An experimental evaluation of a loop versus a reference design for two-channel microarrays

MOTIVATION: Despite theoretical arguments that so-called 'loop designs' for two-channel DNA microarray experiments are more efficient, biologists continue to use 'reference designs'. We describe two sets of microarray experiments with RNA from two different biological systems (TPA-stimulated mammalian cells and Streptomyces coelicolor). In each case, both a loop and a reference design were used with the same RNA preparations with the aim of studying their relative efficiency. RESULTS: The results of these experiments show that (1) the loop design attains a much higher precision than the reference design, (2) multiplicative spot effects are a large source of variability, and if they are not accounted for in the mathematical model, for example, by taking log-ratios or including spot effects, then the model will perform poorly. The first result is reinforced by a simulation study. Practical recommendations are given on how simple loop designs can be extended to more realistic experimental designs and how standard statistical methods allow the experimentalist to use and interpret the results from loop designs in practice. AVAILABILITY: The data and R code are available at http://exgen.ma.umist.ac.uk CONTACT: veronica.vinciotti@brunel.ac.uk.     

Comparison of microarray designs for class comparison and class discovery

MOTIVATION: Two-color microarray experiments in which an aliquot derived from a common RNA sample is placed on each array are called reference designs. Traditionally, microarray experiments have used reference designs, but designs without a reference have recently been proposed as alternatives. RESULTS: We develop a statistical model that distinguishes the different levels of variation typically present in cancer data, including biological variation among RNA samples, experimental error and variation attributable to phenotype. Within the context of this model, we examine the reference design and two designs which do not use a reference, the balanced block design and the loop design, focusing particularly on efficiency of estimates and the performance of cluster analysis. We calculate the relative efficiency of designs when there are a fixed number of arrays available, and when there are a fixed number of samples available. Monte Carlo simulation is used to compare the designs when the objective is class discovery based on cluster analysis of the samples. The number of discrepancies between the estimated clusters and the true clusters were significantly smaller for the reference design than for the loop design. The efficiency of the reference design relative to the loop and block designs depends on the relation between inter- and intra-sample variance. These results suggest that if cluster analysis is a major goal of the experiment, then a reference design is preferable. If identification of differentially expressed genes is the main concern, then design selection may involve a consideration of several factors.     

Design of Large Time-Course Microarray Experiments with Two Channels

In this article we propose two practical types of designs for large time-course, dual-channel microarray experiments. One type consists of several interwoven loops, and the other type combines reference and loop designs. By representing the experiment as a graph, where the timepoints are nodes and the arrays are edges, we demonstrate how the time contrasts between any two timepoints can be estimated, provided that there is a path of edges linking them. In addition, we give a general formula for the variance of such contrasts. The efficiency of the proposed designs is evaluated by estimating the variances of the log-ratios of the comparisons of interest.     

CASCADE: a novel quasi all paths-based network analysis algorithm for clustering biological interactions

Background

As an alternative to the frequently used "reference design" for two-channel microarrays, other designs have been proposed. These designs have been shown to be more profitable from a theoretical point of view (more replicates of the conditions of interest for the same number of arrays). However, the interpretation of the measurements is less straightforward and a reconstruction method is needed to convert the observed ratios into the genuine profile of interest (e.g. a time profile). The potential advantages of using these alternative designs thus largely depend on the success of the profile reconstruction. Therefore, we compared to what extent different linear models agree with each other in reconstructing expression ratios and corresponding time profiles from a complex design.

Results

On average the correlation between the estimated ratios was high, and all methods agreed with each other in predicting the same profile, especially for genes of which the expression profile showed a large variance across the different time points. Assessing the similarity in profile shape, it appears that, the more similar the underlying principles of the methods (model and input data), the more similar their results. Methods with a dye effect seemed more robust against array failure. The influence of a different normalization was not drastic and independent of the method used.

Conclusion

Including a dye effect such as in the methods lmbr_dye, anovaFix and anovaMix compensates for residual dye related inconsistencies in the data and renders the results more robust against array failure. Including random effects requires more parameters to be estimated and is only advised when a design is used with a sufficient number of replicates. Because of this, we believe lmbr_dye, anovaFix and anovaMix are most appropriate for practical use.     

Normalization of two-channel microarrays accounting for experimental design and intensity-dependent relationships

In normalizing two-channel expression arrays, the ANOVA approach explicitly incorporates the experimental design in its model, and the MA plot-based approach accounts for intensity-dependent biases. However, both approaches can lead to inaccurate normalization in fairly common scenarios. We propose a method called efficient Common Array Dye Swap (eCADS) for normalizing two-channel microarrays that accounts for both experimental design and intensity-dependent biases. Under reasonable experimental designs, eCADS preserves differential expression relationships and requires only a single array per sample pair.     

