Biomedical subjects

Somnath Datta

Publications and source records attributed to Somnath Datta.

11 recordsLinked to original sources

PubMed2006

Evaluation of clustering algorithms for gene expression data.

BACKGROUND: Cluster analysis is an integral part of high dimensional data analysis. In the context of large scale gene expression data, a filtered set of genes are grouped together according to their expression profiles using one of numerous clustering algorithms that exist in the statistics and machine learning literature. A closely related problem is that of selecting a clustering algorithm that is "optimal" in some sense from a rather impressive list of clustering algorithms that currently exist. RESULTS: In this paper, we propose two validation measures each with two parts: one measuring the statistical consistency (stability) of the clusters produced and the other representing their biological functional congruence. Smaller values of these indices indicate better performance for a clustering algorithm. We illustrate this approach using two case studies with publicly available gene expression data sets: one involving a SAGE data of breast cancer patients and the other involving a time course cDNA microarray data on yeast. Six well known clustering algorithms UPGMA, K-Means, Diana, Fanny, Model-Based and SOM were evaluated. CONCLUSION: No single clustering algorithm may be best suited for clustering genes into functional groups via expression profiles for all data sets. The validation measures introduced in this paper can aid in the selection of an optimal algorithm, for a given data set, from a collection of available clustering algorithms.

Algorithms↗

PubMed2006

Methods for evaluating clustering algorithms for gene expression data using a reference set of functional classes.

BACKGROUND: A cluster analysis is the most commonly performed procedure (often regarded as a first step) on a set of gene expression profiles. In most cases, a post hoc analysis is done to see if the genes in the same clusters can be functionally correlated. While past successes of such analyses have often been reported in a number of microarray studies (most of which used the standard hierarchical clustering, UPGMA, with one minus the Pearson's correlation coefficient as a measure of dissimilarity), often times such groupings could be misleading. More importantly, a systematic evaluation of the entire set of clusters produced by such unsupervised procedures is necessary since they also contain genes that are seemingly unrelated or may have more than one common function. Here we quantify the performance of a given unsupervised clustering algorithm applied to a given microarray study in terms of its ability to produce biologically meaningful clusters using a reference set of functional classes. Such a reference set may come from prior biological knowledge specific to a microarray study or may be formed using the growing databases of gene ontologies (GO) for the annotated genes of the relevant species. RESULTS: In this paper, we introduce two performance measures for evaluating the results of a clustering algorithm in its ability to produce biologically meaningful clusters. The first measure is a biological homogeneity index (BHI). As the name suggests, it is a measure of how biologically homogeneous the clusters are. This can be used to quantify the performance of a given clustering algorithm such as UPGMA in grouping genes for a particular data set and also for comparing the performance of a number of competing clustering algorithms applied to the same data set. The second performance measure is called a biological stability index (BSI). For a given clustering algorithm and an expression data set, it measures the consistency of the clustering algorithm's ability to produce biologically meaningful clusters when applied repeatedly to similar data sets. A good clustering algorithm should have high BHI and moderate to high BSI. We evaluated the performance of ten well known clustering algorithms on two gene expression data sets and identified the optimal algorithm in each case. The first data set deals with SAGE profiles of differentially expressed tags between normal and ductal carcinoma in situ samples of breast cancer patients. The second data set contains the expression profiles over time of positively expressed genes (ORF's) during sporulation of budding yeast. Two separate choices of the functional classes were used for this data set and the results were compared for consistency. CONCLUSION: Functional information of annotated genes available from various GO databases mined using ontology tools can be used to systematically judge the results of an unsupervised clustering algorithm as applied to a gene expression data set in clustering genes. This information could be used to select the right algorithm from a class of clustering algorithms for the given data set.

Algorithms↗

PubMed2006

Molecular pathogenesis of Parkinson's disease: identification of mutations in the Parkin gene in Indian patients.

Parkinson's disease (PD), the second most common neurodegenerative disorder, affects at least 1% of the population over the age of 50. However, very little information is available regarding the molecular basis of PD among Indians. Since the largest number of mutations have been detected in the Parkin gene among all known PD loci, we aim to use Parkin as the candidate gene to assess its role in PD-related pathogenesis in Indian patients. A total of 138 PD patients, with the mean age of onset being 47+/-14 (age range, 5-77 years), and 100 controls were recruited for the study from eastern India. Parkin mutations were detected by amplification of exons of the gene along with the flanking splice junctions by polymerase chain reaction, single-stranded conformation polymorphism and DNA sequencing. A total of 18 nucleotide variants including six novel changes were detected. These include five missense mutations (Gln34Arg, Arg42Cys, Arg42His, Tyr143Cys and Arg334Cys) detected in eight patients in heterozygous condition and a homozygous deletion encompassing exons 3 and 4 in two sibs affected with PD. Clinical features of the Parkin mutants were compared. Among eastern Indian PD patients, mutation in Parkin was identified in 7.24% cases.

Adolescent↗

PubMed2006

Nonparametric estimation of stage occupation probabilities in a multistage model with current status data.

