Consolidated strategy for the analysis of microarray spike-in data

As the number of users of microarray technology continues to grow, so does the importance of platform assessments and comparisons. Spike-in experiments have been successfully used for internal technology assessments by microarray manufacturers and for comparisons of competing data analysis approaches. The microarray literature is saturated with statistical assessments based on spike-in experiment data. Unfortunately, the statistical assessments vary widely and are applicable only in specific cases. This has introduced confusion into the debate over best practices with regards to which platform, protocols and data analysis tools are best. Furthermore, cross-platform comparisons have proven difficult because reported concentrations are not comparable. In this article, we introduce two new spike-in experiments, present a novel statistical solution that enables cross-platform comparisons, and propose a comprehensive procedure for assessments based on spike-in experiments. The ideas are implemented in a user friendly Bioconductor package: spkTools. We demonstrated the utility of our tools by presenting the first spike-in-based comparison of the three major platforms–Affymetrix, Agilent and Illumina.     

Sample size for detecting differentially expressed genes in microarray experiments

Background  

Microarray experiments are often performed with a small number of biological replicates, resulting in low statistical power for detecting differentially expressed genes and concomitant high false positive rates. While increasing sample size can increase statistical power and decrease error rates, with too many samples, valuable resources are not used efficiently. The issue of how many replicates are required in a typical experimental system needs to be addressed. Of particular interest is the difference in required sample sizes for similar experiments in inbred vs. outbred populations (e.g. mouse and rat vs. human).     

Empirical characterization of the expression ratio noise structure in high-density oligonucleotide arrays

Background  

High-density oligonucleotide arrays (HDONAs) are a powerful tool for assessing differential mRNA expression levels. To establish the statistical significance of an observed change in expression, one must take into account the noise introduced by the enzymatic and hybridization steps, called type I noise. We undertake an empirical characterization of the experimental repeatability of results by carrying out statistical analysis of a large number of duplicate HDONA experiments.     

The design of in vivo multifraction experiments to estimate the alpha-beta ratio

Using statistical methods, the designs of multifraction experiments which are likely to give the most precise estimate of the alpha-beta ratio in the linear-quadratic model are investigated. The aim of the investigation is to try to understand what features of an experimental design make it efficient for estimating alpha/beta rather than to recommend a specific design. A plot of the design on an nd2 versus nd graph is suggested, and this graph is called the design plot. The best designs are those which have a large spread in the isoeffect direction in the design plot, which means that a wide range of doses per fraction should be used. For binary response assays, designs with expected response probabilities near to 0.5 are most efficient. Furthermore, dose points with expected response probabilities outside the range 0.1 to 0.9 contribute negligibly to the efficiency with which alpha/beta can be estimated. For "top-up" experiments, the best designs are those which replace as small a portion as possible of the full experiment with the top-up scheme. In addition, from a statistical viewpoint, it makes no difference whether a single large top-up dose or several smaller top-up doses are used; however, other considerations suggest that two or more top-up doses may be preferable. The practical realities of designing experiments as well as the somewhat idealized statistical considerations are discussed.     

The state of the art in the analysis of two-dimensional gel electrophoresis images

Software-based image analysis is a crucial step in the biological interpretation of two-dimensional gel electrophoresis experiments. Recent significant advances in image processing methods combined with powerful computing hardware have enabled the routine analysis of large experiments. We cover the process starting with the imaging of 2-D gels, quantitation of spots, creation of expression profiles to statistical expression analysis followed by the presentation of results. Challenges for analysis software as well as good practices are highlighted. We emphasize image warping and related methods that are able to overcome the difficulties that are due to varying migration positions of spots between gels. Spot detection, quantitation, normalization, and the creation of expression profiles are described in detail. The recent development of consensus spot patterns and complete expression profiles enables one to take full advantage of statistical methods for expression analysis that are well established for the analysis of DNA microarray experiments. We close with an overview of visualization and presentation methods (proteome maps) and current challenges in the field. An erratum to this article can be found at     

Statistical Analyses for Multistage Experiment Designs

Suppose that t experiments are conducted simultaneously on the same set of experimental units. For example, suppose that t mutually orthogonal latin square experiment designs are used for the t experiments on n² experimental units. Statistical literature is voluminous on construction of such designs, but contains relatively little and incomplete results on statistical analyses for such designs. Six statistical analyses are presented for a pair of orthogonal latin square experiment designs. Then, the methods are generalized for t mutually orthogonal experiment designs. The results are also extended to a set of t mutually balanced Youden experiment designs.     

