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Statistical regression models are used for predicting outcomes based on the values of some predictor variables or for describing the association of an outcome with predictors. With a data set at hand, a regression model can be easily fit with standard software packages. This bears the risk that data analysts may rush to perform sophisticated analyses without sufficient knowledge of basic properties, associations in and errors of their data, leading to wrong interpretation and presentation of the modeling results that lacks clarity. Ignorance about special features of the data such as redundancies or particular distributions may even invalidate the chosen analysis strategy. Initial data analysis (IDA) is prerequisite to regression analyses as it provides knowledge about the data needed to confirm the appropriateness of or to refine a chosen model building strategy, to interpret the modeling results correctly, and to guide the presentation of modeling results. In order to facilitate reproducibility, IDA needs to be preplanned, an IDA plan should be included in the general statistical analysis plan of a research project, and results should be well documented. Biased statistical inference of the final regression model can be minimized if IDA abstains from evaluating associations of outcome and predictors, a key principle of IDA. We give advice on which aspects to consider in an IDA plan for data screening in the context of regression modeling to supplement the statistical analysis plan. We illustrate this IDA plan for data screening in an example of a typical diagnostic modeling project and give recommendations for data visualizations., (© 2024. The Author(s).)

Quantitative bias analysis (QBA) permits assessment of the expected impact of various imperfections of the available data on the results and conclusions of a particular real-world study. This article extends QBA methodology to multivariable time-to-event analyses with right-censored endpoints, possibly including time-varying exposures or covariates. The proposed approach employs data-driven simulations, which preserve important features of the data at hand while offering flexibility in controlling the parameters and assumptions that may affect the results. First, the steps required to perform data-driven simulations are described, and then two examples of real-world time-to-event analyses illustrate their implementation and the insights they may offer. The first example focuses on the omission of an important time-invariant predictor of the outcome in a prognostic study of cancer mortality, and permits separating the expected impact of confounding bias from non-collapsibility. The second example assesses how imprecise timing of an interval-censored event - ascertained only at sparse times of clinic visits - affects its estimated association with a time-varying drug exposure. The simulation results also provide a basis for comparing the performance of two alternative strategies for imputing the unknown event times in this setting. The R scripts that permit the reproduction of our examples are provided., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

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., (© 2023. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.)

Patient-reported outcomes (PROs) are increasingly used in single-arm cancer studies. We reviewed 60 papers published between 2018 and 2021 of single-arm studies of cancer treatment with PRO data for current practice on design, analysis, reporting, and interpretation. We further examined the studies' handling of potential bias and how they informed decision making. Most studies (58; 97%) analysed PROs without stating a predefined research hypothesis. 13 (22%) of the 60 studies used a PRO as a primary or co-primary endpoint. Definitions of PRO objectives, study population, endpoints, and missing data strategies varied widely. 23 studies (38%) compared the PRO data with external information, most often by using a clinically important difference value; one study used a historical control group. Appropriateness of methods to handle missing data and intercurrent events (including death) were seldom discussed. Most studies (51; 85%) concluded that PRO results supported treatment. Conducting and reporting of PROs in cancer single-arm studies need standards and a critical discussion of statistical methods and possible biases. These findings will guide the Setting International Standards in Analysing Patient-Reported Outcomes and Quality of Life Data in Cancer Clinical Trials-Innovative Medicines Initiative (SISAQOL-IMI) in developing recommendations for the use of PRO-measures in single-arm studies., Competing Interests: Declaration of interests This publication reflects the views of the individual authors and should not be construed to represent official views or policies of the European Medicines Agency, the US Food and Drug Administration, US National Cancer Institute, Medicines and Healthcare Products Regulatory Agency, Institute for Quality and Efficiency in Health Care, Health Canada, the Norwegian Medicines Agency, the American Society of Clinical Oncology or the European Society for Medical Oncology, or any other institution, organisation, or entity. This publication reflects the authors’ view and neither Innovative Medicines Initiative nor the European Federation of Pharmaceutical Industries and Associations are responsible for any use that might be made of the information contained therein. JCR reports payments for clinical lessons for neurologists by IMeedu Het Centrale Brein, support for attending the European Epilepsy Congress (Geneva; July, 2022) by Arvelle Therapeutics, and is an unpaid chair of the European Organisation for Research and Treatment of Cancer's Quality of Life Group, and unpaid member of the Scientific Advisory Board of the Dutch Epilepsy Foundation. AR is currently an employee of Modus Outcomes. SR is a current employee of Pfizer and a previous employee of Novartis Pharma. RS is a current employee of Pfizer. All other authors declare no competing interests., (Copyright © 2023 Elsevier Ltd. All rights reserved.)

