Evaluation of Animal Carcinogenicity Studies: Cochran‐Armitage Trend Test vs. Multiple Contrast Tests

Typical animal carcinogenicity studies involve the comparison of several dose groups to a negative control. The uncorrected asymptotic Cochran‐Armitage trend test with equally spaced dose scores is the most frequently used test in such set‐ups. However, this test based on a weighted linear regression on proportions. It is well known that the Cochran‐Armitage test lacks in power for other shapes than the assumed linear one. Therefore, dichotomous multiple contrast tests are introduced. These build the maximum over several single contrasts, where each of them is chosen appropriately to cover a specific dose‐response shape. An extensive power study has been conducted to compare multiple contrast tests with the approaches used so far. Crucial results will be presented in this paper. Moreover, exact tests and continuity corrected versions are introduced and compared to the traditional uncorrected approaches regarding size and power behaviour. A trend test for any shape of the dose‐response relationship for either crude tumour rates or mortality‐ adjusted rates based on the simple Poly‐3 transformation is proposed for evaluation of carcinogenicity studies.     

A Test Procedure of Equivalence in Ordinal Data with Matched‐Pairs

There are many epidemiologic studies or clinical trials, in which we may wish to establish an equivalence rather than to detect a difference between the distributions of responses. In this paper, we develop test procedures to detect equivalence with respect to the tail marginal distributions and the marginal proportions when the underlying data are on an ordinal scale with matched pairs. We include a numerical example concerning the unaided distance vision of two eyes over 7477 women to illustrate the practical usefulness of the proposed procedure. Finally, we include a brief discussion on the relation between the test procedures developed here and an asymptotic interval estimator proposed elsewhere for the simple difference in dichotomous data with matched‐pairs.     

Graphical aid for determining power of clinical trials involving two groups.

Physicians need to evaluate clinical research critically, and determining the power of a study is an essential component of research evaluation. This report presents a graphical aid that permits rapid power determination for clinical trials with two groups. Power curves were developed for dichotomous outcomes by setting two tail alpha at 0.05 and varying the sample size, the control group response rate, and the clinically important difference between control and experimental groups as defined by the user. Use of the graphical aid was demonstrated to a group of 18 medical students, residents, fellows, and faculty in a 15 minute session. Evaluation of the trainees'' application of the aid showed a small average bias of -0.0003 and an average variance of 0.006. Ninety percent of power estimates were within 0.05 of the true value determined by formula. This graphical aid is recommended as a rapid and accurate method for determining power in the critical appraisal of clinical research.     

Assessing overdispersion and dose-response in the male dominant lethal assay.

In dominant lethal studies the primary variables of interest are typically expressed as discrete counts or proportions (e.g., live implants, resorptions, percent pregnant). Simple statistical sampling models for discrete data such as binomial or Poisson generally do not fit this type of data because of extra-binomial or extra-Poisson departures from variability predicted under these simple models. Extra-variability in the fetal response may originate from parental contributions. These can lead to over- or under-dispersion seen as, e.g., extra-binomial variability in the proportion response. Utilizing a large control database, we investigated the relative impact of extra-variability from male or female contributions on the endpoints of interest. Male-related effects did not seem to contribute to overdispersion in our database; female-related effects were, however, evidenced. Various statistical methods were considered to test for significant treatment differences under these forms of sampling variability. Computer simulations were used to evaluate these methods and to determine which are most appropriate for practical use in the evaluation of dominant lethal data. Our results suggest that distribution-free statistical methods such as a nonparametric permutation test or rank-based tests for trend can be recommended for use.     

