Larry P. Ammann

The Human Red Blood Cell Proteome and Interactome

The red blood cell or erythrocyte is easily purified, readily available, and has a relatively simple structure. Therefore, it has become a very well studied cell in terms of protein composition and function. RBC proteomic studies performed over the last five years, by several laboratories, have identified 751 proteins within the human erythrocyte. As RBCs contain few internal structures, the proteome will contain far fewer proteins than nucleated cells. In this minireview, we summarize the current knowledge of the RBC proteome, discuss alterations in this partial proteome in varied human disease states, and demonstrate how in silico studies of the RBC interactome can lead to considerable insight into disease diagnosis, severity, and drug or gene therapy response. To make these latter points we focus on what is known concerning changes in the RBC proteome in Sickle Cell Disease.

Robust Principal Components

This paper proposes a new algorithm to obtain an eigenvalue decomposition for the sample covariance matrix of a multivariate dataset. The algorithm is based on the rotation technique employed by Ammann and Van Ness (1988a,b) to obtain a robust solution to an errors-in-variables problem. When this rotation technique is combined with an iterative reweighting of the data, a robust eigenvalue decomposition is obtained. This robust eigenvalue decomposition has important applications to principal component analysis. Monte Carlo simulations are performed to compare ordinary principal component analysis using the standard eigenvalue decomposition with this algorithm, referred to as ROPRC. It is seen that ROPRC is reasonably efficient compared to an eigenvalue decomposition when Gaussian data is available, and that ROPRC is much better than the eigenvalue decomposition if outliers are present or if the data has a heavy-tailed distribution. The algorithm returns useful numerical diagnostic information in the form o...

Robust Singular Value Decompositions: A New Approach to Projection Pursuit

Abstract Robust location and covariance estimators are developed via general M estimation for covariance matrix eigenvectors and eigenvalues. The solution to this GM estimation problem is obtained by transforming it into a series of robust regression problems based on a new algorithm for the singular value decomposition. It is shown here that the singular value decomposition can be represented as an iteration of two steps: a least squares regression fit of the data matrix followed by a rotation to the regression hyperplanes. An algorithm to obtain the solution to this GM estimation problem is presented, along with results of a Monte Carlo study and examples of its application. In addition, it is shown how the output of this algorithm can be used to numerically search for multivariate outliers, which is especially useful in exploratory data analysis with high-dimensional data and large sample sizes, where standard graphical techniques are difficult to implement. Because the algorithm computes robust estima...

Efficiencies of Interblock Rank Statistics for Repeated Measures Designs

Abstract For factorial designs, tests that rely on the method of n rankings, for example, the Friedman test, suffer a potential loss of power since they depend only on within-block ranks. This deficiency is overcome by ranking across blocks as is done in the aligned rank tests and the rank transform procedures. This article examines a broad class of powerful interblock rank statistics for testing for both treatment effects and ordered alternatives and for performing multiple comparisons in a two-way repeated measures design. Pitman efficiencies are obtained for tests that closely resemble the rank transform test and for aligned rank tests under weaker hypotheses than assumed by Puri and Sen (1971). In addition, several serious limitations of the rank transform procedure for repeated measures designs are presented. Limitations of the rank transform procedures, in particular, merit such study because they are recommended without reservation by the SAS manual for use with PROC ANOVA and PROC GLM and are very...

Efficacies of rank-transform statistics in two-way models with no interaction

Abstract To test for treatment effects in a two-way model when the classical assumptions of normality of errors and constancy of variance cannot be verified, Hora and Conover (1984) proposed a rank test in which the entire data set is ranked, the ranks are scored, and then the classical analysis of variance F statistic is applied to the scored ranks. They showed that the limiting null distribution of this test statistic is a chi-squared distribution divided by its degrees of freedom. Simulation results suggest that this procedure, called the rank-transform procedure, has good power properties. This article determines the asymptotic relative efficiency of the rank-transform procedure relative to the classical F statistic. To do this, vectors of linear rank statistics are shown to have a limiting multivariate normal distribution under a sequence of Pitman alternatives. This work is based on the results of Hajek (1968). The rank-transform statistic is then expressed as a quadratic form in the vectors, divide...

