Volume 2, Issue 1

We describe the use of a statistical model in a genome-wide microarray-based yeast genetic screen performed by imposing different genetic selections on thousands of yeast mutants in parallel. A mixture model is fitted to data obtained from oligonucleotide arrays hybridized to 20-mer oligonucleotide ``barcodes'' and a procedure based on the fitted model is used to search for mutants differentially represented under experimental and control conditions. The fitted stochastic model provides a way to assess uncertainty. We demonstrate the usefulness of the model by applying it to the problem of screening for components of the nonhomologous end joining (NHEJ) pathway and identified known components of the NHEJ pathway.

Usually, a pedigree is sampled and included in the sample that is analyzed after following a predefined non-random sampling design comprising several specific procedures. To obtain a pedigree analysis result free from the bias caused by the sampling procedures, a correction is applied to the pedigree likelihood. The sampling procedures usually considered are: the pedigree ascertainment, determining whether a population unit is to be sampled; the intrafamilial pedigree extension, determining what part of the pedigree is to be sampled; and selective censoring of the sampled pedigree, determining whether it should be included in the sample to be analyzed.The probability of pedigree ascertainment is determined by the total set of potential probands in the true pedigree from which the sampled pedigree is obtained and we indicate how the necessary information on this set can be collected. If insufficient information on this set is observed, it is impossible to correct the pedigree likelihood adequately. Here we show that, if only the structure of this set is known, then an ascertainment-model-based pedigree likelihood can be obtained by conditioning on this structure. An ascertainment-model-free (AMF) pedigree likelihood can be correctly constructed by conditioning on all the data in this set, i.e. on both its structure and its phenotypic content. However, if this set has missing data, the AMF likelihood becomes undefined, which limits the utility of this AMF approach originally proposed by Ewens and Shute (1986). We also consider the sampling correction necessary when the pedigrees included in the sample analyzed have been subjected to censoring. The forms of likelihood correction developed here provide asymptotically unbiased estimators of the genetic model only if the formulated model is correct, which means that it must correctly allow for the most important features of the true inheritance of the trait studied. Otherwise, if no special case of the formulated general model is close to the true inheritance model, then the forms of likelihood correction proposed here result in biases, the magnitude and direction of which depend on both the true model and the general analysis model that should subsume it.

We derive and validate an estimator for the parameters of a transformation for the joint calibration (normalization) and variance stabilization of microarray intensity data. With this, the variances of the transformed intensities become approximately independent of their expected values. The transformation is similar to the logarithm in the high intensity range, but has a smaller slope for intensities close to zero. Applications have shown better sensitivity and specificity for the detection of differentially expressed genes. In this paper, we describe the theoretical aspects of the method. We incorporate calibration and variance-mean dependence into a statistical model and use a robust variant of the maximum-likelihood method to estimate the transformation parameters. Using simulations, we investigate the size of the estimation error and its dependence on sample size and the presence of outliers. We find that the error decreases with the square root of the number of probes per array and that the estimation is robust against the presence of differentially expressed genes. Software is publicly available as an R package through the Bioconductor project (http://www.bioconductor.org).

Two channel microarray data often contain systematic variations that can be minimized by data transformation prior to further analysis. The most commonly observed effects are revealed by viewing scatter plots of the logarithm of the ratio by the average logarithmic intensity of the two color channels (RI plots). In this paper we present a general model for signal intensity data with multiple error sources. We demonstrate how these sources of error influence the shape of an RI plot. We then compare some currently available transformation strategies in terms of their mechanism and performance on both simulated and real microarray data. A linlog transformation is proposed to stabilize the variance of the log ratios. We also propose a regional smoothing method to remove variation in log ratios due to spatial heterogeneity on the microarray surface. The discussed transformations represent an important initial step in microarray data analysis for both ratio-based and ANOVA methods.