Power analysis to determine sample size for monitoring vegetation change in salt marsh habitats

Numerous initiatives are underway throughout New England and elsewhere to quantify salt marsh vegetation change, mostly in response to habitat restoration, sea level rise, and nutrient enrichment. To detect temporal changes in vegetation at a marsh or to compare vegetation among different marshes with a degree of statistical certainty an adequate sample size is required. Based on sampling 1 m² vegetation plots from 11 New England salt marsh data sets, we conducted a power analysis to determine the minimum number of samples that were necessary to detect change between vegetation communities. Statistical power was determined for sample sizes of 5, 10, 15, and 20 vegetation plots at an alpha level of 0.05. Detection of subtle differences between vegetation data sets (e.g., comparing vegetation in the same marsh over two consecutive years) can be accomplished using a sample size of 20 plots with a reasonable probability of detecting a difference when one truly exists. With a lower sample size, and thus lower power, there is an increased probability of not detecting a difference when one exists (e.g., Type II error). However, if investigators expect to detect major changes in vegetation (e.g., such as those between an un-impacted and a highly impacted marsh) then a sample size of 5, 10, or 15 plots may be appropriate while still maintaining adequate power. Due to the relative ease of collecting vegetation data, we suggest a minimum sample size of 20 randomly located 1 m² plots when developing monitoring designs to detect vegetation community change of salt marshes. The sample size of 20 plots per New England salt marsh is appropriate regardless of marsh size or permanency (permanent or non-permanent) of the plots.     

Accession of sweet stimuli to receptors. I. Absolute dominance of one molecular species in binary mixtures

Intensity/time studies of sweetness response in pure solutions of each of nine different sweet stimuli have been carried out. Both variables exhibit simple power functions of the form Intensity (S) = kscns and Persistence (P) = kpcnp. In binary mixtures of these nine stimuli a depression (or negative synergism) of both sweetness intensity and persistence is observed which is predictable from the low exponents of the power functions. Combination of both power functions allows the "effective concentration" of each stimulus in a binary mixture to be calculated from its observed intensity/time characteristics. All "effective concentrations" calculable in this way show absolute dominance of one stimulus in mixtures of two irrespective of the relative proportions of the two stimuli. It is suggested that the "effective concentrations" may reflect real concentrations of a single molecular species in the microenvironment of the receptor. Thus the accession of sweet molecules to ordered, localized concentrations at the receptor is ultimately dependent on chemical structure.     

How many replicates of arrays are required to detect gene expression changes in microarray experiments? A mixture model approach

Background  

It has been recognized that replicates of arrays (or spots) may be necessary for reliably detecting differentially expressed genes in microarray experiments. However, the often-asked question of how many replicates are required has barely been addressed in the literature. In general, the answer depends on several factors: a given magnitude of expression change, a desired statistical power (that is, probability) to detect it, a specified Type I error rate, and the statistical method being used to detect the change. Here, we discuss how to calculate the number of replicates in the context of applying a nonparametric statistical method, the normal mixture model approach, to detect changes in gene expression.     

Statistical power analysis of a 2-year field study and design of experiments to evaluate non-target effects of genetically modified Bacillius thuringiensis corn

Abstract 1. A 2‐year field study was conducted in 2000 and 2001 at a farm in Monmouth, Illinois to evaluate the effect of MON 863, a transgenic corn event that expresses the Cry3Bb1 protein for control of corn rootworms, on diverse groups of arthropod populations in a corn ecosystem. 2. The field study employed a split‐plot design with MON 863 and conventional corn as the main plots and several insecticide treatments as subplots; each main plot was replicated four times (i.e. n = 4 block replications for each corn variety). A large number of arthropod taxa were trapped, taxonomically characterised, and counted in all plots. A mixed linear repeated‐measures model was used for analysis of each taxon collected to determine if there was an effect of MON 863 or insecticide regime on that taxonomic group. 3. This report describes the results of a power analysis to determine the ability of the study design to detect an effect of MON 863 corn on the abundance of different groups of arthropods. A 50% difference in average taxon abundance between MON 863 and conventional corn plots was the criterion used in assessing the power. 4. A statistical power analysis of the taxonomic group comparisons made in the 2‐year field study (with independent assignment of treatments each year) showed that only about 28% (22 of 56) of the statistical comparisons made with single years of data achieved ≥80% power to detect a 50% difference in population density. When data from both years of the study were analysed jointly, this level of power was obtained for 86% (24 of 28) the comparisons made. 5. Graphical examination of the mean abundance and coefficient of variation (CV) for different taxa indicated that high abundance (> 5 trap captures per plot per sampling period) and low CV (< 100%) contributed to high statistical power (> 80%). Taxa with extremely low abundance (mean trap captures < 1 individual per plot per sampling period) generally had high CV (> 100%), and statistical comparisons for those taxa had lower power (< 80%). 6. The relevance of these findings for designing field studies on the effects of genetically modified crops on non‐target arthropods with desired levels of power is discussed.     

