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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.

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.

Additional file 1.

Aims Annual opportunistic screening for cervical carcinoma has been done in Germany since 1971. The creation of this S3 guideline meets an important need, outlined in the National Cancer Plan, with regard to screening for cervical cancer, as this guideline aims to provide important information and support for planned organized screening for cervical cancer in Germany. Methods With the financial support of German Cancer Aid, 21 professional societies developed evidence-based statements and recommendations (classified using the GRADE system) for the screening, management and treatment of precancerous conditions of the cervix. Two independent scientific institutes compiled systematic reviews for this guideline. Recommendations The second part of this short summary deals with the triage, treatment and follow-up care of cervical dysplasia. With regard to those women who do not participate in screening, the guideline authors recommend sending out repeat invitation letters or an HPV self-collection kit. Colposcopy should be carried out for further investigation if cytology findings are Pap II-p and HPV test results are positive or if the results of an HPV 16 or HPV 18 screening test are positive. A single abnormal Pap smear should be triaged and investigated using HPV testing or p16/Ki67 dual staining.

Non‐linear exposure‐outcome relationships such as between body mass index (BMI) and mortality are common. They are best explored as continuous functions using individual participant data from multiple studies. We explore two two‐stage methods for meta‐analysis of such relationships, where the confounder‐adjusted relationship is first estimated in a non‐linear regression model in each study, then combined across studies. The “metacurve” approach combines the estimated curves using multiple meta‐analyses of the relative effect between a given exposure level and a reference level. The “mvmeta” approach combines the estimated model parameters in a single multivariate meta‐analysis. Both methods allow the exposure‐outcome relationship to differ across studies. Using theoretical arguments, we show that the methods differ most when covariate distributions differ across studies; using simulated data, we show that mvmeta gains precision but metacurve is more robust to model mis‐specification. We then compare the two methods using data from the Emerging Risk Factors Collaboration on BMI, coronary heart disease events, and all‐cause mortality (>80 cohorts, >18 000 events). For each outcome, we model BMI using fractional polynomials of degree 2 in each study, with adjustment for confounders. For metacurve, the powers defining the fractional polynomials may be study‐specific or common across studies. For coronary heart disease, metacurve with common powers and mvmeta correctly identify a small increase in risk in the lowest levels of BMI, but metacurve with study‐specific powers does not. For all‐cause mortality, all methods identify a steep U‐shape. The metacurve and mvmeta methods perform well in combining complex exposure‐disease relationships across studies.

The validity and practical utility of observational medical research depends critically on good study design, appropriate statistical analysis methods, accurate interpretation of results, and consideration of sources of potential bias in the data. Statistical methodology has seen substantial development[for full text, please go to the a.m. URL], 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

Willi Sauerbrei on behalf of TG2. 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 full text, please go to the a.m. URL], 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

Background: Over the last two decades combination of variable selection and shrinkage has grown in popularity due to the need to correct for overestimation bias and to improve the prediction accuracy of a model. Several statistical approaches have been developed such as the non-negative garrote (NNG)[for full text, please go to the a.m. URL], 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

Additional file 1. Web supplement.

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. Electronic supplementary material The online version of this article (10.1186/s12874-019-0802-0) contains supplementary material, which is available to authorized users.

Non-linear exposure-outcome relationships such as between body mass index (BMI) and mortality are common. They are best explored as continuous functions using individual participant data from multiple studies. We explore two two-stage methods for meta-analysis of such relationships, where the confounder-adjusted relationship is first estimated in a non-linear regression model in each study, then combined across studies. The "metacurve" approach combines the estimated curves using multiple meta-analyses of the relative effect between a given exposure level and a reference level. The "mvmeta" approach combines the estimated model parameters in a single multivariate meta-analysis. Both methods allow the exposure-outcome relationship to differ across studies. Using theoretical arguments, we show that the methods differ most when covariate distributions differ across studies; using simulated data, we show that mvmeta gains precision but metacurve is more robust to model mis-specification. We then compare the two methods using data from the Emerging Risk Factors Collaboration on BMI, coronary heart disease events, and all-cause mortality (>80 cohorts, >18 000 events). For each outcome, we model BMI using fractional polynomials of degree 2 in each study, with adjustment for confounders. For metacurve, the powers defining the fractional polynomials may be study-specific or common across studies. For coronary heart disease, metacurve with common powers and mvmeta correctly identify a small increase in risk in the lowest levels of BMI, but metacurve with study-specific powers does not. For all-cause mortality, all methods identify a steep U-shape. The metacurve and mvmeta methods perform well in combining complex exposure-disease relationships across studies.

