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Abstract Background 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.

Abstract Background The multivariable fractional polynomial (MFP) approach combines variable selection using backward elimination with a function selection procedure (FSP) for fractional polynomial (FP) functions. It is a relatively simple approach which can be easily understood without advanced training in statistical modeling. For continuous variables, a closed test procedure is used to decide between no effect, linear, FP1, or FP2 functions. Influential points (IPs) and small sample sizes can both have a strong impact on a selected function and MFP model. Methods 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 eight subsamples, we also investigated the effects of sample size and model replicability, the latter by using three non-overlapping subsamples with the same sample size. For better illustration, a structured profile was used to provide an overview of all analyses conducted. Results The results showed that one or more IPs can drive the functions and models selected. In addition, with a small sample size, MFP was not able to detect some non-linear functions and the selected model differed substantially from the true underlying model. However, when the sample size was relatively large and regression diagnostics were carefully conducted, MFP selected functions or models that were similar to the underlying true model. Conclusions For smaller sample size, IPs and low power are important reasons that the MFP approach may not be able to identify underlying functional relationships for continuous variables and selected models might differ substantially from the true model. However, for larger sample sizes, a carefully conducted MFP analysis is often a suitable way to select a multivariable regression model which includes continuous variables. In such a case, MFP can be the preferred approach to derive a multivariable descriptive model.

Abstract Background Factors contributing to the lack of understanding of research studies include poor reporting practices, such as selective reporting of statistically significant findings or insufficient methodological details. Systematic reviews have shown that prognostic factor studies continue to be poorly reported, even for important aspects, such as the effective sample size. The REMARK reporting guidelines support researchers in reporting key aspects of tumor marker prognostic studies. The REMARK profile was proposed to augment these guidelines to aid in structured reporting with an emphasis on including all aspects of analyses conducted. Methods A systematic search of prognostic factor studies was conducted, and fifteen studies published in 2015 were selected, three from each of five oncology journals. A paper was eligible for selection if it included survival outcomes and multivariable models were used in the statistical analyses. For each study, we summarized the key information in a REMARK profile consisting of details about the patient population with available variables and follow-up data, and a list of all analyses conducted. Results Structured profiles allow an easy assessment if reporting of a study only has weaknesses or if it is poor because many relevant details are missing. Studies had incomplete reporting of exclusion of patients, missing information about the number of events, or lacked details about statistical analyses, e.g., subgroup analyses in small populations without any information about the number of events. Profiles exhibit severe weaknesses in the reporting of more than 50% of the studies. The quality of analyses was not assessed, but some profiles exhibit several deficits at a glance. Conclusions A substantial part of prognostic factor studies is poorly reported and analyzed, with severe consequences for related systematic reviews and meta-analyses. We consider inadequate reporting of single studies as one of the most important reasons that the clinical relevance of most markers is still unclear after years of research and dozens of publications. We conclude that structured reporting is an important step to improve the quality of prognostic marker research and discuss its role in the context of selective reporting, meta-analysis, study registration, predefined statistical analysis plans, and improvement of marker research.

Abstract 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.

Abstract Background No standards exist for the handling and reporting of data quality in health research. This work introduces a data quality framework for observational health research data collections with supporting software implementations to facilitate harmonized data quality assessments. Methods Developments were guided by the evaluation of an existing data quality framework and literature reviews. Functions for the computation of data quality indicators were written in R. The concept and implementations are illustrated based on data from the population-based Study of Health in Pomerania (SHIP). Results The data quality framework comprises 34 data quality indicators. These target four aspects of data quality: compliance with pre-specified structural and technical requirements (integrity); presence of data values (completeness); inadmissible or uncertain data values and contradictions (consistency); unexpected distributions and associations (accuracy). R functions calculate data quality metrics based on the provided study data and metadata and R Markdown reports are generated. Guidance on the concept and tools is available through a dedicated website. Conclusions The presented data quality framework is the first of its kind for observational health research data collections that links a formal concept to implementations in R. The framework and tools facilitate harmonized data quality assessments in pursue of transparent and reproducible research. Application scenarios comprise data quality monitoring while a study is carried out as well as performing an initial data analysis before starting substantive scientific analyses but the developments are also of relevance beyond research.

