Meta-analysis of studies with missing data

Summary .  Consider a meta-analysis of studies with varying proportions of patient-level missing data, and assume that each primary study has made certain missing data adjustments so that the reported estimates of treatment effect size and variance are valid. These estimates of treatment effects can be combined across studies by standard meta-analytic methods, employing a random-effects model to account for heterogeneity across studies. However, we note that a meta-analysis based on the standard random-effects model will lead to biased estimates when the attrition rates of primary studies depend on the size of the underlying study-level treatment effect. Perhaps ignorable within each study, these types of missing data are in fact not ignorable in a meta-analysis. We propose three methods to correct the bias resulting from such missing data in a meta-analysis: reweighting the DerSimonian–Laird estimate by the completion rate; incorporating the completion rate into a Bayesian random-effects model; and inference based on a Bayesian shared-parameter model that includes the completion rate. We illustrate these methods through a meta-analysis of 16 published randomized trials that examined combined pharmacotherapy and psychological treatment for depression.     

Shannon's Measure and its Use in the Analysis of Cancer Data

In this paper, Shannon's measure of uncertainty is explored in the analysis of cancer data. The term ‘cancer diversity’ is defined and its potential application is illustrated.     

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.     

Seasonal distribution and prevalence of dung beetles (Coleoptera: Scarabaeidae) in Kurukshetra,Northern India

A total of 8306 individuals as 29 species from 3 subfamilies (Hybosorinae, Aphodiinae, Scarabaeinae) were trapped by pitfall bait trapping. The maximum number of species of Scarabaeinae (68.97%) and number of individuals of Aphodiinae (56.84%) take part in the formation of a community. The number of species, number of individuals, diversity and dominance changes throughout the season. Seasonal prevalence of 82.76% of species and 50.81% of individuals was found in June. Aphodius campestris was found to be more attracted to the pitfall bait traps. The beetle community found in May shows the maximum Shannon's Diversity Index (2.46) but Margalef's Diversity Index was highest in August (3.06). Environmental factors play an important role in the occurrence and abundance of dung beetles. In the present study non-significant but positive correlations between temperature and species richness, abundance and diversity were found. Percent relative humidity showed a positive correlation with abundance only, and negative correlations with species richness and diversity.     

Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines

Dominant phenotype of a genetic marker provides incomplete information about the marker genotype of an individual. A consequence of using this incomplete information for mapping quantitative trait loci (QTL) is that the inference of the genotype of a putative QTL flanked by a marker with dominant phenotype will depend on the genotype or phenotype of the next marker. This dependence can be extended further until a marker genotype is fully observed. A general algorithm is derived to calculate the probability distribution of the genotype of a putative QTL at a given genomic position, conditional on all observed marker phenotypes in the region with dominant and missing marker information for an individual. The algorithm is implemented for various populations stemming from two inbred lines in the context of mapping QTL. Simulation results show that if only a proportion of markers contain missing or dominant phenotypes, QTL mapping can be almost as efficient as if there were no missing information in the data. The efficiency of the analysis, however, may decrease substantially when a very large proportion of markers contain missing or dominant phenotypes and a genetic map has to be reconstructed first on the same data as well. So it is important to combine dominant markers with codominant markers in a QTL mapping study. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Allelematch: an R package for identifying unique multilocus genotypes where genotyping error and missing data may be present

We present allelematch, an R package, to automate the identification of unique multilocus genotypes in data sets where the number of individuals is unknown, and where genotyping error and missing data may be present. Such conditions commonly occur in noninvasive sampling protocols. Output from the software enables a comparison of unique genotypes and their matches, and facilitates the review of differences between profiles. The software has a variety of applications in molecular ecology, and may be valuable where a large number of samples must be processed, unique genotypes identified, and repeated observations made over space and time. We used simulations to assess the performance of allelematch and found that it can reliably and accurately determine the correct number of unique genotypes (± 3%) across a broad range of data set properties. We found that the software performs with highest accuracy when genotyping error is below 4%. The R package is available from the Comprehensive R Archive Network (http://cran.r-project.org/). Supplementary documentation and tutorials are provided.     

Extreme homogenization: The past,present and future of mammal assemblages on islands

Aim

We documented how the similarity of mammal assemblages on continental and oceanic islands has changed since initial human colonization, since European arrival and overall. We investigated how levels of similarity might change in the future.

Location

Continental and oceanic islands worldwide.