Statistical design of reverse dye microarrays

MOTIVATION: In cDNA microarray experiments all samples are labelled with either Cy3 dye or Cy5 dye. Certain genes exhibit dye bias-a tendency to bind more efficiently to one of the dyes. The common reference design avoids the problem of dye bias by running all arrays 'forward', so that the samples being compared are always labelled with the same dye. But comparison of samples labelled with different dyes is sometimes of interest. In these situations, it is necessary to run some arrays 'reverse'-with the dye labelling reversed-in order to correct for the dye bias. The design of these experiments will impact one's ability to identify genes that are differentially expressed in different tissues or conditions. We address the design issue of how many specimens are needed, how many forward and reverse labelled arrays to perform, and how to optimally assign Cy3 and Cy5 labels to the specimens. RESULTS: We consider three types of experiments for which some reverse labelling is needed: paired samples, samples from two predefined groups, and reference design data when comparison with the reference is of interest. We present simple probability models for the data, derive optimal estimators for relative gene expression, and compare the efficiency of the estimators for a range of designs. In each case, we present the optimal design and sample size formulas. We show that reverse labelling of individual arrays is generally not required.     

Fractional simplex designs for interaction screening in complex mixtures

In mixture experiments, one may be interested in estimating not only main effects but also some interactions. Main effects and significant interactions in a mixture may be estimated through appropriate mixture experiments, such as simplex-centroid designs. However, for mixtures with a large number of factors, the run size for these designs becomes impractically large. A subset of a full simplex-centroid design may be used, but the problem remains regarding which factor-level settings should be selected. In this paper, we propose a solution that considers design points with either one or p individual nonzero factor-level settings. These fractional simplex designs provide a means of screening for interactions and of investigating the behavior of many-component mixtures as a whole while greatly reducing the run size compared with full simplex-centroid designs. The means of construction of the design arrays is described, and designs for < or = 31 factors are presented. Some of the proposed methodology is illustrated using generated data.     

Factorial and time course designs for cDNA microarray experiments

Microarrays are powerful tools for surveying the expression levels of many thousands of genes simultaneously. They belong to the new genomics technologies which have important applications in the biological, agricultural and pharmaceutical sciences. There are myriad sources of uncertainty in microarray experiments, and rigorous experimental design is essential for fully realizing the potential of these valuable resources. Two questions frequently asked by biologists on the brink of conducting cDNA or two-colour, spotted microarray experiments are 'Which mRNA samples should be competitively hybridized together on the same slide?' and 'How many times should each slide be replicated?' Early experience has shown that whilst the field of classical experimental design has much to offer this emerging multi-disciplinary area, new approaches which accommodate features specific to the microarray context are needed. In this paper, we propose optimal designs for factorial and time course experiments, which are special designs arising quite frequently in microarray experimentation. Our criterion for optimality is statistical efficiency based on a new notion of admissible designs; our approach enables efficient designs to be selected subject to the information available on the effects of most interest to biologists, the number of arrays available for the experiment, and other resource or practical constraints, including limitations on the amount of mRNA probe. We show that our designs are superior to both the popular reference designs, which are highly inefficient, and to designs incorporating all possible direct pairwise comparisons. Moreover, our proposed designs represent a substantial practical improvement over classical experimental designs which work in terms of standard interactions and main effects. The latter do not provide a basis for meaningful inference on the effects of most interest to biologists, nor make the most efficient use of valuable and limited resources.     

An experimental loop design for the detection of constitutional chromosomal aberrations by array CGH

Background  

Comparative genomic hybridization microarrays for the detection of constitutional chromosomal aberrations is the application of microarray technology coming fastest into routine clinical application. Through genotype-phenotype association, it is also an important technique towards the discovery of disease causing genes and genomewide functional annotation in human. When using a two-channel microarray of genomic DNA probes for array CGH, the basic setup consists in hybridizing a patient against a normal reference sample. Two major disadvantages of this setup are (1) the use of half of the resources to measure a (little informative) reference sample and (2) the possibility that deviating signals are caused by benign copy number variation in the "normal" reference instead of a patient aberration. Instead, we apply an experimental loop design that compares three patients in three hybridizations.     