Appendix: R code. (PDF 57 kb)

This.pdf contains a short description of the GDC data set as well as some additional results. (PDF 208 kb)

Prediction models in health care use predictors to estimate for an individual the probability that a condition or disease is already present (diagnostic model) or will occur in the future (prognostic model). Publications on prediction models have become more common in recent years, and competing prediction models frequently exist for the same outcome or target population. Health care providers, guideline developers, and policymakers are often unsure which model to use or recommend, and in which persons or settings. Hence, systematic reviews of these studies are increasingly demanded, required, and performed. A key part of a systematic review of prediction models is examination of risk of bias and applicability to the intended population and setting. To help reviewers with this process, the authors developed PROBAST (Prediction model Risk Of Bias ASsessment Tool) for studies developing, validating, or updating (for example, extending) prediction models, both diagnostic and prognostic. PROBAST was developed through a consensus process involving a group of experts in the field. It includes 20 signaling questions across 4 domains (participants, predictors, outcome, and analysis). This explanation and elaboration document describes the rationale for including each domain and signaling question and guides researchers, reviewers, readers, and guideline developers in how to use them to assess risk of bias and applicability concerns. All concepts are illustrated with published examples across different topics. The latest version of the PROBAST checklist, accompanying documents, and filled-in examples can be downloaded from www.probast.org.

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. 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. 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.

For most types of studies in the health sciences reporting guidelines are available for many years. Nevertheless, there is convincing evidence that the quality of reporting is still poor. The REMARK guidelines for prognostic factor studies were published more than a decade ago and in the corresponding[zum vollständigen Text gelangen Sie über die oben angegebene URL], 62. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (GMDS)

Research questions have become more complex, stimulating continuous efforts to develop new and even more complex statistical methods. Tremendous progress in methodology for analyzing clinical and epidemiological studies has been made, but has it reached researchers who analyze observational studies?[zum vollständigen Text gelangen Sie über die oben angegebene URL], 62. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie e.V. (GMDS)

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.

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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.

In the last few years, increasing attention has been devoted to the problem of the stability of multivariable regression models, understood as the resistance of the model to small changes in the data on which it has been fitted. Resampling techniques, mainly based on the bootstrap, have been developed to address this issue. In particular, the approaches based on the idea of "inclusion frequency" consider the repeated implementation of a variable selection procedure, for example backward elimination, on several bootstrap samples. The analysis of the variables selected in each iteration provides useful information on the model stability and on the variables' importance. Recent findings, nevertheless, show possible pitfalls in the use of the bootstrap, and alternatives such as subsampling have started to be taken into consideration in the literature. Based on model selection frequencies and variable inclusion frequencies, we aim to empirically compare these two different resampling techniques, investigating the effect of their use in a model selection procedure for multivariable regression. We conduct our investigations by analyzing two real data examples and by performing a simulation study. Our results reveal some advantages in using a subsampling technique rather than the bootstrap in this context.

In biomedical literature numerous prediction models for clinical outcomes have been developed based either on clinical data or, more recently, on high-throughput molecular data (omics data). Prediction models based on both types of data, however, are less common, although some recent studies suggest that a suitable combination of clinical and molecular information may lead to models with better predictive abilities. This is probably due to the fact that it is not straightforward to combine data with different characteristics and dimensions (poorly characterized high dimensional omics data, well-investigated low dimensional clinical data). In this paper we analyze two publicly available datasets related to breast cancer and neuroblastoma, respectively, in order to show some possible ways to combine clinical and omics data into a prediction model of time-to-event outcome. Different strategies and statistical methods are exploited. The results are compared and discussed according to different criteria, including the discriminative ability of the models, computed on a validation dataset.