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., (© 2023. The Author(s).)

In 2005, several experts in tumor biomarker research publishe the REporting recommendations for Tumor MARKer prognostic studies (REMARK) criteria. Coupled with the subsequent Biospecimen Reporting for Improved Study Quality (BRISQ) criteria, these initiatives provide a framework for transparently reporting of the methods of study conduct and analyses., (© 2022. This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply.)

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., Competing Interests: The authors have declared that no competing interests exist.

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., (© 2022. The Author(s).)

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., (© 2022. The Author(s).)

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., Competing Interests: The authors have declared that no competing interests exist.

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.

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., (© 2020 The Authors. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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., Competing Interests: The authors have declared that no competing interests exist.

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., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2020. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

Data integration, i.e. the use of different sources of information for data analysis, is becoming one of the most important topics in modern statistics. Especially in, but not limited to, biomedical applications, a relevant issue is the combination of low-dimensional (e.g. clinical data) and high-dimensional (e.g. molecular data such as gene expressions) data sources in a prediction model. Not only the different characteristics of the data, but also the complex correlation structure within and between the two data sources, pose challenging issues. In this paper, we investigate these issues via simulations, providing some useful insight into strategies to combine low- and high-dimensional data in a regression prediction model. In particular, we focus on the effect of the correlation structure on the results, while accounting for the influence of our specific choices in the design of the simulation study., (© The Author(s) 2019. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.)

Background: Most randomized controlled trials (RCTs) and meta-analyses of RCTs examine effect modification (also called a subgroup effect or interaction), in which the effect of an intervention varies by another variable (e.g., age or disease severity). Assessing the credibility of an apparent effect modification presents challenges; therefore, we developed the Instrument for assessing the Credibility of Effect Modification Analyses (ICEMAN)., Methods: To develop ICEMAN, we established a detailed concept; identified candidate credibility considerations in a systematic survey of the literature; together with experts, performed a consensus study to identify key considerations and develop them into instrument items; and refined the instrument based on feedback from trial investigators, systematic review authors and journal editors, who applied drafts of ICEMAN to published claims of effect modification., Results: The final instrument consists of a set of preliminary considerations, core questions (5 for RCTs, 8 for meta-analyses) with 4 response options, 1 optional item for additional considerations and a rating of credibility on a visual analogue scale ranging from very low to high. An accompanying manual provides rationales, detailed instructions and examples from the literature. Seventeen potential users tested ICEMAN; their suggestions improved the user-friendliness of the instrument., Interpretation: The Instrument for assessing the Credibility of Effect Modification Analyses offers explicit guidance for investigators, systematic reviewers, journal editors and others considering making a claim of effect modification or interpreting a claim made by others., Competing Interests: Competing interests: None declared., (© 2020 Joule Inc. or its licensors.)

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.

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.

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., (© 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

Aims Annual opportunistic screening for cervical carcinoma has been carried out 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 the 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 first part of this short summary presents the pathological basis and considers various questions related to screening for cervical cancer. As also reported in earlier reviews, the meta-analysis by Kleijnen Systematic Reviews showed that HPV-based screening offers better protection against invasive cervical cancer compared to cytology-based screening. The authors of this guideline therefore recommend - in accordance with the guideline of the Joint National Committee of Germany (Gemeinsamer Bundesauschuss, G-BA) - that women aged 35 and above should be examined at regular intervals (at least every 3 years) and undergo HPV-based screening. Co-testing can also be carried out. Women between the ages of 20 and 35 should have cytological screening every 2 years.

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.