Ashkenazi Jewish centenarians do not demonstrate enrichment in mitochondrial haplogroup J

Background

Association of mitochondrial haplogroup J with longevity has been reported in several population subgroups. While studies from northern Italy and Finland, have described a higher frequency of haplogroup J among centenarians in comparison to non-centenarian, several other studies could not replicate these results and suggested various explanations for the discrepancy.

Methodology/Principal Findings

We have evaluated haplogroup frequencies among Ashkenazi Jewish centenarians using two different sets of matched controls. No difference was observed in the haplogroup J frequencies between the centenarians or either matched control group, despite adequate statistical power to detect such a difference. Furthermore, the lack of association was robust to population substructure in the Ashkenazi Jewish population. Given this discrepancy with the previous reported associations in the northern Italian and the Finnish populations, we conducted re-analysis of these previously published data, which supported one of several possible explanations: i) inadequate matching of cases and controls; ii) inadequate adjustment for multiple comparison testing; iii) cryptic population stratification.

Conclusions/Significance

There does not exist a universal association of mitochondrial haplogroup J with longevity across all population groups. Reported associations in specialized populations may reflect genetic or other interactions specific to those populations or else cryptic confounding influences, such as inadequate matching attributable to population substructure, which are of general relevance to all studies of the possible association of mitochondrial DNA haplogroups with common complex phenotypes.     

大鼠爬板实验装置的设计制作及其在脑损伤实验中的应用

目的设计制作一种大鼠爬板实验装置,以使科研工作者能轻松快捷地通过爬板实验检测大鼠脑损伤后神经功能的改变,并提高实验数据的准确性。方法将成年雄性SD大鼠随机分为Tβ4组、PBS组和sham组。分别采用新装置和原装置对3组大鼠进行爬板实验,检测记录术后1～7d的神经功能缺失评分,并进行统计分析。结果用新装置进行检测：Tβ4组和PBS组的神经功能缺失评分均在逐步平缓下降,5 d后,仍可检测到神经功能缺失;两组之间的差异（P〈0.05）在3 d后,均可检出。Tβ4组与sham组之间的差异（P〈0.05）,前3d均可检出。PBS组与sham组之间的差异（P〈0.05）,术后一直可以检出。用原装置进行检测：Tβ4组和PBS组的神经功能缺失评分呈跳跃式下降,5 d后,不再能检出神经功能缺失;两组之间的差异（P〈0.05）,只在第4天时检出。Tβ4组与sham组之间的差异（P〈0.05）,只在前2 d检出。PBS组与sham组之间的差异（P〈0.05）,只前在前4 d检出。结论新的实验装置制作简单,实验操作便利;可以提高实验数据的准确性,能更好地检测出因实验因素所造成的统计学差异。     

Lack of statistical power as a major limitation in understanding MHC‐mediated immunocompetence in wild vertebrate populations

Disentangling the sources of variation in developing an effective immune response against pathogens is of major interest to immunoecology and evolutionary biology. To date, the link between immunocompetence and genetic variation at the major histocompatibility complex (MHC) has received little attention in wild animals, despite the key role of MHC genes in activating the adaptive immune system. Although several studies point to a link between MHC and immunocompetence, negative findings have also been reported. Such disparate findings suggest that limited statistical power might be affecting studies on this topic, owing to insufficient sample sizes and/or a generally small effect of MHC on the immunocompetence of wild vertebrates. To clarify this issue, we investigated the link between MHC variation and seven immunocompetence proxies in a large sample of barn owls and estimated the effect sizes and statistical power of this and published studies on this topic. We found that MHC poorly explained variation in immunocompetence of barn owls, with small‐to‐moderate associations between MHC and immunocompetence in owls (effect size: .1 ≥ r ≤ .3) similar to other vertebrates studied to date. Such small‐to‐moderate effects were largely associated with insufficient power, which was only sufficient (>0.8) to detect moderate‐to‐large effect sizes (r ≥ .3). Thus, studies linking MHC variation with immunocompetence in wild populations are underpowered to detect MHC effects, which are likely to be of generally small magnitude. Larger sample sizes (>200) will be required to achieve sufficient power in future studies aiming to robustly test for a link between MHC variation and immunocompetence.     

