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

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

A review of spline function procedures in R

Background: With progress on both the theoretical and the computational fronts the use of spline modelling has become an established tool in statistical regression analysis. An important issue in spline modelling is the availability of user friendly, well documented software packages. Following the idea of the STRengthening Analytical Thinking for Observational Studies initiative to provide users with guidance documents on the application of statistical methods in observational research, the aim of this article is to provide an overview of the most widely used spline-based techniques and their implementation in R. Methods: In this work, we focus on the R Language for Statistical Computing which has become a hugely popular statistics software. We identified a set of packages that include functions for spline modelling within a regression framework. Using simulated and real data we provide an introduction to spline modelling and an overview of the most popular spline functions. Results: We present a series of simple scenarios of univariate data, where different basis functions are used to identify the correct functional form of an independent variable. Even in simple data, using routines from different packages would lead to different results. Conclusions: This work illustrate challenges that an analyst faces when working with data. Most differences can be attributed to the choice of hyper-parameters rather than the basis used. In fact an experienced user will know how to obtain a reasonable outcome, regardless of the type of spline used. However, many analysts do not have sufficient knowledge to use these powerful tools adequately and will need more guidance

Introduction to statistical simulations in health research

In health research, statistical methods are frequently used to address a wide variety of research questions. For almost every analytical challenge, different methods are available. But how do we choose between different methods and how do we judge whether the chosen method is appropriate for our specific study? Like in any science, in statistics, experiments can be run to find out which methods should be used under which circumstances. The main objective of this paper is to demonstrate that simulation studies, that is, experiments investigating synthetic data with known properties, are an invaluable tool for addressing these questions. We aim to provide a first introduction to simulation studies for data analysts or, more generally, for researchers involved at different levels in the analyses of health data, who (1) may rely on simulation studies published in statistical literature to choose their statistical methods and who, thus, need to understand the criteria of assessing the validity and relevance of simulation results and their interpretation; and/or (2) need to understand the basic principles of designing statistical simulations in order to efficiently collaborate with more experienced colleagues or start learning to conduct their own simulations. We illustrate the implementation of a simulation study and the interpretation of its results through a simple example inspired by recent literature, which is completely reproducible using the R-script available from online supplemental file 1

Systematic review of education and practical guidance on regression modeling for medical researchers who lack a strong statistical background: Study protocol

In the last decades, statistical methodology has developed rapidly, in particular in the field of regression modeling. Multivariable regression models are applied in almost all medical research projects. Therefore, the potential impact of statistical misconceptions within this field can be enormous Indeed, the current theoretical statistical knowledge is not always adequately transferred to the current practice in medical statistics. Some medical journals have identified this problem and published isolated statistical articles and even whole series thereof. In this systematic review, we aim to assess the current level of education on regression modeling that is provided to medical researchers via series of statistical articles published in medical journals. The present manuscript is a protocol for a systematic review that aims to assess which aspects of regression modeling are covered by statistical series published in medical journals that intend to train and guide applied medical researchers with limited statistical knowledge. Statistical paper series cannot easily be summarized and identified by common keywords in an electronic search engine like Scopus. We therefore identified series by a systematic request to statistical experts who are part or related to the STRATOS Initiative (STRengthening Analytical Thinking for Observational Studies). Within each identified article, two raters will independently check the content of the articles with respect to a predefined list of key aspects related to regression modeling. The content analysis of the topic-relevant articles will be performed using a predefined report form to assess the content as objectively as possible. Any disputes will be resolved by a third reviewer. Summary analyses will identify potential methodological gaps and misconceptions that may have an important impact on the quality of analyses in medical research. This review will thus provide a basis for future guidance papers and tutorials in the field of regression modeling which will enable medical researchers 1) to interpret publications in a correct way, 2) to perform basic statistical analyses in a correct way and 3) to identify situations when the help of a statistical expert is required

Statistical analysis of high-dimensional biomedical data: a gentle introduction to analytical goals, common approaches and challenges

International audienceBackground: In high-dimensional data (HDD) settings, the number of variables associated with each observation is very large. Prominent examples of HDD in biomedical research include omics data with a large number of variables such as many measurements across the genome, proteome, or metabolome, as well as electronic health records data that have large numbers of variables recorded for each patient. The statistical analysis of such data requires knowledge and experience, sometimes of complex methods adapted to the respective research questions. Methods: Advances in statistical methodology and machine learning methods offer new opportunities for innovative analyses of HDD, but at the same time require a deeper understanding of some fundamental statistical concepts. Topic group TG9 “High-dimensional data” of the STRATOS (STRengthening Analytical Thinking for Observational Studies) initiative provides guidance for the analysis of observational studies, addressing particular statistical challenges and opportunities for the analysis of studies involving HDD. In this overview, we discuss key aspects of HDD analysis to provide a gentle introduction for non-statisticians and for classically trained statisticians with little experience specific to HDD. Results: The paper is organized with respect to subtopics that are most relevant for the analysis of HDD, in particular initial data analysis, exploratory data analysis, multiple testing, and prediction. For each subtopic, main analytical goals in HDD settings are outlined. For each of these goals, basic explanations for some commonly used analysis methods are provided. Situations are identified where traditional statistical methods cannot, or should not, be used in the HDD setting, or where adequate analytic tools are still lacking. Many key references are provided. Conclusions: This review aims to provide a solid statistical foundation for researchers, including statisticians and non-statisticians, who are new to research with HDD or simply want to better evaluate and understand the results of HDD analyses

Doug Altman: Driving critical appraisal and improvements in the quality of methodological and medical research.

Doug Altman was a visionary leader and one of the most influential medical statisticians of the last 40 years. Based on a presentation in the "Invited session in memory of Doug Altman" at the 40th Annual Conference of the International Society for Clinical Biostatistics (ISCB) in Leuven, Belgium and our long-standing collaborations with Doug, we discuss his contributions to regression modeling, reporting, prognosis research, as well as some more general issues while acknowledging that we cannot cover the whole spectrum of Doug's considerable methodological output. His statement "To maximize the benefit to society, you need to not just do research but do it well" should be a driver for all researchers. To improve current and future research, we aim to summarize Doug's messages for these three topics