Multistage models are used to describe individuals (or experimental units) moving through a succession of "stages" corresponding to distinct states (e.g., healthy, diseased, diseased with complications, dead). The resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied. Traditional survival analysis is the simplest example of a multistage model, where individuals begin in an initial stage (say, alive) and move irreversibly to a second stage (death). In this article, we consider general multistage models with a directed tree structure (progressive models) in which individuals traverse through stages in a possibly non-Markovian manner. We construct nonparametric estimators of stage occupation probabilities and marginal cumulative transition hazards. Empirical calculations of these quantities are not possible due to the lack of complete data. We consider current status information which represents a more severe form of censoring than the commonly used right censoring. Asymptotic validity of our estimators can be justified using consistency results for nonparametric regression estimators. Finite-sample behavior of our estimators is studied by simulation, in which we show that our estimators based on these limited data compare well with those based on complete data. We also apply our method to a real-life data set arising from a cardiovascular diseases study in Taiwan.

Biometry↗

PubMed2005

Empirical Bayes screening of many p-values with applications to microarray studies.

MOTIVATION: Statistical tests for the detection of differentially expressed genes lead to a large collection of p-values one for each gene comparison. Without any further adjustment, these p-values may lead to a large number of false positives, simply because the number of genes to be tested is huge, which might mean wastage of laboratory resources. To account for multiple hypotheses, these p-values are typically adjusted using a single step method or a step-down method in order to achieve an overall control of the error rate (the so-called familywise error rate). In many applications, this may lead to an overly conservative strategy leading to too few genes being flagged. RESULTS: In this paper we introduce a novel empirical Bayes screening (EBS) technique to inspect a large number of p-values in an effort to detect additional positive cases. In effect, each case borrows strength from an overall picture of the alternative hypotheses computed from all the p-values, while the entire procedure is calibrated by a step-down method so that the familywise error rate at the complete null hypothesis is still controlled. It is shown that the EBS has substantially higher sensitivity than the standard step-down approach for multiple comparison at the cost of a modest increase in the false discovery rate (FDR). The EBS procedure also compares favorably when compared with existing FDR control procedures for multiple testing. The EBS procedure is particularly useful in situations where it is important to identify all possible potentially positive cases which can be subjected to further confirmatory testing in order to eliminate the false positives. We illustrated this screening procedure using a data set on human colorectal cancer where we show that the EBS method detected additional genes related to colon cancer that were missed by other methods. This novel empirical Bayes procedure is advantageous over our earlier proposed empirical Bayes adjustments due to the following reasons: (i) it offers an automatic screening of the p-values the user may obtain from a univariate (i.e., gene by gene) analysis package making it extremely easy to use for a non-statistician, (ii) since it applies to the p-values, the tests do not have to be t-tests; in particular they could be F-tests which might arise in certain ANOVA formulations with expression data or even nonparametric tests, (iii) the empirical Bayes adjustment uses nonparametric function estimation techniques to estimate the marginal density of the transformed p-values rather than using a parametric model for the prior distribution and is therefore robust against model mis-specification. AVAILABILITY: R code for EBS is available from the authors upon request. SUPPLEMENTARY INFORMATION: http://www.stat.uga.edu/~datta/EBS/supp.htm

Algorithms↗

PubMed2004

Standardization and denoising algorithms for mass spectra to classify whole-organism bacterial specimens.

MOTIVATION: Application of mass spectrometry in proteomics is a breakthrough in high-throughput analyses. Early applications have focused on protein expression profiles to differentiate among various types of tissue samples (e.g. normal versus tumor). Here our goal is to use mass spectra to differentiate bacterial species using whole-organism samples. The raw spectra are similar to spectra of tissue samples, raising some of the same statistical issues (e.g. non-uniform baselines and higher noise associated with higher baseline), but are substantially noisier. As a result, new preprocessing procedures are required before these spectra can be used for statistical classification. RESULTS: In this study, we introduce novel preprocessing steps that can be used with any mass spectra. These comprise a standardization step and a denoising step. The noise level for each spectrum is determined using only data from that spectrum. Only spectral features that exceed a threshold defined by the noise level are subsequently used for classification. Using this approach, we trained the Random Forest program to classify 240 mass spectra into four bacterial types. The method resulted in zero prediction errors in the training samples and in two test datasets having 240 and 300 spectra, respectively.

Algorithms↗

PubMed2004

An empirical bayes adjustment to increase the sensitivity of detecting differentially expressed genes in microarray experiments.