Analysing body condition: mass, volume or density?

1. Body condition (defined as the relative amount of energy reserves in the body) is an animal trait with strong ecological implications. In some animal taxa (e.g. arthropods), the external volume of the body part in which most nutrients are stored (e.g. abdomen) is used interchangeably with body mass to estimate body condition, making the implicit assumption that abdomen residual volume is a good surrogate of residual mass. However, the degree of correlation between these two measures should largely depend on the density of the nutrients stored. 2. We simulated two food-supplemented experimental groups of animals, each storing a slightly different amount of lipids either in their abdomens or in their entire bodies, and explored (i) how different estimates of condition were able to detect fixed differences between the groups; and (ii) how the amount of lipids stored could affect the outcome of non-intrusive measures of condition on a dichotomous variable (e.g. survival, mating success). We found that density body condition (body mass statistically controlled for structural body size and body volume) has much greater power to detect differences between experimental groups or effects on binary response variables than do classic mass/size or volume/size condition indices. 3. Using data on Lycosa tarantula (L.), a burrowing wolf spider, we report dramatic differences among these three indices in their ability to detect sex differences in the effect of feeding treatment on body condition at maturity. In particular, a plot of residual mass against residual volume reflecting nutrient density suggests that poorly fed spiders are nutritionally unbalanced, since well-fed spiders invest in nutrients of very different density. 4. Furthermore, using data on Scathophaga stercoraria (L.), the yellow dung fly, we found that an index of density condition was better at distinguishing condition differences among three populations than were mass or volume condition estimates alone. 5. We propose that including these three surrogates of condition (mass, volume and density) will substantially improve the accuracy of non-intrusive estimates of body condition, thus providing more powerful tools with direct application in a wide range of disciplines.     

The Impact of Phenotypic and Genetic Heterogeneity on Results of Genome Wide Association Studies of Complex Diseases

Phenotypic misclassification (between cases) has been shown to reduce the power to detect association in genetic studies. However, it is conceivable that complex traits are heterogeneous with respect to individual genetic susceptibility and disease pathophysiology, and that the effect of heterogeneity has a larger magnitude than the effect of phenotyping errors. Although an intuitively clear concept, the effect of heterogeneity on genetic studies of common diseases has received little attention. Here we investigate the impact of phenotypic and genetic heterogeneity on the statistical power of genome wide association studies (GWAS). We first performed a study of simulated genotypic and phenotypic data. Next, we analyzed the Wellcome Trust Case-Control Consortium (WTCCC) data for diabetes mellitus (DM) type 1 (T1D) and type 2 (T2D), using varying proportions of each type of diabetes in order to examine the impact of heterogeneity on the strength and statistical significance of association previously found in the WTCCC data. In both simulated and real data, heterogeneity (presence of “non-cases”) reduced the statistical power to detect genetic association and greatly decreased the estimates of risk attributed to genetic variation. This finding was also supported by the analysis of loci validated in subsequent large-scale meta-analyses. For example, heterogeneity of 50% increases the required sample size by approximately three times. These results suggest that accurate phenotype delineation may be more important for detecting true genetic associations than increase in sample size.     