Background: With longer follow-up times, the proportional hazards assumption is questionable in the Cox model. Cox already suggested to include an interaction between a covariate and a function of time, i.e. a time-varying effect. Since then, several approaches have been proposed for modelling time-varying,[for full text, please go to the a.m. URL], Mainz//2011; 56. Jahrestagung der Deutschen Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie (gmds), 6. Jahrestagung der Deutschen Gesellschaft für Epidemiologie (DGEpi)

Assessing the instability of a multivariable model is important but is rarely done in practice. Model instability occurs when selected predictors—and for multivariable fractional polynomial modeling, selected functions of continuous predictors—are sensitive to small changes in the data. Bootstrap analysis is a useful technique for investigating variations among selected models in samples drawn at random with replacement. Such samples mimic datasets that are structurally similar to that under study and that could plausibly have arisen instead. The bootstrap inclusion fraction of a candidate variable usefully indicates the importance of the variable. We describe Stata tools for stability analysis in the context of the mfp command for multivariable model building. We offer practical guidance and illustrate the application of the tools to a study in prostate cancer.

There is increasing interest in the medical world in the possibility of tailoring treatment to the individual patient. Statistically, the relevant task is to identify interactions between covariates and treatments, such that the patient’s value of a given covariate influences how strongly (or even whether) they are likely to respond to a treatment. The most valuable data are obtained in randomized controlled clinical trials of novel treatments in comparison with a control treatment. We describe two techniques to detect and model such interactions. The first technique, multivariable fractional polynomials interaction, is based on fractional polynomials methodology, and provides a method of testing for continuous-bybinary interactions and by modeling the treatment effect as a function of a continuous covariate. The second technique, subpopulation treatment-effect pattern plot, aims to do something similar but is focused on producing a nonparametric estimate of the treatment effect, expressed graphically. Stata programs for both of these techniques are described. Real data for brain and breast cancer are used as examples.

Spline functions provide a useful and flexible basis for modeling relationships with continuous predictors. However, to limit instability and provide sensible regression models in the multivariable setting, a principled approach to model selection and function estimation is important. Here the multivariable fractional polynomials approach to model building is transferred to regression splines. The essential features are specifying a maximum acceptable complexity for each continuous function and applying a closed-test approach to each continuous predictor to simplify the model where possible. Important adjuncts are an initial choice of scale for continuous predictors (linear or logarithmic), which often helps one to generate realistic, parsimonious final models; a goodness-of-fit test for a parametric function of a predictor; and a preliminary predictor transformation to improve robustness.

An important aspect of cancer research is the development of better prognostic tools for clinicians. These tools aim at predicting the survival time outcome of patients. Such tools are crucial as they assist clinicians in the choice of the best treatment strategy for each patient. An accurate prognostic model could help to save patients from unnecessary treatments. This thesis is centred around the development of prognostic models in their three key aspects. These three aspects are the selection of relevant markers, the learning of the prognosis model itself and its validation. We proposed the Coxlogit model for feature selection from survival and classification data. Classification and survival prediction are two common tasks in cancer research. With the Coxlogit model, we propose to model together these two tasks to improve the prediction and the feature selection. The Coxlogit model can be seen as a regularized mixture of a Cox and logistic models. The relevance of a prognostic model is typically assessed with a hazard ratio between the predicted risk groups. We identified some limitations of the hazard ratio in this particular context. More precisely, it appears to be very sensitive to the choice of discretization of the risk scores and has extreme values with unbalanced risk groups. We investigate the effect of the discretization in risk groups for the hazard ratio and other related metrics. A new metric, the balanced hazard ratio, is also proposed to solve those issues. The biomedical part of this thesis investigates the use of hypoxia related gene signatures as potential prognostic markers. In controlled experiments, cell lines were submitted to normoxia, hypoxia and cycling hypoxia and then used to deduce molecular signatures. Promising prognosis results were found on real breast cancer data. Moreover, these hypoxia related gene signatures turn out to be an added value to the standard clinical prognostic models. (FSA - Sciences de l'ingénieur) -- UCL, 2015