Background: We used two models to simulate a proposed noninferiority trial of radiotherapy (RT) omission in low-risk invasive breast cancer to illustrate how modeling could be used to predict the trial's outcomes, inform trial design, and contribute to practice debates., Methods: The proposed trial was a prospective randomized trial of no-RT vs RT in women age 40 to 74 years undergoing lumpectomy and endocrine therapy for hormone receptor-positive, human epidermal growth factor receptor 2-negative, stage I breast cancer with an Oncotype DX score of 18 or lower. The primary endpoint was recurrence-free interval (RFI), including locoregional recurrence, distant recurrence, and breast cancer death. Noninferiority required the two-sided 90% confidence interval of the RFI hazard ratio (HR) for no-RT vs RT to be entirely below 1.7. Model inputs included published data. The trial was simulated 1000 times, and results were summarized as percent concluding noninferiority and mean (standard deviation) of hazard ratios for Model GE and Model M, respectively., Results: Noninferiority was demonstrated in 18.0% and 3.7% for the two models. The respective means (SD) of the RFI hazard ratios were 1.8 (0.7) and 2.4 (0.9); most were locoregional recurrences. The mean five-year RFI rates for no-RT vs RT (SD) were 92.7% (2.9%) vs 95.5% (2.2%) and 88.4% (2.0%) vs 94.5% (1.6%). Both models showed little or no difference in breast cancer-specific or overall survival. Alternative definitions of low risk based on combinations of age and grade produced similar results., Conclusions: The proposed trial was unlikely to show noninferiority of omitting radiotherapy even using alternative definitions of low-risk, as the endpoint included local recurrence. Future trials regarding radiotherapy should address absolute reduction in recurrence and impact of type of recurrence on the patient.

Background: Radiotherapy after breast conservation has become the standard of care. Prior meta-analyses on effects of radiotherapy predated availability of gene expression profiling (GEP) to assess recurrence risk and/or did not include all relevant outcomes. This analysis used GEP information with pooled individual-level data to evaluate the impact of omitting radiotherapy on recurrence and mortality., Methods: We considered trials that evaluated or administered radiotherapy after lumpectomy in women with low-risk breast cancer. Women included had undergone lumpectomy and were treated with hormonal therapy for stage I, ER+ and/or PR+, HER2- breast cancer with Oncotype scores no greater than 18. Recurrence-free interval (RFI), type of RFI (locoregional or distant), and breast cancer-specific and overall survival were compared between no radiotherapy and radiotherapy using adjusted Cox models. All statistical tests were two-sided., Results: The final sample included 1778 women from seven trials. Omission of radiotherapy was associated with an overall adjusted hazard ratio of 2.59 (95% confidence interval [CI] = 1.38 to 4.89, P = .003) for RFI. There was a statistically significant increase in any first locoregional recurrence (P = .001), but not distant recurrence events (P = .90), or breast cancer-specific (P = .85) or overall survival (P = .61). Five-year RFI rate was high (93.5% for no radiotherapy vs 97.9% for radiotherapy; absolute reduction = 4.4%, 95% CI = 0.7% to 8.1%, P = .03). The effects of radiotherapy varied across subgroups, with lower RFI rates for those with Oncotype scores of less than 11 (vs 11-18), older (vs younger), and ER+/PR+ status (vs other)., Conclusions: Omission of radiotherapy in hormone-sensitive patients with low recurrence risk may lead to a modest increase in locoregional recurrence event rates, but does not appear to increase the rate of distant recurrence or death.

