Sensitivity analysis of longitudinal binary data with non-monotone missing values

This paper highlights the consequences of incomplete observations in the analysis of longitudinal binary data, in particular non-monotone missing data patterns. Sensitivity analysis is advocated and a method is proposed based on a log-linear model. A sensitivity parameter that represents the relationship between the response mechanism and the missing data mechanism is introduced. It is shown that although this parameter is identifiable, its estimation is highly questionable. A far better approach is to consider a range of plausible values and to estimate the parameters of interest conditionally upon each value of the sensitivity parameter. This allows us to assess the sensitivity of study's conclusion to assumptions regarding the missing data mechanism. The method is applied to a randomized clinical trial comparing the efficacy of two treatment regimens in patients with persistent asthma.     

Imputation of missing covariate values in epigenome-wide analysis of DNA methylation data

DNA methylation is a widely studied epigenetic mechanism and alterations in methylation patterns may be involved in the development of common diseases. Unlike inherited changes in genetic sequence, variation in site-specific methylation varies by tissue, developmental stage, and disease status, and may be impacted by aging and exposure to environmental factors, such as diet or smoking. These non-genetic factors are typically included in epigenome-wide association studies (EWAS) because they may be confounding factors to the association between methylation and disease. However, missing values in these variables can lead to reduced sample size and decrease the statistical power of EWAS. We propose a site selection and multiple imputation (MI) method to impute missing covariate values and to perform association tests in EWAS. Then, we compare this method to an alternative projection-based method. Through simulations, we show that the MI-based method is slightly conservative, but provides consistent estimates for effect size. We also illustrate these methods with data from the Atherosclerosis Risk in Communities (ARIC) study to carry out an EWAS between methylation levels and smoking status, in which missing cell type compositions and white blood cell counts are imputed.     

Clustering DNA sequences by feature vectors

We represent all DNA sequences as points in twelve-dimensional space in such a way that homologous DNA sequences are clustered together, from which a new genomic space is created for global DNA sequences comparison of millions of genes simultaneously. More specifically, basing on the contents of four nucleotides, their distances from the origin and their distribution along the sequences, a twelve-dimensional vector is given to any DNA sequence. The applicability of this analysis on global comparison of gene structures was tested on myoglobin, beta-globin, histone-4, lysozyme, and rhodopsin families. Members from each family exhibit smaller vector distances relative to the distances of members from different families. The vector distance also distinguishes random sequences generated based on same bases composition. Sequence comparisons showed consistency with the BLAST method. Once the new gene is discovered, we can compute the location of this new gene in our genomic space. It is natural to predict that the properties of this new gene are similar to the properties of known genes that are locating near by. Biologists can do various experiments to test these properties.     

A faster circular binary segmentation algorithm for the analysis of array CGH data

MOTIVATION: Array CGH technologies enable the simultaneous measurement of DNA copy number for thousands of sites on a genome. We developed the circular binary segmentation (CBS) algorithm to divide the genome into regions of equal copy number. The algorithm tests for change-points using a maximal t-statistic with a permutation reference distribution to obtain the corresponding P-value. The number of computations required for the maximal test statistic is O(N2), where N is the number of markers. This makes the full permutation approach computationally prohibitive for the newer arrays that contain tens of thousands markers and highlights the need for a faster algorithm. RESULTS: We present a hybrid approach to obtain the P-value of the test statistic in linear time. We also introduce a rule for stopping early when there is strong evidence for the presence of a change. We show through simulations that the hybrid approach provides a substantial gain in speed with only a negligible loss in accuracy and that the stopping rule further increases speed. We also present the analyses of array CGH data from breast cancer cell lines to show the impact of the new approaches on the analysis of real data. AVAILABILITY: An R version of the CBS algorithm has been implemented in the "DNAcopy" package of the Bioconductor project. The proposed hybrid method for the P-value is available in version 1.2.1 or higher and the stopping rule for declaring a change early is available in version 1.5.1 or higher.     

Simple binary vectors for DNA transfer to plant cells

Summary Cosmid binary vectors for the introduction of DNA into plant cells have been constructed. These vectors are derived from the replicon of the broad host range plasmid pRK2 and contain the T-DNA border regions between which have been placed a chimaeric gene conferring resistance to kanamycin in plant cells. Appropriate restriction endonuclease targets have also been placed between the border regions. These binary vectors, in conjunction with appropriate Agrobacterium strains, are capable of delivering DNA to plant cells in cocultivation experiments with very high efficiency. The transformation frequency is shown to be somewhat dependent on the replicon used. re]19850121 rv]19850506 ac]19850513     

Characterization of missing values in untargeted MS-based metabolomics data and evaluation of missing data handling strategies

Background

Untargeted mass spectrometry (MS)-based metabolomics data often contain missing values that reduce statistical power and can introduce bias in biomedical studies. However, a systematic assessment of the various sources of missing values and strategies to handle these data has received little attention. Missing data can occur systematically, e.g. from run day-dependent effects due to limits of detection (LOD); or it can be random as, for instance, a consequence of sample preparation.

