Rolf Sundberg

Second-order calibration: bilinear least squares regression and a simple alternative

Abstract We consider calibration of second-order, or hyphenated instruments generating bilinear two-way data for each specimen. The bilinear regression model is to be estimated from a number of specimens of known composition. We propose a simple estimator and study how it works on real and simulated data. The estimator, which we call the SVD (singular value decomposition) estimator is usually not much less efficient than bilinear least squares. The advantages of our method over bilinear least squares are that it is faster and more easily computed, its standard errors are explicit (and derived in the paper), and it has a simpler correlation structure.

A statistical methodology for drug-drug interaction surveillance

Interaction between drug substances may yield excessive risk of adverse drug reactions (ADRs) when two drugs are taken in combination. Collections of individual case safety reports (ICSRs) related to suspected ADR incidents in clinical practice have proven to be very useful in post-marketing surveillance for pairwise drug--ADR associations, but have yet to reach their full potential for drug-drug interaction surveillance. In this paper, we implement and evaluate a shrinkage observed-to-expected ratio for exploratory analysis of suspected drug-drug interaction in ICSR data, based on comparison with an additive risk model. We argue that the limited success of previously proposed methods for drug-drug interaction detection based on ICSR data may be due to an underlying assumption that the absence of interaction is equivalent to having multiplicative risk factors. We provide empirical examples of established drug-drug interaction highlighted with our proposed approach that go undetected with logistic regression. A database wide screen for suspected drug-drug interaction in the entire WHO database is carried out to demonstrate the feasibility of the proposed approach. As always in the analysis of ICSRs, the clinical validity of hypotheses raised with the proposed method must be further reviewed and evaluated by subject matter experts.

Multigene Analysis Can Discriminate Between Ulcerative Colitis, Crohn's Disease, and Irritable Bowel Syndrome

BACKGROUND & AIMS Inflammatory bowel diseases (IBDs) and the irritable bowel syndrome (IBS) are heterogeneous disorders of the gastrointestinal tract and can profoundly affect the quality of life. Because many of the symptoms of IBD are similar to those of IBS, the former may be misdiagnosed. In addition, the 2 major forms of IBD, ulcerative colitis (UC) and Crohns disease (CD), have overlapping nonspecific, pathologic features leading to difficulties in assessing colonic inflammation and hence the term IBD unclassified has been proposed. The aim of this study was to identify and assess the utility of a certain set of marker genes that could help to distinguish IBS from IBD, and further to discriminate between UC and CD. METHODS Subtractive suppression hybridization was used to identify IBD-specific genes in colonic mucosal biopsy specimens. In quantitative polymerase chain reaction experiments, the differential expressions of identified genes then were analyzed using a classification algorithm and the possible clinical value of these marker genes was evaluated in a total of 301 patients in 3 stepwise studies. RESULTS Seven marker genes were identified as differentially expressed in IBD, making it possible to discriminate between patients suffering from UC, CD, or IBS with area under the receiver-operating characteristic curves ranging from 0.915 to 0.999 (P < .0001) using the clinical diagnosis as gold standard. CONCLUSIONS Expression profiling of relevant marker genes in colonic biopsy specimens from patients with IBD/IBS-like symptoms may enable swift and reliable determination of diagnosis, ultimately improving disease management.

Multivariate Calibration — Direct and Indirect Regression Methodology

This paper tries first to introduce and motivate the methodology of multivariate calibration. Next a review is given, mostly avoiding technicalities, of the somewhat messy theory of the subject. Two approaches are distinguished: the estimation approach (controlled calibration) and the prediction approach (natural calibration). Among problems discussed are the choice of estimator, the choice of confidence region, methodology for handling situations with more variables than observations, near-collinearities (with counter-measures like ridge type regression, principal components regression, partial least squares regression and continuum regression), pretreatment of data, and cross-validation vs true prediction. Examples discussed in detail concern estimation of the age of a rhinoceros from its horn lengths (low-dimensional), and nitrate prediction in waste-water from high-dimensional spectroscopic measurements.

An iterative method for solution of the likelihood equations for incomplete data from exponential families

The paper deals with the numerical solution of the likelihood equations for incomplete data from exponential families, that is for data being a function of exponential family data. Illustrative examples especially studied in this paper concern grouped and censored normal samples and normal mixtures. A simple iterative method of solution is proposed and studied. It is shown that the sequence of iterates converges to a relative maximum of the likelihood function, and that the convergence is geometric with a factor of convergence which for large samples equals the maxi-mal relative loss of Fisher information due to the incompleteness of data. This large sample factor of convergence is illustrated diagrammaticaily for the examples mentioned above. Experiences of practical application are mentioned.