Influence of protein structure databases on the predictive power of statistical pair potentials

A long standing goal in protein structure studies is the development of reliable energy functions that can be used both to verify protein models derived from experimental constraints as well as for theoretical protein folding and inverse folding computer experiments. In that respect, knowledge-based statistical pair potentials have attracted considerable interests recently mainly because they include the essential features of protein structures as well as solvent effects at a low computing cost. However, the basis on which statistical potentials are derived have been questioned. In this paper, we investigate statistical pair potentials derived from protein three-dimensional structures, addressing in particular questions related to the form of these potentials, as well as to the content of the database from which they are derived. We have shown that statistical pair potentials depend on the size of the proteins included in the database, and that this dependence can be reduced by considering only pairs of residue close in space (i.e., with a cutoff of 8 Å). We have shown also that statistical potentials carry a memory of the quality of the database in terms of the amount and diversity of secondary structure it contains. We find, for example, that potentials derived from a database containing α-proteins will only perform best on α-proteins in fold recognition computer experiments. We believe that this is an overall weakness of these potentials, which must be kept in mind when constructing a database. Proteins 31:139–149, 1998. © 1998 Wiley-Liss, Inc.     

Guidelines for the design and statistical analysis of experiments in papers submitted to ATLA

In vitro experiments need to be well designed and correctly analysed if they are to achieve their full potential to replace the use of animals in research. An "experiment" is a procedure for collecting scientific data in order to answer a hypothesis, or to provide material for generating new hypotheses, and differs from a survey because the scientist has control over the treatments that can be applied. Most experiments can be classified into one of a few formal designs, the most common being completely randomised, and randomised block designs. These are quite common with in vitro experiments, which are often replicated in time. Some experiments involve a single independent (treatment) variable, while other "factorial" designs simultaneously vary two or more independent variables, such as drug treatment and cell line. Factorial designs often provide additional information at little extra cost. Experiments need to be carefully planned to avoid bias, be powerful yet simple, provide for a valid statistical analysis and, in some cases, have a wide range of applicability. Virtually all experiments need some sort of statistical analysis in order to take account of biological variation among the experimental subjects. Parametric methods using the t test or analysis of variance are usually more powerful than non-parametric methods, provided the underlying assumptions of normality of the residuals and equal variances are approximately valid. The statistical analyses of data from a completely randomised design, and from a randomised-block design are demonstrated in Appendices 1 and 2, and methods of determining sample size are discussed in Appendix 3. Appendix 4 gives a checklist for authors submitting papers to ATLA.     

Optimal experimental design and sample size for the statistical evaluation of data from somatic mutation and recombination tests (SMART) in Drosophila

In genetic toxicology it is important to know whether chemicals should be regarded as clearly hazardous or whether they can be considered sufficiently safe, which latter would be the case from the genotoxicologist's view if their genotoxic effects are nil or at least significantly below a predefined minimal effect level. A previously presented statistical decision procedure which allows one to make precisely this distinction is now extended to the question of how optimal experimental sample size can be determined in advance for genotoxicity experiments using the somatic mutation and recombination tests (SMART) of Drosophila. Optimally, the statistical tests should have high power to minimise the chance for statistically inconclusive results. Based on the normal test, the statistical principles are explained, and in an application to the wing spot assay, it is shown how the practitioner can proceed to optimise sample size to achieve numerically satisfactory conditions for statistical testing. The somatic genotoxicity assays of Drosophila are in principle based on somatic spots (mutant clones) that are recovered in variable numbers on individual flies. The underlying frequency distributions are expected to be of the Poisson type. However, some care seems indicated with respect to this latter assumption, because pooling of data over individuals, sexes, and experiments, for example, can (but need not) lead to data which are overdispersed, i.e, the data may show more variability than theoretically expected. It is an undesired effect of overdispersion that in comparisons of pooled totals it can lead to statistical testing which is too liberal, because overall it yields too many seemingly significant results. If individual variability considered alone is not contradiction with Poisson expectation, however, experimental planning can help to minimise the undesired effects of overdispersion on statistical testing of pooled totals. The rule for the practice is to avoid disproportionate sampling. It is recalled that for optimal power in statistical testing, it is preferable to use equal total numbers of flies in the control and treated series. Statistical tests which are based on Poisson expectations are too liberal if there is overdispersion in the data due to excess individual variability. In this case we propose to use the U test as a non-parametric two-sample test and to adjust the estimated optimal sample size according to (i) the overdispersion observed in a large historical control and (ii) the relative efficiency of the U test in comparison to the t test and related parametric tests.     