Background: Cancer prognostic biomarkers have shown disappointing clinical applicability. The objective of this study was to classify and estimate how study results are overinterpreted and misreported in prognostic factor studies in oncology., Methods: This systematic review focused on 17 oncology journals with an impact factor above 7. PubMed was searched for primary clinical studies published in 2015, evaluating prognostic factors. We developed a classification system, focusing on three domains: misleading reporting (selective, incomplete reporting, misreporting), misleading interpretation (unreliable statistical analysis, spin) and misleading extrapolation of the results (claiming irrelevant clinical applicability, ignoring uncertainty)., Results: Our search identified 10,844 articles. The 98 studies included investigated a median of two prognostic factors (Q1-Q3, 1-7). The prognostic factors' effects were selectively and incompletely reported in 35/98 and 24/98 full texts, respectively. Twenty-nine articles used linguistic spin in the form of strong statements. Linguistic spin rejecting non-significant results was found in 34 full-text results and 15 abstract results sections. One in five articles had discussion and/or abstract conclusions that were inconsistent with the study findings. Sixteen reports had discrepancies between their full-text and abstract conclusions., Conclusions: Our study provides evidence of frequent overinterpretation of findings of prognostic factor assessment in high-impact medical oncology journals.

The Reporting Recommendations for Tumor Marker Prognostic Studies (REMARK) were developed to address widespread deficiencies in the reporting of such studies. The REMARK checklist consists of 20 items to report for published tumor marker prognostic studies. A detailed paper was published explaining the rationale behind checklist items, providing positive examples and giving empirical evidence of the quality of reporting. REMARK provides a comprehensive overview to educate on good reporting and provide a valuable reference for the many issues to consider when designing, conducting, and analyzing tumor marker studies and prognostic studies in medicine in general. Despite support for REMARK from major cancer journals, prognostic factor research studies remain poorly reported. To encourage dissemination and uptake of REMARK, we have produced this considerably abridged version of the detailed explanatory manuscript, which may also serve as a brief guide to key issues for investigators planning tumor marker prognostic studies. To summarize the current situation, more recent papers investigating the quality of reporting and related reporting guidelines are cited, but otherwise the literature is not updated. Another important impetus for this paper is that it serves as a basis for literal translations into other languages. Translations will help to bring key information to a larger audience world-wide. Many more details can be found in the original paper.

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.

In most epidemiologic studies and in clinical research generally, there are variables with a spike at zero, namely variables for which a proportion of individuals have zero exposure (e.g., never smokers) and among those exposed the variable has a continuous distribution. Different options exist for modeling such variables, such as categorization where the nonexposed form the reference group, or ignoring the spike by including the variable in the regression model with or without some transformation or modeling procedures. It has been shown that such situations can be analyzed by adding a binary indicator (exposed/nonexposed) to the regression model, and a method based on fractional polynomials with which to estimate a suitable functional form for the positive portion of the spike-at-zero variable distribution has been developed. In this paper, we compare different approaches using data from 3 case-control studies carried out in Germany: the Mammary Carcinoma Risk Factor Investigation (MARIE), a breast cancer study conducted in 2002-2005 (Flesch-Janys et al., Int J Cancer. 2008;123(4):933-941); the Rhein-Neckar Larynx Study, a study of laryngeal cancer conducted in 1998-2000 (Dietz et al., Int J Cancer. 2004;108(6):907-911); and a lung cancer study conducted in 1988-1993 (Jöckel et al., Int J Epidemiol. 1998;27(4):549-560). Strengths and limitations of different procedures are demonstrated, and some recommendations for practical use are given., (© The Author 2017. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Objectives: A recent individual patient data (IPD) meta-analysis suggested that patients with moderate or severe acute respiratory distress syndrome (ARDS) benefit from higher positive end-expiratory pressure (PEEP) ventilation strategies. However, thresholds for continuous variables (eg, hypoxaemia) are often arbitrary and linearity assumptions in regression approaches may not hold; the multivariable fractional polynomial interaction (MFPI) approach can address both problems. The objective of this study was to apply the MFPI approach to investigate interactions between four continuous patient baseline variables and higher versus lower PEEP on clinical outcomes., Setting: Pooled data from three randomised trials in intensive care identified by a systematic review., Participants: 2299 patients with acute lung injury requiring mechanical ventilation., Interventions: Higher (N=1136) versus lower PEEP (N=1163) ventilation strategy., Outcome Measures: Prespecified outcomes included mortality, time to death and time-to-unassisted breathing. We examined the following continuous baseline characteristics as potential effect modifiers using MFPI: PaO2/FiO2 (arterial partial oxygen pressure/ fraction of inspired oxygen), oxygenation index, respiratory system compliance (tidal volume/(inspiratory plateau pressure-PEEP)) and body mass index (BMI)., Results: We found that for patients with PaO2/FiO2 below 150 mm Hg, but above 100 mm Hg or an oxygenation index above 12 (moderate ARDS), higher PEEP reduces hospital mortality, but the beneficial effect appears to level off for patients with very severe ARDS. Patients with mild ARDS (PaO2/FiO2 above 200 mm Hg or an oxygenation index below 10) do not seem to benefit from higher PEEP and might even be harmed. For patients with a respiratory system compliance above 40 mL/cm H2O or patients with a BMI above 35 kg/m(2), we found a trend towards reduced mortality with higher PEEP, but there is very weak statistical confidence in these findings., Conclusions: MFPI analyses suggest a nonlinear effect modification of higher PEEP ventilation by PaO2/FiO2 and oxygenation index with reduced mortality for some patients suffering from moderate ARDS., Study Registration Number: CRD42012003129., (Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/)