Symmetrical decorations enhance the attractiveness of faces and abstract designs

In humans and several other species, face and body symmetry have been found to enhance physical attractiveness. A proposed explanation is that symmetry is a phenotypic indicator of biological fitness. Throughout the world, symmetrical designs also are a common feature in face and body painting and the decorative arts. The implication is that symmetrical designs might provide an additional way to enhance physical attractiveness. To find out, we conducted three experiments, two with human faces and one with abstract or nonrepresentational designs. In Experiments 1 and 2, we showed undergraduate students photographs of pairs of faces and instructed them to choose the more attractive face in each pair. The photographs were of physically symmetrical and asymmetrical faces (as indexed by facial features) that had been decorated with either symmetrical or asymmetrical designs of the kind used in many preindustrial societies. As indexed by the number of times they were chosen, symmetrical faces were judged to be more attractive than asymmetrical faces; adding asymmetrical designs to symmetrical faces decreased their attractiveness; and adding symmetrical designs to asymmetrical faces increased their attractiveness. In Experiment 3, undergraduates made similar choices from pairs of abstract designs taken from several cultures and modified in shape, coloration, and orientation of design features. Symmetrical designs again were judged to be more attractive, with shape and coloration playing the more important roles. We interpret the results as suggesting that the same mechanisms underlying the judgment of physical attractiveness also underlie cultural practices of face painting and abstract art.     

Effect of pooling samples on the efficiency of comparative studies using microarrays

MOTIVATION: Many biomedical experiments are carried out by pooling individual biological samples. However, pooling samples can potentially hide biological variance and give false confidence concerning the data significance. In the context of microarray experiments for detecting differentially expressed genes, recent publications have addressed the problem of the efficiency of sample pooling, and some approximate formulas were provided for the power and sample size calculations. It is desirable to have exact formulas for these calculations and have the approximate results checked against the exact ones. We show that the difference between the approximate and the exact results can be large. RESULTS: In this study, we have characterized quantitatively the effect of pooling samples on the efficiency of microarray experiments for the detection of differential gene expression between two classes. We present exact formulas for calculating the power of microarray experimental designs involving sample pooling and technical replications. The formulas can be used to determine the total number of arrays and biological subjects required in an experiment to achieve the desired power at a given significance level. The conditions under which pooled design becomes preferable to non-pooled design can then be derived given the unit cost associated with a microarray and that with a biological subject. This paper thus serves to provide guidance on sample pooling and cost-effectiveness. The formulation in this paper is outlined in the context of performing microarray comparative studies, but its applicability is not limited to microarray experiments. It is also applicable to a wide range of biomedical comparative studies where sample pooling may be involved.     

ILOOP – a web application for two-channel microarray interwoven loop design

Microarray technology is widely applied to address complex scientific questions. However, there remain fundamental issues on how to design experiments to ensure that the resulting data enables robust statistical analysis. Interwoven loop design has several advantages over other designs. However it suffers in the complexity of design. We have implemented an online web application which allows users to find optimal loop designs for two-color microarray experiments. Given a number of conditions (such as treatments or time points) and replicates, the application will find the best possible design of the experiment and output experimental parameters. It is freely available from http://mcbc.usm.edu/iloop.     

Nonparametric Methods in Crossover Trials

The crossover design is often used in biomedical trials since it eliminates between subject variability. This paper is concerned with the statistical analysis of data arising from such trials when assumptions like normality do not necessarily apply. Nonparametric analysis of the two-period, two-treatment design was first described by Koch in a paper 1972. The purpose of this paper is to study nonparametric methods in crossover designs with three or more treatments and an equal number of periods. The proposed test for direct treatment effects is based on within subject comparisons after removing a possible period effect. With only two treatments this test reduces to the twosided Wilcoxon signed rank test. By simulation experiments the validity of the significance level of the test when using the asymptotic distribution of the test statistic are manifested and the power against different alternatives illustrated. A test for first order carryover effects can be constructed by a straightforward generalization of the test proposed by Koch in 1972. However, since this test is based on between subject comparisons its power will be low. Our recommendation is to consider the crossover design rather than the parallel group design if the carryover effects are assumed to be neglible or positive and smaller then the direct treatment effects.     

Dose and litter allocations in the design of teratological studies for detecting hormesis

BACKGROUND: Hormesis is being recognized in the field of toxicology due to the stimulating effects of some toxic compounds at low exposure levels. Therefore, it is desirable that experimental designs for toxicological studies be flexible enough to aid in the detection of hormetic effects. Current designs may still not have enough power to do this. METHODS: A simulation study was conducted to determine teratological study designs that would yield more power over standard designs in detecting hormesis. Developmental toxicity endpoints of interest are the number of dead/resorbed or malformed fetuses in a litter. The simulation designs mimic teratological experiments in terms of sample size and number of dose levels. Modified designs with even dose spacing at low levels and reallocated litters are investigated to determine the power of hormetic detection. RESULTS: Designs with reallocated litters (with more litters at low exposure levels than at high levels) and even dose spacing have more power than those with equal litters per group and uneven dose spacing. CONCLUSIONS: Through appropriate modifications of current experimental designs, such as reallocation of litters and even dose spacing, we can better detect hormetic effects.     