In low-dimensional data and within the framework of a classical linear regression model, we intend to compare variable selection methods and investigate the role of shrinkage of regression estimates in a simulation study. Our primary aim is to build descriptive models that capture the data structure parsimoniously, while our secondary aim is to derive a prediction model. Simulation studies are an important tool in statistical methodology research if they are well designed, executed, and reported. However, bias in favor of an "own" preferred method is prevalent in most simulation studies in which a new method is proposed and compared with existing methods. To overcome such bias, neutral comparison studies, which disregard the superiority or inferiority of a particular method, have been proposed. In this paper, we designed a simulation study with key principles of neutral comparison studies in mind, though certain unintentional biases cannot be ruled out. To improve the design and reporting of a simulation study, we followed the recently proposed ADEMP structure, which entails defining the aims (A), data-generating mechanisms (D), estimand/target of analysis (E), methods (M), and performance measures (P). To ensure the reproducibility of results, we published the protocol before conducting the study. In addition, we presented earlier versions of the design to several experts whose feedback influenced certain aspects of the design. We will compare popular penalized regression methods (lasso, adaptive lasso, relaxed lasso, and nonnegative garrote) that combine variable selection and shrinkage with classical variable selection methods (best subset selection and backward elimination) with and without post-estimation shrinkage of parameter estimates.

Although regression models play a central role in the analysis of medical research projects, there still exist many misconceptions on various aspects of modeling leading to faulty analyses. Indeed, the rapidly developing statistical methodology and its recent advances in regression modeling do not seem to be adequately reflected in many medical publications. This problem of knowledge transfer from statistical research to application was identified by some medical journals, which have published series of statistical tutorials and (shorter) papers mainly addressing medical researchers. The aim of this review was to assess the current level of knowledge with regard to regression modeling contained in such statistical papers. We searched for target series by a request to international statistical experts. We identified 23 series including 57 topic-relevant articles. Within each article, two independent raters analyzed the content by investigating 44 predefined aspects on regression modeling. We assessed to what extent the aspects were explained and if examples, software advices, and recommendations for or against specific methods were given. Most series (21/23) included at least one article on multivariable regression. Logistic regression was the most frequently described regression type (19/23), followed by linear regression (18/23), Cox regression and survival models (12/23) and Poisson regression (3/23). Most general aspects on regression modeling, e.g. model assumptions, reporting and interpretation of regression results, were covered. We did not find many misconceptions or misleading recommendations, but we identified relevant gaps, in particular with respect to addressing nonlinear effects of continuous predictors, model specification and variable selection. Specific recommendations on software were rarely given. Statistical guidance should be developed for nonlinear effects, model specification and variable selection to better support medical researchers who perform or interpret regression analyses.

Abstract Background How to select variables and identify functional forms for continuous variables is a key concern when creating a multivariable model. Ad hoc ‘traditional’ approaches to variable selection have been in use for at least 50 years. Similarly, methods for determining functional forms for continuous variables were first suggested many years ago. More recently, many alternative approaches to address these two challenges have been proposed, but knowledge of their properties and meaningful comparisons between them are scarce. To define a state of the art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge, many outstanding issues in multivariable modelling remain. Our main aims are to identify and illustrate such gaps in the literature and present them at a moderate technical level to the wide community of practitioners, researchers and students of statistics. Methods We briefly discuss general issues in building descriptive regression models, strategies for variable selection, different ways of choosing functional forms for continuous variables and methods for combining the selection of variables and functions. We discuss two examples, taken from the medical literature, to illustrate problems in the practice of modelling. Results Our overview revealed that there is not yet enough evidence on which to base recommendations for the selection of variables and functional forms in multivariable analysis. Such evidence may come from comparisons between alternative methods. In particular, we highlight seven important topics that require further investigation and make suggestions for the direction of further research. Conclusions Selection of variables and of functional forms are important topics in multivariable analysis. To define a state of the art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge, further comparative research is required.