Methods

We investigated patterns of missing data in an MS-based metabolomics experiment of serum samples from the German KORA F4 cohort (n?=?1750). We then evaluated 31 imputation methods in a simulation framework and biologically validated the results by applying all imputation approaches to real metabolomics data. We examined the ability of each method to reconstruct biochemical pathways from data-driven correlation networks, and the ability of the method to increase statistical power while preserving the strength of established metabolic quantitative trait loci.

Results

Run day-dependent LOD-based missing data accounts for most missing values in the metabolomics dataset. Although multiple imputation by chained equations performed well in many scenarios, it is computationally and statistically challenging. K-nearest neighbors (KNN) imputation on observations with variable pre-selection showed robust performance across all evaluation schemes and is computationally more tractable.

Conclusion

Missing data in untargeted MS-based metabolomics data occur for various reasons. Based on our results, we recommend that KNN-based imputation is performed on observations with variable pre-selection since it showed robust results in all evaluation schemes.

     

Circular binary segmentation for the analysis of array-based DNA copy number data

DNA sequence copy number is the number of copies of DNA at a region of a genome. Cancer progression often involves alterations in DNA copy number. Newly developed microarray technologies enable simultaneous measurement of copy number at thousands of sites in a genome. We have developed a modification of binary segmentation, which we call circular binary segmentation, to translate noisy intensity measurements into regions of equal copy number. The method is evaluated by simulation and is demonstrated on cell line data with known copy number alterations and on a breast cancer cell line data set.     

Normalization of single-channel DNA array data by principal component analysis

MOTIVATION: Detailed comparison and analysis of the output of DNA gene expression arrays from multiple samples require global normalization of the measured individual gene intensities from the different hybridizations. This is needed for accounting for variations in array preparation and sample hybridization conditions. RESULTS: Here, we present a simple, robust and accurate procedure for the global normalization of datasets generated with single-channel DNA arrays based on principal component analysis. The procedure makes minimal assumptions about the data and performs well in cases where other standard procedures produced biased estimates. It is also insensitive to data transformation, filtering (thresholding) and pre-screening.     

Molecular-beacon-based array for sensitive DNA analysis

Molecular beacon (MB) DNA probes provide a new way for sensitive label-free DNA/protein detection in homogeneous solution and biosensor development. However, a relatively low fluorescence enhancement after the hybridization of the surface-immobilized MB hinders its effective biotechnological applications. We have designed new molecular beacon probes to enable a larger separation between the surface and the surface-bound MBs. Using these MB probes, we have developed a DNA array on avidin-coated cover slips and have improved analytical sensitivity. A home-built wide-field optical setup was used for imaging the array. Our results show that linker length, pH, and ionic strength have obvious effects on the performance of the surface-bound MBs. The fluorescence enhancement of the new MBs after hybridization has been increased from 2 to 5.5. The MB-based DNA array could be used for DNA detection with high sensitivity, enabling simultaneous multiple-target bioanalysis in a variety of biotechnological applications.     

Optimal association with partly missing key vectors

A new association scheme which can still recall appropriate data when some key elements are missing (blank) is presented. The traditional associative memory models are designed to deal with complete (memorized) keys, but in the real world, key elements are often missing due to error, equipment failure, observation difficulty, etc. The traditional models, in this case, can not have an optimal association except for special cases. When an incomplete key containing blanks is given, we wish to get the same data, as nearly as possible, as would be obtained with the complete key. In this paper, the optimal associative memory model which operates with partly missing keys is proposed. The model is constructed on the basis of the theory of the pseudoinverse of matrices. Even from the incomplete keys which contain a large percentage of blanks, the model recalls the appropriate data optimally under the MSE criterion. From the results of computer simulations, we can show that the model has the expected ability.     

Multivariate methods for clustered binary data with multiple subclasses, with application to binary longitudinal data.

Clustered binary data occur frequently in biostatistical work. Several approaches have been proposed for the analysis of clustered binary data. In Rosner (1984, Biometrics 40, 1025-1035), a polychotomous logistic regression model was proposed that is a generalization of the beta-binomial distribution and allows for unit- and subunit-specific covariates, while controlling for clustering effects. One assumption of this model is that all pairs of subunits within a cluster are equally correlated. This is appropriate for ophthalmologic work where clusters are generally of size 2, but may be inappropriate for larger cluster sizes. A beta-binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses. To include covariates, an extension of the polychotomous logistic regression model is proposed, which allows one to estimate effects of unit-, class-, and subunit-specific covariates, while controlling for clustering using the beta-binomial mixture model. This model is applied to the analysis of respiratory symptom data in children collected over a 14-year period in East Boston, Massachusetts, in relation to maternal and child smoking, where the unit is the child and symptom history is divided into early-adolescent and late-adolescent symptom experience.     