Current issues for DNA microarrays: platform comparison, double linear amplification, and universal RNA reference

DNA microarray technology has been widely used to simultaneously determine the expression levels of thousands of genes. A variety of approaches have been used, both in the implementation of this technology and in the analysis of the large amount of expression data. However, several practical issues still have not been resolved in a satisfactory manner, and among the most critical is the lack of agreement in the results obtained in different array platforms. In this study, we present a comparison of several microarray platforms [Affymetrix oligonucleotide arrays, custom complementary DNA (cDNA) arrays, and custom oligo arrays printed with oligonucleotides from three different sources] as well as analysis of various methods used for microarray target preparation and the reference design. The results indicate that the pairwise correlations of expression levels between platforms are relative low overall but that the log ratios of the highly expressed genes are strongly correlated, especially between Affymetrix and cDNA arrays. The microarray measurements were compared with quantitative real-time-polymerase chain reaction (QRT-PCR) results for 23 genes, and the varying degrees of agreement for each platform were characterized. We have also developed and tested a double amplification method which allows the use of smaller amounts of starting material. The added round of amplification produced reproducible results as compared to the arrays hybridized with single round amplified targets. Finally, the reliability of using a universal RNA reference for two-channel microarrays was tested and the results suggest that comparisons of multiple experimental conditions using the same control can be accurate.     

Optimal response-adaptive designs for continuous responses in phase III trials

Optimal response-adaptive designs in phase III clinical trial set up are gaining more interest. Most of the available designs are not based on any optimal consideration. An optimal design for binary responses is given by Rosenberger et al. (2001) and one for continuous responses is provided by Biswas and Mandal (2004). Recently, Zhang and Rosenberger (2006) proposed another design for normal responses. This paper illustrates that the Zhang and Rosenberger (2006) design is not suitable for normally distributed responses, in general. The approach cannot be extended for other continuous response cases, such as exponential or gamma. In this paper, we first describe when the optimal design of Zhang and Rosenberger (2006) fails. We then suggest the appropriate adjustments for designs in different continuous distributions. A unified framework to find optimal response-adaptive designs for two competing treatments is proposed. The proposed methods are illustrated using some real data.     

Missing channels in two-colour microarray experiments: Combining single-channel and two-channel data

Background  

There are mechanisms, notably ozone degradation, that can damage a single channel of two-channel microarray experiments. Resulting analyses therefore often choose between the unacceptable inclusion of poor quality data or the unpalatable exclusion of some (possibly a lot of) good quality data along with the bad. Two such approaches would be a single channel analysis using some of the data from all of the arrays, and an analysis of all of the data, but only from unaffected arrays. In this paper we examine a 'combined' approach to the analysis of such affected experiments that uses all of the unaffected data.     

Construction of Lattice Square Designs

Khare and Federer (1981) presented a simple method for constructing incomplete block designs for any number of treatments. Their procedure is extended to constructing lattice square designs. Using variety cutting, lattice square designs are available for any number of treatments.     

Replication, Variation and Normalisation in Microarray Experiments

INTRODUCTION: Microarray experiments often have complex designs that include sample pooling, biological and technical replication, sample pairing and dye-swapping. This article demonstrates how statistical modelling can illuminate issues in the design and analysis of microarray experiments, and this information can then be used to plan effective studies. METHODS: A very detailed statistical model for microarray data is introduced, to show the possible sources of variation that are present in even the simplest microarray experiments. Based on this model, the efficacy of common experimental designs, normalisation methodologies and analyses is determined. RESULTS: When the cost of the arrays is high compared with the cost of samples, sample pooling and spot replication are shown to be efficient variance reduction methods, whereas technical replication of whole arrays is demonstrated to be very inefficient. Dye-swap designs can use biological replicates rather than technical replicates to improve efficiency and simplify analysis. When the cost of samples is high and technical variation is a major portion of the error, technical replication can be cost effective. Normalisation by centreing on a small number of spots may reduce array effects, but can introduce considerable variation in the results. Centreing using the bulk of spots on the array is less variable. Similarly, normalisation methods based on regression methods can introduce variability. Except for normalisation methods based on spiking controls, all normalisation requires that most genes do not differentially express. Methods based on spatial location and/or intensity also require that the nondifferentially expressing genes are at random with respect to location and intensity. Spotting designs should be carefully done so that spot replicates are widely spaced on the array, and genes with similar expression patterns are not clustered. DISCUSSION: The tools for statistical design of experiments can be applied to microarray experiments to improve both efficiency and validity of the studies. Given the high cost of microarray experiments, the benefits of statistical input prior to running the experiment cannot be over-emphasised.