Abstract Background Omics data can be very informative in survival analysis and may improve the prognostic ability of classical models based on clinical risk factors for various diseases, for example breast cancer. Recent research has focused on integrating omics and clinical data, yet has often ignored the need for appropriate model building for clinical variables. Medical literature on classical prognostic scores, as well as biostatistical literature on appropriate model selection strategies for low dimensional (clinical) data, are often ignored in the context of omics research. The goal of this paper is to fill this methodological gap by investigating the added predictive value of gene expression data for models using varying amounts of clinical information. Methods We analyze two data sets from the field of survival prognosis of breast cancer patients. First, we construct several proportional hazards prediction models using varying amounts of clinical information based on established medical knowledge. These models are then used as a starting point (i.e. included as a clinical offset) for identifying informative gene expression variables using resampling procedures and penalized regression approaches (model based boosting and the LASSO). In order to assess the added predictive value of the gene signatures, measures of prediction accuracy and separation are examined on a validation data set for the clinical models and the models that combine the two sources of information. Results For one data set, we do not find any substantial added predictive value of the omics data when compared to clinical models. On the second data set, we identify a noticeable added predictive value, however only for scenarios where little or no clinical information is included in the modeling process. We find that including more clinical information can lead to a smaller number of selected omics predictors. Conclusions New research using omics data should include all available established medical knowledge in order to allow an adequate evaluation of the added predictive value of omics data. Including all relevant clinical information in the analysis might also lead to more parsimonious models. The developed procedure to assess the predictive value of the omics data can be readily applied to other scenarios.

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.

Abstract 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.

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.

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.

Although biomarkers are perceived as highly relevant for future clinical practice, few biomarkers reach clinical utility for several reasons. Among them, poor reporting of studies is one of the major problems. To aid improvement, reporting guidelines like REMARK for tumour marker prognostic (TMP) studies were introduced several years ago. The aims of this project were to assess whether reporting quality of TMP-studies improved in comparison to a previously conducted study assessing reporting quality of TMP-studies (PRE-study) and to assess whether articles citing REMARK (citing group) are better reported, in comparison to articles not citing REMARK (not-citing group). For the POST-study, recent articles citing and not citing REMARK (53 each) were identified in selected journals through systematic literature search and evaluated in same way as in the PRE-study. Ten of the 20 items of the REMARK checklist were evaluated and used to define an overall score of reporting quality. The observed overall scores were 53.4% (range: 10%-90%) for the PRE-study, 57.7% (range: 20%-100%) for the not-citing group and 58.1% (range: 30%-100%) for the citing group of the POST-study. While there is no difference between the two groups of the POST-study, the POST-study shows a slight but not relevant improvement in reporting relative to the PRE-study. Not all the articles of the citing group, cited REMARK appropriately. Irrespective of whether REMARK was cited, the overall score was slightly higher for articles published in journals requesting adherence to REMARK than for those published in journals not requesting it: 59.9% versus 51.9%, respectively. Several years after the introduction of REMARK, many key items of TMP-studies are still very poorly reported. A combined effort is needed from authors, editors, reviewers and methodologists to improve the current situation. Good reporting is not just nice to have but is essential for any research to be useful.

BACKGROUND:Prognostic factors and prognostic models play a key role in medical research and patient management. The Nottingham Prognostic Index (NPI) is a well-established prognostic classification scheme for patients with breast cancer. In a very simple way, it combines the information from tumor size, lymph node stage and tumor grade. For the resulting index cutpoints are proposed to classify it into three to six groups with different prognosis. As not all prognostic information from the three and other standard factors is used, we will consider improvement of the prognostic ability using suitable analysis approaches. METHODS AND FINDINGS:Reanalyzing overall survival data of 1560 patients from a clinical database by using multivariable fractional polynomials and further modern statistical methods we illustrate suitable multivariable modelling and methods to derive and assess the prognostic ability of an index. Using a REMARK type profile we summarize relevant steps of the analysis. Adding the information from hormonal receptor status and using the full information from the three NPI components, specifically concerning the number of positive lymph nodes, an extended NPI with improved prognostic ability is derived. CONCLUSIONS:The prognostic ability of even one of the best established prognostic index in medicine can be improved by using suitable statistical methodology to extract the full information from standard clinical data. This extended version of the NPI can serve as a benchmark to assess the added value of new information, ranging from a new single clinical marker to a derived index from omics data. An established benchmark would also help to harmonize the statistical analyses of such studies and protect against the propagation of many false promises concerning the prognostic value of new measurements. Statistical methods used are generally available and can be used for similar analyses in other diseases.

The REMARK (Reporting Recommendations for Tumor Marker Prognostic Studies) guideline includes a checklist which aims to improve the reporting of these types of studies. Here, we expand on the REMARK checklist to enhance its use and effectiveness through better understanding of the intent of each item and why the information is important to report. Each checklist item of the REMARK guideline is explained in detail and accompanied by published examples of good reporting. The paper provides a comprehensive overview to educate on good reporting and provide a valuable reference of issues to consider when designing, conducting, and analyzing tumor marker studies and prognostic studies in medicine in general.