaborative Cross, robustly characterizing the genetic architecture of 48 phenotypes.     

Biometric-genetic analysis of genotype dissimilarity in diallel crosses of spring wheat

A new biometric-genetic model and parameters described in [1] have been used for analysis of pair dissimilarity between spring wheat cultivars and F1 hybrids obtained by diallel crossing. The dissimilarity between the reactions of different genotypes estimated by a growth trait (plant height) served as a metric. The mode of inheritance of dissimilarity has been determined, and the cultivars that are the most dissimilar in allelic composition have been detected.