Stephan Morgenthaler

Random walk and gap plots of DNA sequences

Genomic sequence analysis is usually performed with the help of specialized software packages written for molecular biologists. The scope of such pre-programmed techniques is quite limited. Because DNA sequences contain a large amount of information, analysis of such sequences without underlying assumptions may provide additional insights. The present article proposes two new graphical representations as examples of such methods. The random walk plot is designed to show the base composition in a compact form, whereas the gap plot visualizes positional correlations. The random walk plot represents the DNA sequence as a curve, a random walk, in a plane. The four possible moves, left/right and up/down, are used to encode the four possible bases. Gap plots provide a tool to exhibit various features in a sequence. They visualize the periodic patterns within a sequence, both with regard to a single type of base or between two types of bases.

Population risk and physiological rate parameters for colon cancer. The union of an explicit model for carcinogenesis with the public health records of the United States

The relationship between the molecular mechanisms of mutagenesis and the actual processes by which most people get cancer is still poorly understood. One missing link is a physiologically based but quantitative model uniting the processes of mutation, cell growth and turnover. Any useful model must also account for human heterogeneity for inherited traits and environmental experiences. Such a coherent algebraic model for the age-specific incidence of cancer has been developing over the past 50 years. This development has been spurred primarily by the efforts of Nordling [N.O. Nordling, A new theory on the cancer-inducing mechanism, Br. J. Cancer 7 (1953) 68-72], Armitage and Doll [P. Armitage, R. Doll, The age distribution of cancer and a multi-stage theory of carcinogenesis, Br. J. Cancer 8 (1) (1954) 1-12; P. Armitage, R. Doll, A two-stage theory of carcinogenesis in relation to the age distribution of human cancer, Br. J. Cancer 9 (2) (1957) 161-169], and Moolgavkar and Knudson [S.H. Moolgavkar, A.G. Knudson Jr., Mutation and cancer: a model for human carcinogenesis. JNCI 66 (6) (1981) 1037-1052], whose work defined two rate-limiting stages identified with initiation and promotion stages in experimental carcinogenesis. Unfinished in these efforts was an accounting of population heterogeneity and a complete description of growth and genetic change during the growth of adenomas. In an attempt to complete a unified model, we present herein the first means to explicitly compute the essential parameters of the two-stage initiation-promotion model using colon cancer as an example. With public records from the 1930s to the present day, we first calculate the fraction at primary risk for each birth year cohort and note historical changes. We then calculate the product of rates for n initiation-mutations, the product of rates for m promotion-mutations and the average growth rate of the intermediate adenomatous colonies from which colon carcinomas arise. We find that the population fraction at primary risk for colon cancer risk was historically invariant at about 42% for the birth year cohorts from 1860 through 1930. This was true for each of the four cohorts we examined (European- and African-Americans of each gender). Additionally, the data indicate an historical increase in the initiation-mutation rates for the male cohorts and the promotion-mutation rates for the female cohorts. Interestingly, the calculated rates for initiation-mutations are in accord with mutation rates derived from observations of mutations in peripheral blood cells drawn from persons of different ages. Adenoma growth rates differed significantly between genders but were essentially historically invariant. In its present form, the model has also allowed us to calculate the rate of loss of heterozygosity (LOH) or loss of genomic imprinting (LOI) in adenomas to result in the high LOH/LOI fractions in tumors. But it has not allowed us to specify the number of events m required during promotion.

Leverage and Breakdown in L 1 Regression

Abstract In this article the notion of leverage of a design point when fitting a linear regression model is interpreted geometrically. In the case of least squares fitting, the leverage indicators based on the diagonal of the hat matrix are widely applied. By interpreting these hat matrix indicators geometrically, leverage can be generalized to groups of design points, as well as to other methods of fitting. The article introduces a leverage indicator that is appropriate for L 1 regression and discusses some aspects of this new diagnostic. It is shown that, in the case of L 1 regression, the leverage indicators have a precise interpretation. They tell us about the breakdown and/or the exactness of fit. As an application, the article considers the maximal possible breakdown value of L 1 regression and the choice of designs that achieve this maximum.