Time period

Human settlement of islands to the present, as well as projections for the future.

Major taxa studied

Mammals.

Methods

We used mammal occurrence data on islands to calculate the change in similarity using a pairwise approach based on Jaccard's index and a multisite approach based on Jaccard's and Sørensen's measures. We divided the mammal assemblages into two time periods, before and after island colonization or trade began with Europeans. We unpacked the mechanisms driving changes in similarity, exploring how initial similarity interacts with seven types of species turnover events to determine overall change. Finally, we calculated how future similarity levels will change if past trends in introductions and extinctions continue.

Results

Mammals, on both continental and oceanic islands, show one of the most pronounced cases of homogenization ever observed, and on oceanic islands mammals show the largest increase in homogenization ever observed for a terrestrial group. Most of the homogenization observed to date has been driven by recent historical changes, not by changes that occurred before European arrival. If current patterns of species introductions and extinctions continue, then oceanic islands will experience little additional homogenization, whereas continental islands will homogenize greatly beyond current levels.

Main conclusions

Mammal assemblages on oceanic islands show nearly an order of magnitude greater change in similarity than plant and bird assemblages. Projections of future similarity indicate that continental and oceanic islands are on different trajectories of change. These trajectories could be altered by management actions, but in some cases those actions that would be impactful run counter to current conservation norms.     

Siberian wild rye (Elymus sibiricus L.): Genetic diversity of germplasm determined using DNA fingerprinting and SCoT markers

Elymus sibiricus is a perennial, self-pollinating, allotetraploid grass native to northern Asia. It is widely used in cultivated pastures and natural grassland due to excellent cold and drought tolerance, good forage quality, and adaptability to a variety of habitats. Information on the genetic diversity and variation among worldwide E. sibiricus germplasm is limited but necessary for germplasm collection, conservation and effective commercial use. In this study we ana lyzed genetic diversity and variation of 69 E. sibiricus accessions from the species range and constructed DNA fingerprinting profiles of 24 accessions using SCoT markers. A total of 173 bands were generated from 16 SCoT primers, 154 of which were polymorphic with 89.0% of polymorphic bands (PPB) occurring at the species level. The PPB within 8 geographical regions ranged from 2.3 to 54.3 %. Genetic variation was greater within geographical regions (57.9%) than between regions (42.1%). The 24 accessions from Qinghai-Tibet Plateau, Mongolia Plateau, Kazakhstan, and Russia were distinguished by their unique fingerprinting. This is the first report using SCoT markers for identifying cultivars and accessions of E. sibiricus. The DNA fingerprinting profiles of E. sibiricus were useful in germplasm collection and identification. The genetic diversity of worldwide E. sibiricus germplasm has been substantially affected by ecogeographical factors. Our results suggest that collecting and evaluating E. sibiricus germplasm from major geographic regions and unique environments broadens the available genetic base and illustrates the range of variation.     

DNA diversity of human populations from Eastern Europe and Siberia studied by multilocus DNA fingerprinting

We used DNA fingerprinting with M13 phage DNA as a probe to estimate the degree of genomic variability and genetic relationships in a heterogeneous group of 13 populations from Eastern Europe and Siberia. The popultaions belong to three language families: Indo-European (Slavonic: Russians, Byelorussians), Uralic (Finno-Ugric: Maris, Mordvinians, Udmurts), and Altaic (Turkic: Bashkirs, Tatars, Chuvashes, Yakuts). Multivariate statistical analyses were used (multidimensional scaling, cluster, and multiple correspondence analyses), and coefficients of gene differentiation (Gst) were evaluated. The level of interpopulation subdivision in the various ethnic groups appeared to be different: the Byelorussian populations revealed no regional differences, in contrast to the Bashkir populations, which formed a heterogeneous group. The populations subdivided into three general clusters: Slavonic populations formed a separate tight cluster characterized by a minimal level of interpopulation diversity, Bashkir and Yakut populations formed the second cluster, and the Finno-Ugric and several populations of the Turkic linguistic groups formed the third cluster. The robustness of these results obtained by different statistical data treatments reveals that multilocus DNA fingerprinting can be reliably used for population studies.Communicated by G. P. Georgiev     