Objectives: When study groups fail to publish their results, a subsequent systematic review may come to incorrect conclusions when combining information only from published studies. p53 expression measured by immunohistochemistry is a potential prognostic factor in bladder cancer. Although numerous studies have been conducted, its role is still under debate. The assumption that unpublished studies too harbour evidence on this research topic leads to the question about the attributable effect when adding this information and comparing it with published data. Thus, the aim was to identify published and unpublished studies and to explore their differences potentially affecting the conclusion on its function as a prognostic biomarker., Design: Systematic review of published and unpublished studies assessing p53 in bladder cancer in Germany between 1993 and 2007., Results: The systematic search revealed 16 studies of which 11 (69%) have been published and 5 (31%) have not. Key reason for not publishing the results was a loss of interest of the investigators. There were no obviously larger differences between published and unpublished studies. However, a meaningful meta-analysis was not possible mainly due to the poor (ie, incomplete) reporting of study results., Conclusions: Within this well-defined population of studies, we could provide empirical evidence for the failure of study groups to publish their results that was mainly caused by loss of interest. This fact may be coresponsible for the role of p53 as a prognostic factor still being unclear. We consider p53 and the restriction to studies in Germany as a specific example, but the critical issues are probably similar for other prognostic factors and other countries., (Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/)

In epidemiology and clinical research, predictors often take value zero for a large amount of observations while the distribution of the remaining observations is continuous. These predictors are called variables with a spike at zero. Examples include smoking or alcohol consumption. Recently, an extension of the fractional polynomial (FP) procedure, a technique for modeling nonlinear relationships, was proposed to deal with such situations. To indicate whether or not a value is zero, a binary variable is added to the model. In a two stage procedure, called FP-spike, the necessity of the binary variable and/or the continuous FP function for the positive part are assessed for a suitable fit. In univariate analyses, the FP-spike procedure usually leads to functional relationships that are easy to interpret. This paper introduces four approaches for dealing with two variables with a spike at zero (SAZ). The methods depend on the bivariate distribution of zero and nonzero values. Bi-Sep is the simplest of the four bivariate approaches. It uses the univariate FP-spike procedure separately for the two SAZ variables. In Bi-D3, Bi-D1, and Bi-Sub, proportions of zeros in both variables are considered simultaneously in the binary indicators. Therefore, these strategies can account for correlated variables. The methods can be used for arbitrary distributions of the covariates. For illustration and comparison of results, data from a case-control study on laryngeal cancer, with smoking and alcohol intake as two SAZ variables, is considered. In addition, a possible extension to three or more SAZ variables is outlined. A combination of log-linear models for the analysis of the correlation in combination with the bivariate approaches is proposed., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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 recent 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 begun to be taken into consideration in the literature. Using model selection frequencies and variable inclusion frequencies, we empirically compare these two different resampling techniques, investigating the effect of their use in selected classical model selection procedures 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., (© 2015, The International Biometric Society.)