Neuronal spike trains and stochastic point processes. I. The single spike train

In a growing class of neurophysiological experiments, the train of impulses (“spikes”) produced by a nerve cell is subjected to statistical treatment involving the time intervals between spikes. The statistical techniques available for the analysis of single spike trains are described and related to the underlying mathematical theory, that of stochastic point processes, i.e., of stochastic processes whose realizations may be described as series of point events occurring in time, separated by random intervals. For single stationary spike trains, several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order of interspike intervals and those that are order-independent. The interrelations among the several types of calculations are shown, and an attempt is made to ameliorate the current nomenclatural confusion in this field. Applications, interpretations, and potential difficulties of the statistical techniques are discussed, with special reference to types of spike trains encountered experimentally. Next, the related types of analysis are described for experiments which involve repeated presentations of a brief, isolated stimulus. Finally, the effects of nonstationarity, e.g. long-term changes in firing rate, on the various statistical measures are discussed. Several commonly observed patterns of spike activity are shown to be differentially sensitive to such changes. A companion paper covers the analysis of simultaneously observed spike trains.     

Statistical analysis of insect preference in two-choice experiments

Many studies of insect behavior in relation to chemicals from different plants require the use of statistical tests for determining whether attraction, repulsion, or neutrality is significant. In this paper, we propose a simple and efficient nonparametric statistical procedure for testing hypotheses about insect preference in two-choice experiments with individual insects. Three criteria are provided in order to detect the following alternatives to neutrality: (i) general attraction (or repulsion) in a sample population, (ii) strong variability of the individual responses, and (iii) slight but similar behavioral effects. Illustrations are given from two-choice experiments concerning the European corn borer (Ostrinia nubilalisHbn.) female's oviposition behavior.     

The role of the statistician in the Scottish Agricultural and Biological Research Institutes

Several of the Scottish Agricultural and Biological Research Institutes carry out research on domestic animal health and welfare. Statistical services are provided by Biomathematics & Statistics Scotland, a sister research organisation. At one of these institutes, a statistician has been an integral member of the animal experiments and ethics committee for over 10 years, and each animal experiment is examined by the committee statistician as part of the review process. This paper will describe this review process, and then discuss those areas in which statistical advice has had most impact in the reduction of animal numbers. It is suggested that most benefit does not come from simple sample-size calculations, but rather from the application of the principles of good experimental design and close collaboration between the scientist and the statistician in the design and analysis of experiments. The final conclusion is that scientists welcome constructive, long-term statistical input, although budgetary issues can prove to be a barrier.     

An evaluation of Salmonella (Ames) test data in the published literature: application of statistical procedures and analysis of mutagenic potency

We searched the published literature for Salmonella test data on some 450 chemicals. Only 137 of more than 400 articles containing original data satisfied minimum criteria for a quantitative analysis [1751 experiments, comprising data on 152 chemicals (Table 1)]. Many of these papers did not report basic information about the test protocol (Table 2). We used previously described statistical procedures (Bernstein et al., 1982) to estimate the initial slopes of the dose-response curves and corresponding standard errors. We also applied tests for significance and linear goodness-of-fit. We then used the results of these analyses to examine several issues: (1) Linearity of the low dose region of the dose-response curve. We found that the overwhelming majority of curves were linear, though ability to detect non-linearity of dose-response curves in the standard plate test is only limited. 7% of all experiments to which the goodness-of-fit test was applied were curves of increasing slope, and with a few possible exceptions, these were not obviously associated with any particular mutagens, even those generally considered to produce non-linear effects such as MNNG and EMS (Table 3). (2) Performance of the statistical test for significance. Results of the statistical test for significance of the dose-response were compared with author's opinions as to positivity. In almost all cases (94%) results of the statistical test and authors opinions were the same. In the examples of conflicting opinions, the reasons were: (a) the statistical test places more weight than do most authors on the presence of a linear dose-response; (b) most authors tend to require at least a 2-fold increase over the spontaneous background for 'significance', and (c) when the number of spontaneous revertants is small (e.g., TA1537), authors tend to require a larger increase in induced revertants than when the spontaneous background is large, whereas the statistical procedure makes no such distinction. These factors result in the statistical test tending to identify more experiments as positive than do authors, provided there is a linear dose-response, and authors tending to judge more experiments as positive when the dose-response is not linear. (3) Reproducibility. Among the 1751 experiments there were 122 data-sets (a total of 333 experiments) in which the same chemical was tested by two or more different laboratories under the same protocol. 21 of the 122 data-sets had some disagreement between experiments as to whether results were positive or negative (Table 4).(ABSTRACT TRUNCATED AT 400 WORDS)     

Meta-analysis of gene expression microarrays with missing replicates

Background  

Many different microarray experiments are publicly available today. It is natural to ask whether different experiments for the same phenotypic conditions can be combined using meta-analysis, in order to increase the overall sample size. However, some genes are not measured in all experiments, hence they cannot be included or their statistical significance cannot be appropriately estimated in traditional meta-analysis. Nonetheless, these genes, which we refer to as incomplete genes, may also be informative and useful.     

