Added predictive value of high-throughput molecular data to clinical data, and its validation

Hundreds of ''molecular signatures'' have been proposed in the literature to predict patient outcome in clinical settings from high-dimensional data, many of which eventually failed to get validated. Validation of such molecular research findings is thus becoming an increasingly important branch of clinical bioinformatics. Moreover, in practice well-known clinical predictors are often already available. From a statistical and bioinformatics point of view, poor attention has been given to the evaluation of the added predictive value of a molecular signature given that clinical predictors are available. This article reviews procedures that assess and validate the added predictive value of high-dimensional molecular data. It critically surveys various approaches for the construction of combined prediction models using both clinical and molecular data, for validating added predictive value based on independent data, and for assessing added predictive value using a single data set

Use of pre-transformation to cope with outlying values in important candidate genes

Outlying values in predictors often strongly affect the results of statistical analyses in high-dimensional settings. Although they frequently occur with most high-throughput techniques, the problem is often ignored in the literature. We suggest to use a very simple transformation, proposed before in a different context by Royston and Sauerbrei, as an intermediary step between array normalization and high-level statistical analysis. This straightforward univariate transformation identifies extreme values and reduces the influence of outlying values considerably in all further steps of statistical analysis without eliminating the incriminated observation or feature. The use of the transformation and its effects are demonstrated for diverse univariate and multivariate statistical analyses using nine publicly available microarray data sets

The Search for a Simple, Efficient, Less Intrusive Substitute for Our Current Income Tax System

The subject of tax reform seems to emerge as a highly debated topic of discussion every few years because our current income tax system is too complex, inefficient, and intrusive. There are two unique proposals that would change the face of our tax system, the flat tax and the national sales tax. This paper examines these proposals on the grounds of complexity, efficiency, and intrusiveness to determine which plan would be the best substitute for our current income tax system

Does limited virucidal activity of biocides include duck hepatitis B virucidal action?

BACKGROUND: There is agreement that the infectivity assay with the duck hepatitis B virus (DHBV) is a suitable surrogate test to validate disinfectants for hepatitis B virucidal activity. However, since this test is not widely used, information is necessary whether disinfectants with limited virucidal activity also inactivate DHBV. In general, disinfectants with limited virucidal activity are used for skin and sensitive surfaces while agents with full activity are more aggressive. The present study compares the activity of five different biocides against DHBV and the classical test virus for limited virucidal activity, the vaccinia virus strain Lister Elstree (VACV) or the modified vaccinia Ankara strain (MVA). METHODS: Virucidal assay was performed as suspension test according to the German DVV/RKI guideline. Duck hepatitis B virus obtained from congenitally infected Peking ducks was propagated in primary duck embryonic hepatocytes and was detected by indirect immunofluorescent antigen staining. RESULTS: The DHBV was inactivated by the use of 40% ethanol within 1-min and 30% isopropanol within 2-min exposure. In comparison, 40% ethanol within 2-min and 40% isopropanol within 1-min exposure were effective against VACV/MVA. These alcohols only have limited virucidal activity, while the following agents have full activity. 0.01% peracetic acid inactivated DHBV within 2 min and a concentration of 0.005% had virucidal efficacy against VACV/MVA within 1 min. After 2-min exposure, 0.05% glutardialdehyde showed a comparable activity against DHBV and VACV/MVA. This is also the case for 0.7% formaldehyde after a contact time of 30 min. CONCLUSIONS: Duck hepatitis B virus is at least as sensitive to limited virucidal activity as VACV/MVA. Peracetic acid is less effective against DHBV, while the alcohols are less effective against VACV/MVA. It can be expected that in absence of more direct tests the results may be extrapolated to HBV

Investigating treatment-effect modification by a continuous covariate in IPD meta-analysis: an approach using fractional polynomials

Background: In clinical trials, there is considerable interest in investigating whether a treatment effect is similar in all patients, or that one or more prognostic variables indicate a differential response to treatment. To examine this, a continuous predictor is usually categorised into groups according to one or more cutpoints. Several weaknesses of categorization are well known. To avoid the disadvantages of cutpoints and to retain full information, it is preferable to keep continuous variables continuous in the analysis. To handle this issue, the Subpopulation Treatment Effect Pattern Plot (STEPP) was proposed about two decades ago, followed by the multivariable fractional polynomial interaction (MFPI) approach. Provided individual patient data (IPD) from several studies are available, it is possible to investigate for treatment heterogeneity with meta-analysis techniques. Meta-STEPP was recently proposed and in patients with primary breast cancer an interaction of estrogen receptors with chemotherapy was investigated in eight randomized controlled trials (RCTs). Methods: We use data from eight randomized controlled trials in breast cancer to illustrate issues from two main tasks. The first task is to derive a treatment effect function (TEF), that is, a measure of the treatment effect on the continuous scale of the covariate in the individual studies. The second is to conduct a meta-analysis of the continuous TEFs from the eight studies by applying pointwise averaging to obtain a mean function. We denote the method metaTEF. To improve reporting of available data and all steps of the analysis we introduce a three-part profile called MethProf-MA. Results: Although there are considerable differences between the studies (populations with large differences in prognosis, sample size, effective sample size, length of follow up, proportion of patients with very low estrogen receptor values) our results provide clear evidence of an interaction, irrespective of the choice of the FP function and random or fixed effect models. Conclusions: In contrast to cutpoint-based analyses, metaTEF retains the full information from continuous covariates and avoids several critical issues when performing IPD meta-analyses of continuous effect modifiers in randomised trials. Early experience suggests it is a promising approach. Trial registration: Not applicable