In a recent article, Royston (2015, Stata Journal 15: 275-291) introduced the approximate cumulative distribution (acd) transformation of a continuous covariate x as a route toward modeling a sigmoid relationship between x and an outcome variable. In this article, we extend the approach to multivariable modeling by modifying the standard Stata program mfp. The result is a new program, mfpa, that has all the features of mfp plus the ability to fit a new model for user-selected covariates that we call fp1( p 1 , p 2 ). The fp1( p 1 , p 2 ) model comprises the best-fitting combination of a dimension-one fractional polynomial (fp1) function of x and an fp1 function of acd ( x ). We describe a new model-selection algorithm called function-selection procedure with acd transformation, which uses significance testing to attempt to simplify an fp1( p 1 , p 2 ) model to a submodel, an fp1 or linear model in x or in acd ( x ). The function-selection procedure with acd transformation is related in concept to the fsp (fp function-selection procedure), which is an integral part of mfp and which is used to simplify a dimension-two (fp2) function. We describe the mfpa command and give univariable and multivariable examples with real data to demonstrate its use.

In many areas of science where empirical data are analyzed, a task is often to identify important variables with influence on an outcome. Most often this is done by using a variable selection strategy in the context of a multivariable regression model. Using a study on ozone effects in children (n = 496, 24 covariates), we will discuss aspects relevant for deriving a suitable model. With an emphasis on model stability, we will explore and illustrate differences between predictive models and explanatory models, the key role of stopping criteria, and the value of bootstrap resampling (with and without replacement). Bootstrap resampling will be used to assess variable selection stability, to derive a predictor that incorporates model uncertainty, check for influential points, and visualize the variable selection process. For the latter two tasks we adapt and extend recent approaches, such as stability paths, to serve our purposes. Based on earlier experiences and on results from the example, we will argue for simpler models and that predictions are usually very similar, irrespective of the selection method used. Important differences exist for the corresponding variances, and the model uncertainty concept helps to protect against serious underestimation of the variance of a predictor-derived data dependently. Results of stability investigations illustrate severe difficulties in the task of deriving a suitable explanatory model. It seems possible to identify a small number of variables with an important and probably true influence on the outcome, but too often several variables are included whose selection may be a result of chance or may depend on a small number of observations., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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., (Copyright © 2014 John Wiley & Sons, Ltd.)

The validity and practical utility of observational medical research depends critically on good study design, excellent data quality, appropriate statistical methods and accurate interpretation of results. Statistical methodology has seen substantial development in recent times. Unfortunately, many of these methodological developments are ignored in practice. Consequently, design and analysis of observational studies often exhibit serious weaknesses. The lack of guidance on vital practical issues discourages many applied researchers from using more sophisticated and possibly more appropriate methods when analyzing observational studies. Furthermore, many analyses are conducted by researchers with a relatively weak statistical background and limited experience in using statistical methodology and software. Consequently, even 'standard' analyses reported in the medical literature are often flawed, casting doubt on their results and conclusions. An efficient way to help researchers to keep up with recent methodological developments is to develop guidance documents that are spread to the research community at large. These observations led to the initiation of the strengthening analytical thinking for observational studies (STRATOS) initiative, a large collaboration of experts in many different areas of biostatistical research. The objective of STRATOS is to provide accessible and accurate guidance in the design and analysis of observational studies. The guidance is intended for applied statisticians and other data analysts with varying levels of statistical education, experience and interests. In this article, we introduce the STRATOS initiative and its main aims, present the need for guidance documents and outline the planned approach and progress so far. We encourage other biostatisticians to become involved., (© 2014 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

In a large simulation study reported in a companion paper, we investigated the significance levels of 21 methods for investigating interactions between binary treatment and a continuous covariate in a randomised controlled trial. Several of the methods were shown to have inflated type 1 errors. In the present paper, we report the second part of the simulation study in which we investigated the power of the interaction procedures for two sample sizes and with two distributions of the covariate (well and badly behaved). We studied several methods involving categorisation and others in which the covariate was kept continuous, including fractional polynomials and splines. We believe that the results provide sufficient evidence to recommend the multivariable fractional polynomial interaction procedure as a suitable approach to investigate interactions of treatment with a continuous variable. If subject-matter knowledge gives good arguments for a non-monotone treatment effect function, we propose to use a second-degree fractional polynomial approach, but otherwise a first-degree fractional polynomial (FP1) function with added flexibility (FLEX3) is the method of choice. The FP1 class includes the linear function, and the selected functions are simple, understandable, and transferable. Furthermore, software is available. We caution that investigation of interactions in one dataset can only be interpreted in a hypothesis-generating sense and needs validation in new data., (Copyright © 2014 John Wiley & Sons, Ltd.)