Decrease of serotonin receptor 2C in schizophrenia brains identified by high-resolution mRNA expression analysis.

BACKGROUND RNA expression profiling can provide hints for the selection of candidate susceptibility genes, for formulation of hypotheses about the development of a disease, and/or for selection of candidate gene targets for novel drug development. We measured messenger RNA expression levels of 16 candidate genes in brain samples from 55 schizophrenia patients and 55 controls. This is the largest sample so far used to identify genes differentially expressed in schizophrenia brains. METHODS We used a sensitive real-time polymerase chain reaction methodology and a novel statistical approach, including the development of a linear model of analysis of covariance type. RESULTS We found two genes differentially expressed: monoamine oxidase B was significantly increased in schizophrenia brain (p =.001), whereas one of the serotonin receptor genes, serotonin receptor 2C, was significantly decreased (p =.001). Other genes, previously proposed to be differentially expressed in schizophrenia brain, were invariant in our analysis. CONCLUSIONS The differential expression of serotonin receptor 2C is particularly relevant for the development of new atypical antipsychotic drugs. The strategy presented here is useful to evaluate hypothesizes for the development of the disease proposed by other investigators.

A Generalized View on Continuum Regression

In regression with near collinear explanatory variables, the least squares predictor has large variance. Ordinary least squares regression (OLSR) often leads to unrealistic regression coefficients. Several regularized regression methods have been proposed as alternatives. Well-known are principal components regression (PCR), ridge regression (RR) and continuum regression (CR). The latter two involve a continuous metaparameter, offering additional flexibility.For a univariate response variable, CR incorporates OLSR, PLSR, and PCR as special cases, for special values of the metaparameter. CR is also closely related to RR. However, CR can in fact yield regressors that vary discontinuously with the metaparameter. Thus, the relation between CR and RR is not always one-to-one. We develop a new class of regression methods, LSRR, essentially the same as CR, but without discontinuities, and prove that any optimization principle will yield a regressor proportional to a RR, provided only that the principle implies maximizing some function of the regressors sample correlation coefficient and its sample variance. For a multivariate response vector we demonstrate that a number of well-established regression methods are related, in that they are special cases of basically one general procedure. We try a more general method based on this procedure, with two meta-parameters. In a simulation study we compare this method to ridge regression, multivariate PLSR and repeated univariate PLSR. For most types of data studied, all methods do approximately equally well. There are cases where RR and LSRR yield larger errors than the other methods, and we conclude that one-factor methods are not adequate for situations where more than one latent variable are needed to describe the data. Among those based on latent variables, none of the methods tried is superior to the others in any obvious way.

Statistical aspects on fitting the Arrhenius equation

Abstract Motivated by a recent mathematical paper, we discuss statistical parameter estimation in the Arrhenius equation, that relates kinetic reaction rates to temperature. In opposition to the paper in question, we argue theoretically for the appropriateness of using ordinary least squares on log-transformed data and supply some empirical support in this direction.

Multivariate Calibration With More Variables Than Observations

Multivariate calibration involves the use of an estimated (linear) relationship between a q-variate response vector Y and a p-dimensional explanatory vector X to estimate or predict future unknown X from further observed Y. In some applications—for example, when Y represents automatic intensity measurements at q different wavelengths on n chemical standard samples—the feasible sample size n may be restricted, whereas the dimension q can be chosen quite large. In this article, the singular cases appearing when n q, the traditional solutions to the estimation and prediction problems—that is, the generalized least squares estimator and the estimated best linear predictor—are both unique, whereas for smaller n, (q – n + 1)-dimensional hyperplanes of solutions are obtained, the same in both problems. The properties of the predictor are also empirically studied in an example with p = 1, q = 6, and varying n.

THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR IN UP-AND-DOWN EXPERIMENTS FOR QUANTAL DOSE-RESPONSE DATA

Standard maximum likelihood logistic or probit regression has been used in biopharmaceutical practice for inference about tolerance threshold distributions in situations where subjects (patients) have been allocated doses according to an up-and-down design. For example, a steeper dose-response curve than expected was reported in one such study. This article demonstrates that the maximum likelihood estimator systematically and considerably exaggerates the regression parameter with moderately large sample sizes. Thus a probable explanation for finding a steeper curve than expected is the method used to analyze the experiment, that is, the bias in the maximum likelihood estimator. An additional consequence of this bias is that the mean/median/ED50 are estimated with a misleading precision. In particular, confidence intervals are much too narrow. As a conclusion, we warn against conventional logistic or probit regression in combination with up-and-down designs.