Identification of transcription factor binding sites (regulatory motifs) is a major interest in contemporary biology. We propose a new likelihood based method, COMODE, for identifying structural motifs in DNA sequences. Commonly used methods (e.g. MEME, Gibbs motif sampler) model binding sites as families of sequences described by a position weight matrix (PWM) and identify PWMs that maximize the likelihood of observed sequence data under a simple multinomial mixture model. This model assumes that the positions of the PWM correspond to independent multinomial distributions with four cell probabilities. We address supervising the search for DNA binding sites using the information derived from structural characteristics of protein-DNA interactions. We extend the simple multinomial mixture model to a constrained multinomial mixture model by incorporating constraints on the information content profiles or on specific parameters of the motif PWMs. The parameters of this extended model are estimated by maximum likelihood using a nonlinear constraint optimization method. Likelihood-based cross-validation is used to select model parameters such as motif width and constraint type. The performance of COMODE is compared with existing motif detection methods on simulated data that incorporate real motif examples from Saccharomyces cerevisiae. The proposed method is especially effective when the motif of interest appears as a weak signal in the data. Some of the transcription factor binding data of Lee et al. (2002) were also analyzed using COMODE and biologically verified sites were identified.

Visualisation methods for exploring microarray data are particularly important for gaining insight into data from gene expression experiments, such as those concerned with the development of an understanding of gene function and interactions. Further, good visualisation techniques are useful for outlier detection in microarray data and for aiding biological interpretation of results, as well as for presentation of overall summaries of the data. The biplot is particularly useful for the display of microarray data as both the genes and the chips can be simultaneously plotted. In this paper we describe several ordination techniques suitable for exploring microarray data, and we call these the GE-biplot, the Chip-plot and the Gene-plot. The general method is first evaluated on synthetic data simulated in accord with current biological interpretation of microarray data. Then it is applied to two well-known data sets, namely the colon data of Alon et al. (1999) and the leukaemia data of Golub et al. (1999). The usefulness of the approach for interpreting and comparing different analyses of the same data is demonstrated.

Transcription factor binding site (TFBS) detection plays an important role in computational biology, with applications in gene finding and gene regulation. The sites are often modeled by gapless profiles, also known as position-weight matrices. Past research has focused on the significance of profile scores (the ability to avoid false positives), but this alone is not enough: The profile must also possess the power to detect the true positive signals. Several completed genomes are now available, and the search for TFBSs is moving to a large scale; so discriminating signal from noise becomes even more challenging.Since TFBS profiles are usually estimated from only a few experimentally confirmed instances, careful regularization is an important issue. We present a novel method that is well suited for this situation.We further develop measures that help in judging profile quality, based on both sensitivity and selectivity of a profile. It is shown that these quality measures can be efficiently computed, and we propose statistically well-founded methods to choose score thresholds.Our findings are applied to the TRANSFAC database of transcription factor binding sites. The results are disturbing: If we insist on a significance level of 5% in sequences of length 500, only 19% of the profiles detect a true signal instance with 95% success probability under varying background sequence compositions.

Gene expression microarrays have become powerful tools in many areas of biological and biomedical research. These technologies allow researchers to measure the expression levels of thousands of genes in a tissue or cell sample simultaneously. One of the most common types of microarray experiments is simply an exploratory study to compare two samples (e.g. tumor and normal tissue) and look for a list of genes that might be differentially expressed between the two. Differential expression is typically measured by computing a t-statistic or similar statistic for each gene. The genes are then ranked according to the absolute value of the t-statistic, and the twenty or fifty best candidates might be studied in follow-up experiments. When sample sizes are small, the t-statistic can be problematic, because variances are estimated poorly and the "top 20" list is often dominated by the genes with the lowest variance estimates. Lönnstedt and Speed (2001) proposed an empirical Bayes method for avoiding this problem, and showed that their approach has lower false positive and false negative rates than t-statistic-based methods. However, their method was designed mainly for the two-channel microarray, which produces paired data. It is not suitable for technologies such as one-channel arrays that produce unpaired data. We propose a simplification for Lönnstedt and Speed's method, and then extend it to unpaired data with two or more independent treatments. We demonstrate our method on both simulated and real data. When the number of replicates is small, gene rankings based on our statistic appear to be much more reliable than rankings based on the t-statistic.