Use of clones increases the power of physiological experiments on coastal Douglas-fir

The statistical benefit of reduced variability in experiments with clones was quantified with cold hardy Douglas-fir ( Pseudotsuga menziesii var. menziesii [Mirb.] Franco) ramets from six clones from a single full-sib family and a check group of open-pollinated seedlings from a bulk seed collection from the same geographic seed source. All groups were cold deacclimated under controlled conditions. The variability in response for physiological attributes (cold hardiness, root growth potential, days to bud-break) was compared within and among groups by using statistical power analyses. Sample sizes required to detect significant differences of varying magnitude between two hypothetical treatment means were calculated. Differences among clones in the average response exhibited for each physiological attribute were large, but within-clone variability was low, relative to the check group of seedlings. Selection of plant material for a hypothetical experiment from this population of several identifiable clones would have consistently resulted in an experiment with greater power than an experiment using these ramets without the clone identities. From a statistical perspective, the best approach to reduce the number of replicates needed to detect treatment differences was selection of experimental plant material from a single clone, especially with prior screening for the most homogeneous clone for the physiological attributes and time periods of interest. However, from a biological perspective, use of a single clone should be approached with caution because of the lack of representation of natural population variability and the possible inability to broadly apply experimental results.     

Selecting tagging SNPs for association studies using power calculations from genotype data

Recent studies have indicated that linkage disequilibrium (LD) between single nucleotide polymorphism (SNP) markers can be used to derive a reduced set of tagging SNPs (tSNPs) for genetic association studies. Previous strategies for identifying tSNPs have focused on LD measures or haplotype diversity, but the statistical power to detect disease-associated variants using tSNPs in genetic studies has not been fully characterized. We propose a new approach of selecting tSNPs based on determining the set of SNPs with the highest power to detect association. Two-locus genotype frequencies are used in the power calculations. To show utility, we applied this power method to a large number of SNPs that had been genotyped in Caucasian samples. We demonstrate that a significant reduction in genotyping efforts can be achieved although the reduction depends on genotypic relative risk, inheritance mode and the prevalence of disease in the human population. The tSNP sets identified by our method are remarkably robust to changes in the disease model when small relative risk and additive mode of inheritance are employed. We have also evaluated the ability of the method to detect unidentified SNPs. Our findings have important implications in applying tSNPs from different data sources in association studies.     

Towards a reduction in publication bias.

Current practice results in the publication of many research studies in medical and related disciplines which may be criticised on the grounds of inadequate sample size and statistical power. Small studies continue to be carried out with little more than a blind hope of showing the desired effect. Nevertheless, papers based on such work are submitted for publication, especially if the results turn out to be statistically significant. There is confusion about what makes a result suitable for publication. Often there is a preference for statistically significant results at the peer review stage. Consequently published reports of small studies tend to contain too many false positive results and to exaggerate the true effects. The use of a criterion of a posteriori power does not eliminate the bias; a priori power is the criterion of choice. This could be implemented by peer review of study protocols at the planning stage by funding bodies and journals.     

Challenges and opportunities in synthesizing historical geospatial data using statistical models

We classified land cover types from 1940s historical aerial imagery using Object Based Image Analysis (OBIA) and compared these maps with data on recent cover. Few studies have used these kinds of maps to model drivers of cover change, partly due to two statistical challenges: 1) appropriately accounting for spatial autocorrelation and 2) appropriately modeling percent cover which is bounded between 0 and 100 and not normally distributed. We studied the change in woody cover at four sites in California's North Coast using historical (1948) and recent (2009) high spatial resolution imagery. We classified the imagery using eCognition Developer and aggregated the resulting maps to the scale of a Digital Elevation Model (DEM) in order to understand topographic drivers of woody cover change. We used Generalized Additive Models (GAMs) with a quasi-binomial probability distribution to account for spatial autocorrelation and the boundedness of the percent woody cover variable. We explored the relative influences on current percent woody cover of topographic variables (grouped using principal component analysis) reflecting water retention capacity, exposure, and within-site context, as well as historical percent woody cover and geographical coordinates. We estimated these models for pixel sizes of 20, 30, 40, 50, 60, 70, 80, 90, and 100 m, reflecting both tree neighborhood scales and stand scales. We found that historical woody cover had a consistent positive effect on current woody cover, and that the spatial autoregressive term in the model was significant even after controlling for historical cover. Specific topographic variables emerged as important for different sites at different scales, but no overall pattern emerged across sites or scales for any of the topographic variables we tested. This GAM framework for modeling historical data is flexible and could be used with more variables, more flexible relationships with predictor variables, and larger scales. Modeling drivers of woody cover change from historical ecology data sources can be a valuable way to plan restoration and enhance ecological insight into landscape change.     