Exhuming nonnegative garrote from oblivion using suitable initial estimates- illustration in low and high-dimensional real data

The nonnegative garrote (NNG) is among the first approaches that combine variable selection and shrinkage of regression estimates. When more than the derivation of a predictor is of interest, NNG has some conceptual advantages over the popular lasso. Nevertheless, NNG has received little attention. The original NNG relies on least-squares (OLS) estimates, which are highly variable in data with a high degree of multicollinearity (HDM) and do not exist in high-dimensional data (HDD). This might be the reason that NNG is not used in such data. Alternative initial estimates have been proposed but hardly used in practice. Analyzing three structurally different data sets, we demonstrated that NNG can also be applied in HDM and HDD and compared its performance with the lasso, adaptive lasso, relaxed lasso, and best subset selection in terms of variables selected, regression estimates, and prediction. Replacing OLS by ridge initial estimates in HDM and lasso initial estimates in HDD helped NNG select simpler models than competing approaches without much increase in prediction errors. Simpler models are easier to interpret, an important issue for descriptive modelling. Based on the limited experience from three datasets, we assume that the NNG can be a suitable alternative to the lasso and its extensions. Neutral comparison simulation studies are needed to better understand the properties of variable selection methods, compare them and derive guidance for practice

Global, Parameterwise and Joint Shrinkage Factor Estimation

The predictive value of a statistical model can often be improved by applying shrinkage methods. This can be achieved, e.g., by regularized regression or empirical Bayes approaches. Various types of shrinkage factors can also be estimated after a maximum likelihood fit has been obtained: while global shrinkage modifies all regression coefficients by the same factor, parameterwise shrinkage factors differ between regression coefficients. The latter ones have been proposed especially in the context of variable selection. With variables which are either highly correlated or associated with regard to contents, such as dummy variables coding a categorical variable, or several parameters describing a nonlinear effect, parameterwise shrinkage factors may not be the best choice. For such cases, we extend the present methodology by so-called 'joint shrinkage factors', a compromise between global and parameterwise shrinkage. Shrinkage factors are often estimated using leave-one-out resampling. We also discuss a computationally simple and much faster approximation to resampling-based shrinkage factor estimation, can be easily obtained in most standard software packages for regression analyses. This alternative may be relevant for simulation studies and other computerintensive investigations. Furthermore, we provide an R package shrink implementing the mentioned shrinkage methods for models fitted by linear, generalized linear, or Cox regression, even if these models involve fractional polynomials or restricted cubic splines to estimate the influence of a continuous variable by a nonlinear function. The approaches and usage of the package shrink are illustrated by means of two examples

Effects of Influential Points and Sample Size on the Selection and Replicability of Multivariable Fractional Polynomial Models

The multivariable fractional polynomial (MFP) procedure combines variable selection with a function selection procedure (FSP). For continuous variables, a closed test procedure is used to decide between no effect, linear, FP1 or FP2 functions. Influential observations (IPs) and small sample size can both have an impact on a selected fractional polynomial model. In this paper, we used simulated data with six continuous and four categorical predictors to illustrate approaches which can help to identify IPs with an influence on function selection and the MFP model. Approaches use leave-one or two-out and two related techniques for a multivariable assessment. In seven subsamples we also investigated the effects of sample size and model replicability. For better illustration, a structured profile was used to provide an overview of all analyses conducted. The results showed that one or more IPs can drive the functions and models selected. In addition, with a small sample size, MFP might not be able to detect non-linear functions and the selected model might differ substantially from the true underlying model. However, if the sample size is sufficient and regression diagnostics are carefully conducted, MFP can be a suitable approach to select variables and functional forms for continuous variables.Comment: Main paper and a supplementary combine

Discrete dynamics by different concepts of majorization

For the description of complex dynamics of open systems an approach is given by different concepts of majorization (order structure). Discrete diffusion processes with both invariant object number and sink or source can be represented by the development of Young diagrams on lattices. As experimental example we investigated foam decay, dominated by sinks. The relevance of order structures for characterization of certain processes is discussed

The Apollonian decay of beer foam bubble size distribution and the lattices of young diagrams and their correlated mixing functions

We present different methods to characterise the decay of beer foam by measuring the foam heights and recording foam images as a function of time. It turns out that the foam decay does not follow a simple exponential law but a higher-order equation V(t)=a−bt−ct2.5, which can be explained as a superposition of two processes, that is, drainage and bubble rearrangement. The reorganisation of bubbles leads to the structure of an Apollonian gasket with a fractal dimension of D≈1.3058. Starting from foam images, we study the temporal development of bubble size distributions and give a model for the evolution towards the equilibrium state based upon the idea of Ernst Ruch to describe irreversible processes by lattices of Young diagrams. These lattices generally involve a partial order, but one can force a total order by mapping the diagrams onto the interval [0,1] using ordering functions such as the Shannon entropy. Several entropy-like and nonentropy-like mixing functions are discussed in comparison with the Young order, each of them giving a special prejudice for understanding the process of structure formation during beer foam decay