Evaluation of missing data imputation methods for human osteometric measurements

It is not uncommon for biological anthropologists to analyze incomplete bioarcheological or forensic skeleton specimens. As many quantitative multivariate analyses cannot handle incomplete data, missing data imputation or estimation is a common preprocessing practice for such data. Using William W. Howells' Craniometric Data Set and the Goldman Osteometric Data Set, we evaluated the performance of multiple popular statistical methods for imputing missing metric measurements. Results indicated that multiple imputation methods outperformed single imputation methods, such as Bayesian principal component analysis (BPCA). Multiple imputation with Bayesian linear regression implemented in the R package norm2, the Expectation–Maximization (EM) with Bootstrapping algorithm implemented in Amelia, and the Predictive Mean Matching (PMM) method and several of the derivative linear regression models implemented in mice, perform well regarding accuracy, robustness, and speed. Based on the findings of this study, we suggest a practical procedure for choosing appropriate imputation methods.     

Assessment of DNA fingerprinting for determining genetic diversity in sheep populations

Genomic DNA, prepared from 12 animals from four sheep flocks, was digested with either HaeIII or Hin fI and probed with three DNA fingerprinting probes. Mean DNA fingerprint band sharing and band frequency calculated for each flock were used to estimate genetic diversity. Each of the DNA fingerprinting systems showed the same trend in diversity within the sampled flocks, and greater diversity between the flocks than within the flocks. DNA fingerprinting therefore provides a useful measure of genetic diversity in sheep.     

Evolution in populations of Swedish sand lizards: genetic differentiation and loss of variability revealed by multilocus DNA fingerprinting

The Swedish sand lizard (Lacerta agilis) is a relict species from the period of warmth following the last glacial episode and has a fragmented distribution in central Sweden and a more continuous distribution in the southern part of the country. We used this model system of colonization–extinction for a study of genetic variability within and among Swedish populations from different parts of the distribution range using multilocus DNA fingerprinting. The results from the Swedish populations are then contrasted with those from a large Hungarian population in the centre of the species geographical distribution range, which is likely to closely resemble the ancestral founding population of Sweden. Swedish populations have a low level of genetic variability compared with the Hungarian reference population, which showed a genetic variability within the range described for outbred populations. Within the Swedish populations, the average bandsharing was 0.61, the mean heterozygosity 0.45 and the estimated number of alleles 2.7. The figures for the Hungarian population were a bandsharing of 0.19, a heterozygosity of 0.89 and an estimated number of alleles of 9.8. A population bottleneck, common to all Swedish sand lizards, is indicated by less than 20% of the alleles in the Hungarian population being retained in the Swedish populations, and higher bandsharing similarity between different Swedish populations (0.33) as opposed to the Hungarian population (0.19). The limited variability found in Swedish sand lizards is strongly subdivided between populations, with an average F_ST of 0.32, indicating a very limited gene flow between the isolated populations, as well as between populations in the region where the sand lizard has a more or less continuous distribution (F_ST = 0.41).     

多位点DNA指纹技术在保加利亚普通田鼠中的应用探讨

DNA指纹是一种重要的现代分子遗传学标记技术（Jeffreys et al．,1985）,它所揭示的是生物体大量的、无遗传编码信息的、具有高度多态性的卫星DNA（Chen,1996）。这些DNA序列往往占据了生物体基因组总量的80％以上,由于它不编码蛋白基因,在系统发育过程中,通常不被自然选择和人工选择,使得生物变异积累形成个体基因组间的巨大差异。因此,DNA指纹受到生物学家的青睐,以用于生物个体和群体的基因组分析（Burke and Bruford,1987;Buitmap et al．,1991;Weising et al．,1995）。     

Filling the gap in functional trait databases: use of ecological hypotheses to replace missing data

Functional trait databases are powerful tools in ecology, though most of them contain large amounts of missing values. The goal of this study was to test the effect of imputation methods on the evaluation of trait values at species level and on the subsequent calculation of functional diversity indices at community level using functional trait databases. Two simple imputation methods (average and median), two methods based on ecological hypotheses, and one multiple imputation method were tested using a large plant trait database, together with the influence of the percentage of missing data and differences between functional traits. At community level, the complete‐case approach and three functional diversity indices calculated from grassland plant communities were included. At the species level, one of the methods based on ecological hypothesis was for all traits more accurate than imputation with average or median values, but the multiple imputation method was superior for most of the traits. The method based on functional proximity between species was the best method for traits with an unbalanced distribution, while the method based on the existence of relationships between traits was the best for traits with a balanced distribution. The ranking of the grassland communities for their functional diversity indices was not robust with the complete‐case approach, even for low percentages of missing data. With the imputation methods based on ecological hypotheses, functional diversity indices could be computed with a maximum of 30% of missing data, without affecting the ranking between grassland communities. The multiple imputation method performed well, but not better than single imputation based on ecological hypothesis and adapted to the distribution of the trait values for the functional identity and range of the communities. Ecological studies using functional trait databases have to deal with missing data using imputation methods corresponding to their specific needs and making the most out of the information available in the databases. Within this framework, this study indicates the possibilities and limits of single imputation methods based on ecological hypothesis and concludes that they could be useful when studying the ranking of communities for their functional diversity indices.     