MOTIVATION: Detection of differentially expressed genes is one of the major goals of microarray experiments. Pairwise comparison for each gene is not appropriate without controlling the overall (experimentwise) type 1 error rate. Dudoit et al. have advocated use of permutation-based step-down P-value adjustments to correct the observed significance levels for the individual (i.e. for each gene) two sample t-tests. RESULTS: In this paper, we consider an ANOVA formulation of the gene expression levels corresponding to multiple tissue types. We provide resampling-based step-down adjustments to correct the observed significance levels for the individual ANOVA t-tests for each gene and for each pair of tissue type comparisons. More importantly, we introduce a novel empirical Bayes adjustment to the t-test statistics that can be incorporated into the step-down procedure. Using simulated data, we show that the empirical Bayes adjustment improved the sensitivity of detecting differentially expressed genes up to 16%, while maintaining a high level of specificity. This adjustment also reduces the false non-discovery rate to some degree at the cost of a modest increase in the false discovery rate. We illustrate our approach using a human colon cancer dataset consisting of oligonucleotide arrays of normal, adenoma and carcinoma cells. The number of genes with differential expression level declared statistically significant was about 50 when comparing normal to adenoma cells and about five when comparing adenoma to carcinoma cells. This list includes genes previously known to be associated with colon cancer as well as some novel genes. AVAILABILITY: R code for the empirical Bayes adjustment and step-down P-value calculation via resampling are available from the supplementary web-site. SUPPLEMENTARY INFORMATION: http://www.mathstat.gsu.edu/~matsnd/EB/supp.htm

Algorithms↗

PubMed2003

Comparisons and validation of statistical clustering techniques for microarray gene expression data.

MOTIVATION: With the advent of microarray chip technology, large data sets are emerging containing the simultaneous expression levels of thousands of genes at various time points during a biological process. Biologists are attempting to group genes based on the temporal pattern of their expression levels. While the use of hierarchical clustering (UPGMA) with correlation 'distance' has been the most common in the microarray studies, there are many more choices of clustering algorithms in pattern recognition and statistics literature. At the moment there do not seem to be any clear-cut guidelines regarding the choice of a clustering algorithm to be used for grouping genes based on their expression profiles. RESULTS: In this paper, we consider six clustering algorithms (of various flavors!) and evaluate their performances on a well-known publicly available microarray data set on sporulation of budding yeast and on two simulated data sets. Among other things, we formulate three reasonable validation strategies that can be used with any clustering algorithm when temporal observations or replications are present. We evaluate each of these six clustering methods with these validation measures. While the 'best' method is dependent on the exact validation strategy and the number of clusters to be used, overall Diana appears to be a solid performer. Interestingly, the performance of correlation-based hierarchical clustering and model-based clustering (another method that has been advocated by a number of researchers) appear to be on opposite extremes, depending on what validation measure one employs. Next it is shown that the group means produced by Diana are the closest and those produced by UPGMA are the farthest from a model profile based on a set of hand-picked genes. AVAILABILITY: S+ codes for the partial least squares based clustering are available from the authors upon request. All other clustering methods considered have S+ implementation in the library MASS. S+ codes for calculating the validation measures are available from the authors upon request. The sporulation data set is publicly available at http://cmgm.stanford.edu/pbrown/sporulation

Algorithms↗

PubMed2003

Marginal analyses of clustered data when cluster size is informative.

We propose a new approach to fitting marginal models to clustered data when cluster size is informative. This approach uses a generalized estimating equation (GEE) that is weighted inversely with the cluster size. We show that our approach is asymptotically equivalent to within-cluster resampling (Hoffman, Sen, and Weinberg, 2001, Biometrika 73, 13-22), a computationally intensive approach in which replicate data sets containing a randomly selected observation from each cluster are analyzed, and the resulting estimates averaged. Using simulated data and an example involving dental health, we show the superior performance of our approach compared to unweighted GEE, the equivalence of our approach with WCR for large sample sizes, and the superior performance of our approach compared with WCR when sample sizes are small.

Cluster Analysis↗

PubMed2002

Marginal estimation for multi-stage models: waiting time distributions and competing risks analyses.

We provide non-parametric estimates of the marginal cumulative distribution of stage occupation times (waiting times) and non-parametric estimates of marginal cumulative incidence function (proportion of persons who leave stage j for stage j' within time t of entering stage j) using right-censored data from a multi-stage model. We allow for stage and path dependent censoring where the censoring hazard for an individual may depend on his or her natural covariate history such as the collection of stages visited before the current stage and their occupation times. Additional external time dependent covariates that may induce dependent censoring can also be incorporated into our estimates, if available. Our approach requires modelling the censoring hazard so that an estimate of the integrated censoring hazard can be used in constructing the estimates of the waiting times distributions. For this purpose, we propose the use of an additive hazard model which results in very flexible (robust) estimates. Examples based on data from burn patients and simulated data with tracking are also provided to demonstrate the performance of our estimators.

Burns↗

PubMed2002

Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring.

We propose nonparametric estimators of the stage occupation probabilities and transition hazards for a multistage system that is not necessarily Markovian, using data that are subject to dependent right censoring. We assume that the hazard of being censored at a given instant depends on a possibly time-dependent covariate process as opposed to assuming a fixed censoring hazard (independent censoring). The estimator of the integrated transition hazard matrix has a Nelson-Aalen form where each of the counting processes counting the number of transitions between states and the risk sets for leaving each stage have an IPCW (inverse probability of censoring weighted) form. We estimate these weights using Aalen's linear hazard model. Finally, the stage occupation probabilities are obtained from the estimated integrated transition hazard matrix via product integration. Consistency of these estimators under the general paradigm of non-Markov models is established and asymptotic variance formulas are provided. Simulation results show satisfactory performance of these estimators. An analysis of data on graft-versus-host disease for bone marrow transplant patients is used as an illustration.

Biometry↗