Phylogenetic,spatial and environmental components of extinction risk in carnivores

Aim Extinction risk is non‐randomly distributed across phylogeny and space and is influenced by environmental conditions. We quantified the relative contribution of these factors to extinction risk to unveil the underlying macroecological processes and derive predictive models. Location Global. Methods Based on the IUCN global assessments, we divided 192 carnivore species into two dichotomous classes representing different levels of extinction risk. We used spatial proximity, phylogenetic relationship and environmental variables together with phylogenetic eigenvector regression and spatial eigenvector filters to model and predict threat status. Results Our full models explained between 57% and 96% of the variance in extinction risk. Phylogeny and spatial proximity roughly explained between 21% and 70% of the total variation in all analyses, while the explanatory power of environmental conditions was relatively weaker (up to 15%). Phylogeny and spatial proximity contributed equally to the explained variance in the lower threat level, while spatial proximity was the most important factor in the models of the higher threat level. Prediction of threat status achieved 97% correct assignments. Main conclusions Our approach differs fundamentally from current studies of extinction risk because it does not necessarily rely on life‐history information. We clearly show that instead of treating phylogenetic inertia and spatial signal as statistical nuisances, space and phylogeny should be viewed as very useful in explaining a wide range of phenomena in comparative studies.     

Environmental relationships of floristic variation in the alpine vegetation of southeast Australia

Abstract. Australian alpine vegetation is confined to the southeast of the continent and the island of Tasmania. It exhibits strong geographic patterns of floristic variation. These patterns have been attributed to variation in edaphic conditions resulting from geographic variation in substrate, climate and glacial history. This edaphic hypothesis is tested using floristic and environmental data from 166 quadrats distributed throughout the floristic and geographic range of Australian alpine vegetation. Environmental vector fitting in three-dimensional ordination space, the number of significant environmental differences between all pairs of 17 floristic groups and overall statistical analyses of the environmental differences between communities suggest a primacy of climatic variables over edaphic variables in explaining the broad patterns of floristic variation. Continentality, summer warmth, summer rainfall and winter cold all provide a better statistical explanation of floristic variation than the most explanatory of the edaphic variables, extractable P. The environmental variables that best discriminate the groups at each dichotomy of the divisive classification of the floristic data are largely climatic at the upper two levels, with edaphic, topographic and biotic variables being generally more important than climatic variables at the lower levels. Many of the edaphic variables that were most important in discriminating dichotomous groups were relatively insignificant in the broader analyses, suggesting that it is important to partition large data sets for environment/floristic analyses. The results of such partitioning show that the environmental factors most important in influencing floristic variation in alpine vegetation in Australia vary by location and geographic scale.     

Genetic linkage analysis of a dichotomous trait incorporating a tightly linked quantitative trait in affected sib pairs

Many complex diseases are usually considered as dichotomous traits but are also associated with quantitative biological markers or quantitative risk factors. For such dichotomous traits, although their associated quantitative traits may not directly underly the diagnosis of the disease status, if the associated quantitative trait is also linked to the chromosomal regions linked to the dichotomous trait, then joint analysis of dichotomous and quantitative traits should be more efficient than consideration of them separately. Previous studies have focused on the situation when a dichotomous trait can be modeled by a threshold process acting on a single underlying normal liability distribution. However, for many complex disorders, including most psychiatric disorders, diagnosis is generally based on a set of binary or discrete criteria. These traits cannot be modeled on the basis of a threshold process acting on an underlying continuous trait. We propose a likelihood-based method that efficiently combines such a discrete trait and an associated quantitative trait in the analysis, using affected-sib-pair data. Our simulation studies suggest that joint analysis increases the power to detect linkage of dichotomous traits. We also apply the proposed new method to an asthma genome-scan data set and incorporate the total serum immunoglobulin E level in the analysis.