银杏叶部内生真菌多样性的研究

为了解我国特有植物银杏的叶部组织中内生真菌菌群的多样性和演替变化,分别于春、夏、秋季从江苏和山东两省的五个主要银杏栽培地采集健康叶片进行了内生真菌的研究。结果表明:所分离出的1971株内生真菌可归于32属,以交链孢属Alternaria(18.01%)、叶点霉属Phyllosticta(14.66%)和丝核菌属Rhizoctonia(14.56%)为优势菌群。在内生真菌的类群及组成上存在着部位、地区以及季节的差异性,也呈现一定的规律性。多样性指数的计算反映出所获得的银杏叶部内生真菌菌群具有不同的丰富度及均匀度,同时有一定的相似性。     

DNA fingerprinting data and the problem of non-independence among pairwise comparisons

Multilocus DNA fingerprinting is commonly used to assess genetic similarity within and between geographically disjunct populations. Typically, the proportion of DNA fingerprinting bands shared between two individuals ( S _XY) is calculated for all possible pairwise comparisons and the resulting data analyzed parametrically to test differences in mean band-sharing among groups. The degree to which covariation among interdependent S _XY values ( S _ab - S _bc) biases the analyses is often unknown. Here, we assess the extent of covariation in four DNA fingerprinting studies and evaluate the effectiveness of two corrective procedures, a permutation test and a subsampling routine using only independent pairwise comparisons drawn without replacement from the overall data. Covariation among interdependent S _XY values was significantly greater than zero in every data set examined, including those from a bee, a rodent, and two passerine birds. Permutation tests did not correct for interdependence and yielded significance values nearly identical to those derived from uncorrected parametric procedures. In contrast, the subsampling procedure yielded corrected estimates of the standard error that were two to four times larger than those derived parametrically. As a result, comparisons that were significant using parametric tests were either non-significant or only marginally significant with the subsampling routine. We conclude that interdependence among S _XY values poses a substantial obstacle to hypothesis testing that must be addressed in future studies.     

青檀内生真菌菌群多样性的研究

为了解我国特有孑遗植物青檀的内生真菌的菌群组成和变化规律,分别于春秋两季从江苏、安徽、河南和山东4省的5个野生青檀居群地采样进行了内生真菌的分离、鉴定及多样性分析。结果表明,所分离出的3,611株内生真菌归于31属,无性型子囊菌中的腔孢类菌群占49.42%、丝孢类菌群占28.52%,有性型子囊菌菌群占2.52%,其余19.52%的菌群不产孢。在真菌属的水平,以拟茎点霉属Phomopsis（22.10%）和交链孢属Alternaria（20.66%）为优势菌群。南京与枣庄的野生青檀内生真菌菌群组成之间的相似性最高（Cs=0.84）,南京与南阳的相似性最低（Cs=0.60）。在宿主组织中,青檀叶片、叶柄和枝条中都以腔孢类菌群居于优势。春季和秋季青檀内生真菌的组成存在较大差异,春季以丝孢类菌群居多（46.71%）,秋季则以腔孢类菌群居多（55.85%）。     

A case study of the interpretation of linkage data using DNA fingerprinting probes

The statistical power of the technique of DNA fingerprinting relies greatly on the ability of the investigator to make an assumption that the presence or absence of different fingerprint bands are independent. Such linkage equilibrium is unlikely if bands are tightly linked to each other. Thus, when a new organism is to be investigated it is helpful to examine the segregation of parental bands into the offspring to confirm that the bands are not linked. By considering families of the tilapia Oreochrotnis niloticus , we produce statistical tests for linkage that can be applied to DNA fingerprint information. The use of these tests is more difficult and complicated if one parent is missing, but some progress can be made. We recommend that at least ten offspring are examined for segregation in families, since smaller numbers of offspring result in coincidental perfect agreements in band distributions in the absence of any linkage.