A routine for converting regression algorithms into corresponding orthogonal regression algorithms

The routine converts any standard regression algorithm (that calculates both the coefficients and residuals) into a corresponding <italic>orthogonal</italic> regression algorithm. Thus, a standard, or robust, or <italic>L</italic><subscrpt>1</subscrpt> regression algorithm is converted into the corresponding standard, or robust, or <italic>L</italic><subscrpt>1</subscrpt> <italic>orthogonal</italic> algorithm. Such orthogonal procedures are important for three basic reasons. First, they solve the classical errors-in-variables (EV) regression problem. Standard <italic>L</italic><subscrpt>2</subscrpt> orthogonal regression, obtained by converting ordinary least squares regression, is the maximum likelihood solution of the EV problem under Gaussian assumptions. However, this <italic>L</italic><subscrpt>2</subscrpt> solution is known to be unstable under even slight deviations from the model. Thus this routines ability to create <italic>robust</italic> orthogonal regression algorithms from robust ordinary regression algorithms will also be very useful in practice. Second, orthogonal regression is intimately related to principal components procedures. Therefore, this routine can also be used to create corresponding <italic>L</italic><subscrpt>1</subscrpt>, robust, etc., principal components algorithms. And third, orthogonal regression treats the <italic>x</italic> and <italic>y</italic> variables symmetrically. This is very important in many science and engineering modeling problems. Monte Carlo studies, which test the effectiveness of the routine under a variety of types of data, are given.

Centrality Measures for the Human Red Blood Cell Interactome

The red blood cell or erythrocyte is easily purified, readily available, and has a relatively simple structure. Therefore, it has become a very well studied cell in terms of protein composition and function. RBC proteomic studies performed over the last five years, by several laboratories, have identified 751 proteins within the human erythrocyte. Data describing most of their interactions are also available. This allowed us to assemble a preliminary interactome of the red blood cell. Identifying the role of certain proteins in the development of blood diseases, such as sickle cell disease, remains a challenge. To give future studies the benefit of focusing on a smaller subset of proteins, we consider several measures aimed to computationally establish the relative functional significance of protein members of the interactome.

StePSIM – a method for stepwise peak selection and identification of metabolites in 1H NMR spectra

A method for stepwise selection of peaks in NMR spectra from multiple groups is described. This method is based on initial peak-finding among the spectra and uses jacknife classification performance as the basis for selection of peaks. The selection process is followed by the construction of correlation maps to identify sets of multiplets that are related to each of the selected peaks, aiding in the identification of metabolites that are responsible for differences among the groups. For illustrative purposes, this methodology is applied to a data set that contains 52 spectra from renal cell carcinoma and normal renal tissue samples. The new method is denoted as StePSIM, Stepwise Peak Selection and Identification of Metabolites.

Standard and robust orthogonal regression

A fast routine for converting regression algorithms into corresponding orthogonal regression (OR) algorithms was introduced in Ammann and Van Ness (1988). The present paper discusses the properties of various ordinary and robust OR procedures created using this routine. OR minimizes the sum of the orthogonal distances from the regression plane to the data points. OR has three types of applications. First, L 2 OR is the maximum likelihood solution of the Gaussian errors-in-variables (EV) regression problem. This L 2 solution is unstable, thus the robust OR algorithms created from robust regression algorithms should prove very useful. Secondly, OR is intimately related to principal components analysis. Therefore, the routine can also be used to create L 1, robust, etc. principal components algorithms. Thirdly, OR treats the x and y variables symmetrically which is important in many modeling problems. Using Monte Carlo studies this paper compares the performance of standard regression, robust regression, OR,...

On the structure of regular infinitely divisible point processes

A representation for the probability generating functional (p.g.fl.) of a regular infinitely divisible (i.d.) stochastic point process, motivated as a generalization of the Gauss-Poisson process, is presented. The functional is characterized by a sequence of Borel product measures. Necessary and sufficient conditions, in terms of these Borel measures, are given for this representation to be a p.g.fl., thus characterizing all regular i.d. point processes.