Quantifying the role of steric constraints in nucleosome positioning

Statistical positioning, the localization of nucleosomes packed against a fixed barrier, is conjectured to explain the array of well-positioned nucleosomes at the 5′ end of genes, but the extent and precise implications of statistical positioning in vivo are unclear. We examine this hypothesis quantitatively and generalize the idea to include moving barriers as well as nucleosomes actively packed against a barrier. Early experiments noted a similarity between the nucleosome profile aligned and averaged across genes and that predicted by statistical positioning; however, we demonstrate that aligning random nucleosomes also generates the same profile, calling the previous interpretation into question. New rigorous results reformulate statistical positioning as predictions on the variance structure of nucleosome locations in individual genes. In particular, a quantity termed the variance gradient, describing the change in variance between adjacent nucleosomes, is tested against recent high-throughput nucleosome sequencing data. Constant variance gradients provide support for generalized statistical positioning in ∼50% of long genes. Genes that deviate from predictions have high nucleosome turnover and cell-to-cell gene expression variability. The observed variance gradient suggests an effective nucleosome size of 158 bp, instead of the commonly perceived 147 bp. Our analyses thus clarify the role of statistical positioning in vivo.     

Sample size determination for the false discovery rate

MOTIVATION: There is not a widely applicable method to determine the sample size for experiments basing statistical significance on the false discovery rate (FDR). RESULTS: We propose and develop the anticipated FDR (aFDR) as a conceptual tool for determining sample size. We derive mathematical expressions for the aFDR and anticipated average statistical power. These expressions are used to develop a general algorithm to determine sample size. We provide specific details on how to implement the algorithm for a k-group (k > or = 2) comparisons. The algorithm performs well for k-group comparisons in a series of traditional simulations and in a real-data simulation conducted by resampling from a large, publicly available dataset. AVAILABILITY: Documented S-plus and R code libraries are freely available from www.stjuderesearch.org/depts/biostats.     

An image analysis and statistical evaluation program for the assessment of tumour cell invasion in vitro.

Tumour cell invasion is a complex process, which is essential for the formation of metastasis and is therefore of critical clinical importance. For detailed investigations of the invasive process, quantifiable in vitro models of invasion are necessary. In this study we describe an image analysis procedure and a statistical program which facilitate an objective analysis of experiments carried out using the embryonic chick heart invasion model of Mareel. Tumour multicellular spheroids are confronted with embryonic chick heart fragments in culture and are sampled after different time intervals for up to 7 days. Immunohistological sections are then evaluated by an image analysis procedure which provides 9 parameters indicating invasion, proliferation and destruction taking place in the confrontation cultures. The data obtained by image analysis are further evaluated by a statistical program which describes the change with time of each parameter by means of linear regression analysis. Thus the data obtained at various time intervals serve as the source data for a single statistic, namely the slope of the regression line. Confidence intervals and statistical differences between various experiments can be calculated. In order to make the procedure more comprehensible in biological terms, the program provides a full text interpretation of the experimental results. The image analysis procedure in conjunction with statistical evaluation and text interpretation provides a comprehensive tool for the quantitative assessment of experimental invasion in vitro.     

Detachment,displacement and reattachment activity in a freshwater byssate mussel (Limnoperna fortunei): the effects of light,temperature and substratum orientation

The ability of the freshwater bivalve Limnoperna fortunei to voluntarily detach from the substratum, crawl and reattach as a function of illumination, temperature, substratum orientation, and mussel size was investigated. Thirty-two per cent of the 879 experimental animals detached and reattached elsewhere at least once during five- to eight-day experiments. The proportions of mobile mussels were significantly higher in permanent darkness than under permanent illumination. Displacement distances were also higher in darkness, but statistical differences with illuminated individuals were inconclusive. No evidence of circadian rhythms was detected. Mobile mussels were often significantly smaller than non-mobile individuals. It was not possible to detect the effect of water temperature (22°C and 31°C), or substratum orientation (topside and underside) on mussel mobility, but because the power of the statistical tests was low, future experiments are needed to confirm this result. The ability of mussels to voluntarily detach and reattach elsewhere has important implications for biofouling control.