A statistical model to estimate variance in long term-low dose mutation assays: testing of the model in a human lymphoblastoid mutation assay

Long term-low dose mutation assays offer a means to study the genetic effects of environmental mutagens at concentrations relevant to human exposure. These assays involve continuous induction of mutants, serial dilution of cultures and sampling to determine the mutant fraction as a function of time and mutagen concentration. An arithmetic model for the expected variance among identically treated cultures is presented. This model provides means to calculate a predicted variance of the mutant fractions and mutation rates in typical long term-low dose experiments. We have calculated the expected variances of the mutant fraction with this model and compared them to the observed variances among 4 independent experiments in which human lymphoblastoid cells were treated for 5, 10, 15 and 20 days with a non-toxic concentration of the mutagen 4-aminobiphenyl. Mutations at the HPRT locus were measured by determining the 6-thioguanine-resistant mutant fraction. The expected and observed variances of the mutant fractions are in close agreement. This model is adequate to predict the variance of the mutant fraction and should be useful in experimental design and objective evaluation of long term-low dose mutation assays.

A survey of robust statistics

We argue that robust statistics has multiple goals, which are not always aligned. Robust thinking grew out of data analysis and the realisation that empirical evidence is at times supported merely by one or a few observations. The paper examines the outgrowth from this criticism of the statistical method over the last few decades.

Comparing connectomes across subjects and populations at different scales

Brain connectivity can be represented by a network that enables the comparison of the different patterns of structural and functional connectivity among individuals. In the literature, two levels of statistical analysis have been considered in comparing brain connectivity across groups and subjects: 1) the global comparison where a single measure that summarizes the information of each brain is used in a statistical test; 2) the local analysis where a single test is performed either for each node/connection which implies a multiplicity correction, or for each group of nodes/connections where each subset is summarized by one single test in order to reduce the number of tests to avoid a penalizing multiplicity correction. We comment on the different levels of analysis and present some methods that have been proposed at each scale. We highlight as well the possible factors that could influence the statistical results and the questions that have to be addressed in such an analysis.

New directions in statistical data analysis and robustness

Statistical data analysis has been enriched by the development of several new tools. This book discusses the advances which they are making possible - often into unexplored territory - and the trends they are foreshadowing. The topics range from theoretical considerations to practical concerns.

Robust weighted likelihood estimators with an application to bivariate extreme value problems

The authors achieve robust estimation of parametric models through the use of weighted maximum likelihood techniques. A new estimator is proposed and its good properties illustrated through examples. Ease of implementation is an attractive property of the new estimator. The new estimator downweights with respect to the model and can be used for complicated likelihoods such as those involved in bivariate extreme value problems. New weight functions, tailored for these problems, are constructed. The increased insight provided by our robust fits to these bivariate extreme value models is exhibited through the analysis of sea levels at two East Coast sites in the United Kingdom.

Adaptive Strategy for the Statistical Analysis of Connectomes

We study an adaptive statistical approach to analyze brain networks represented by brain connection matrices of interregional connectivity (connectomes). Our approach is at a middle level between a global analysis and single connections analysis by considering subnetworks of the global brain network. These subnetworks represent either the inter-connectivity between two brain anatomical regions or by the intra-connectivity within the same brain anatomical region. An appropriate summary statistic, that characterizes a meaningful feature of the subnetwork, is evaluated. Based on this summary statistic, a statistical test is performed to derive the corresponding p-value. The reformulation of the problem in this way reduces the number of statistical tests in an orderly fashion based on our understanding of the problem. Considering the global testing problem, the p-values are corrected to control the rate of false discoveries. Finally, the procedure is followed by a local investigation within the significant subnetworks. We contrast this strategy with the one based on the individual measures in terms of power. We show that this strategy has a great potential, in particular in cases where the subnetworks are well defined and the summary statistics are properly chosen. As an application example, we compare structural brain connection matrices of two groups of subjects with a 22q11.2 deletion syndrome, distinguished by their IQ scores.

Robust analysis of a response surface design

Abstract The paper discusses the outlier issue in experiments that are carefully planned for the purpose of response surface exploration. In such cases, a second order polynomial is fitted to the measurements in order to identify significant control variables, optimal settings of control variables, likely gains in the value of the response, etc. Outliers among the measurements cannot be avoided and will almost certainly have a highly confusing effect on the least-squares fit, leading to a wrong interpretation of the data. The paper discusses a practical example and uses it to exhibit two possible approaches. A combination of the least-squares technique with an expert knowledge of the design of the experiment can lead to valid interpretations by highlighting the trouble spots. The other possible approach uses robust fitting techniques which are much less easily fooled by outliers and automatically account for them. The second approach is better suited to casual users of response surface methodology.