Statistical analysis of binary data generated from multilocus dominant DNA markers

The use of methodologies such as RAPD and AFLP for studying genetic variation in natural populations is widespread in the ecology community. Because data generated using these methods exhibit dominance, their statistical treatment is less straightforward. Several estimators have been proposed for estimating population genetic parameters, assuming simple random sampling and the Hardy-Weinberg (HW) law. The merits of these estimators remain unclear because no comparative studies of their theoretical properties have been carried out. Furthermore, ascertainment bias has not been explicitly modelled. Here, we present a comparison of a set of candidate estimators of null allele frequency (q), locus-specific heterozygosity (h) and average heterozygosity () in terms of their bias, standard error, and root mean square error (RMSE). For estimating q and h, we show that none of the estimators considered has the least RMSE over the parameter space. Our proposed zero-correction procedure, however, generally leads to estimators with improved RMSE. Assuming a beta model for the distribution of null homozygote proportions, we show how correction for ascertainment bias can be carried out using a linear transform of the sample average of h and the truncated beta-binomial likelihood. Simulation results indicate that the maximum likelihood and empirical Bayes estimator of have negligible bias and similar RMSE. Ascertainment bias in estimators of is most pronounced when the beta distribution is J-shaped and negligible when the latter is inverse J-shaped. The validity of the current findings depends importantly on the HW assumption-a point that we illustrate using data from two published studies.     

Neutrality tests for sequences with missing data

Missing data are common in DNA sequences obtained through high-throughput sequencing. Furthermore, samples of low quality or problems in the experimental protocol often cause a loss of data even with traditional sequencing technologies. Here we propose modified estimators of variability and neutrality tests that can be naturally applied to sequences with missing data, without the need to remove bases or individuals from the analysis. Modified statistics include the Watterson estimator θ(W), Tajima's D, Fay and Wu's H, and HKA. We develop a general framework to take missing data into account in frequency spectrum-based neutrality tests and we derive the exact expression for the variance of these statistics under the neutral model. The neutrality tests proposed here can also be used as summary statistics to describe the information contained in other classes of data like DNA microarrays.     

LSimpute: accurate estimation of missing values in microarray data with least squares methods

Microarray experiments generate data sets with information on the expression levels of thousands of genes in a set of biological samples. Unfortunately, such experiments often produce multiple missing expression values, normally due to various experimental problems. As many algorithms for gene expression analysis require a complete data matrix as input, the missing values have to be estimated in order to analyze the available data. Alternatively, genes and arrays can be removed until no missing values remain. However, for genes or arrays with only a small number of missing values, it is desirable to impute those values. For the subsequent analysis to be as informative as possible, it is essential that the estimates for the missing gene expression values are accurate. A small amount of badly estimated missing values in the data might be enough for clustering methods, such as hierachical clustering or K-means clustering, to produce misleading results. Thus, accurate methods for missing value estimation are needed. We present novel methods for estimation of missing values in microarray data sets that are based on the least squares principle, and that utilize correlations between both genes and arrays. For this set of methods, we use the common reference name LSimpute. We compare the estimation accuracy of our methods with the widely used KNNimpute on three complete data matrices from public data sets by randomly knocking out data (labeling as missing). From these tests, we conclude that our LSimpute methods produce estimates that consistently are more accurate than those obtained using KNNimpute. Additionally, we examine a more classic approach to missing value estimation based on expectation maximization (EM). We refer to our EM implementations as EMimpute, and the estimate errors using the EMimpute methods are compared with those our novel methods produce. The results indicate that on average, the estimates from our best performing LSimpute method are at least as accurate as those from the best EMimpute algorithm.     

A simple method for the analysis of clustered binary data.

A simple method for comparing independent groups of clustered binary data with group-specific covariates is proposed. It is based on the concepts of design effect and effective sample size widely used in sample surveys, and assumes no specific models for the intracluster correlations. It can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing. The method is applied to a variety of problems involving clustered binary data: testing homogeneity of proportions, estimating dose-response models and testing for trend in proportions, and performing the Mantel-Haenszel chi-squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance. Illustrative applications of the method are also presented.     

DNA restriction fingerprint analysis of the soil bacterium Azospirillum.

Total DNAs of 18 strains of Azospirillum from different sources and geographical areas were compared by restriction endonuclease pattern analysis. Fragments obtained with HindIII or BglII were separated by PAGE and stained with silver nitrate. Each strain possessed a unique and reproducible fingerprint with each enzyme, thereby facilitating strain recognition. UPGMA analysis recovered clusters of band patterns that were compared to the distribution of species within the genus Azospirillum.