Background: Categorizing an inherently continuous predictor in prognostic analyses raises several critical methodological issues: dependence of the statistical significance on the number and position of the chosen cut-point(s), loss of statistical power, and faulty interpretation of the results if a non-linear association is incorrectly assumed to be linear. This also applies to a therapeutic context where investigators of randomized clinical trials (RCTs) are interested in interactions between treatment assignment and one or more continuous predictors., Methods/design: Our goal is to apply the multivariable fractional polynomial interaction (MFPI) approach to investigate interactions between continuous patient baseline variables and the allocated treatment in an individual patient data meta-analysis of three RCTs (N = 2,299) from the intensive care field. For each study, MFPI will provide a continuous treatment effect function. Functions from each of the three studies will be averaged by a novel meta-analysis approach for functions. We will plot treatment effect functions separately for each study and also the averaged function. The averaged function with a related confidence interval will provide a suitable basis to assess whether a continuous patient characteristic modifies the treatment comparison and may be relevant for clinical decision-making. The compared interventions will be a higher or lower positive end-expiratory pressure (PEEP) ventilation strategy in patients requiring mechanical ventilation. The continuous baseline variables body mass index, PaO2/FiO2, respiratory compliance, and oxygenation index will be the investigated potential effect modifiers. Clinical outcomes for this analysis will be in-hospital mortality, time to death, time to unassisted breathing, and pneumothorax., Discussion: This project will be the first meta-analysis to combine continuous treatment effect functions derived by the MFPI procedure separately in each of several RCTs. Such an approach requires individual patient data (IPD). They are available from an earlier IPD meta-analysis using different methods for analysis. This new analysis strategy allows assessing whether treatment effects interact with continuous baseline patient characteristics and avoids categorization-based subgroup analyses. These interaction analyses of the present study will be exploratory in nature. However, they may help to foster future research using the MFPI approach to improve interaction analyses of continuous predictors in RCTs and IPD meta-analyses. This study is registered in PROSPERO (CRD42012003129).

Interactions between treatments and covariates in RCTs are a key topic. Standard methods for modelling treatment-covariate interactions with continuous covariates are categorisation or linear functions. Both approaches are easily criticised, but for different reasons. Multivariable fractional polynomial interactions, an approach based on fractional polynomials with the linear interaction model as the simplest special case, was proposed. Four variants of multivariable fractional polynomial interaction (FLEX1-FLEX4), allowing varying flexibility in functional form, were suggested. However, their properties are unknown, and comparisons with other procedures are unavailable. Additionally, we consider various methods based on categorisation and on cubic regression splines. We present the results of a simulation study to determine the significance level (probability of a type 1 error) of various tests for interaction between a binary covariate ('treatment effect') and a continuous covariate in univariate analysis. We consider a simplified setting in which the response variable is conditionally normally distributed, given the continuous covariate. We consider two main cases with the covariate distribution well behaved (approximately symmetric) or badly behaved (positively skewed). We construct nine scenarios with different functional forms for the main effect. In the well-behaved case, significance levels are in general acceptably close to nominal and are slightly better for the larger sample size (n = 250 and 500 were investigated). In the badly behaved case, departures from nominal are more pronounced for several approaches. For a final assessment of these results and recommendations for practice, a study of power is needed., (Copyright © 2013 John Wiley & Sons, Ltd.)

In observational studies, many continuous or categorical covariates may be related to an outcome. Various spline-based procedures or the multivariable fractional polynomial (MFP) procedure can be used to identify important variables and functional forms for continuous covariates. This is the main aim of an explanatory model, as opposed to a model only for prediction. The type of analysis often guides the complexity of the final model. Spline-based procedures and MFP have tuning parameters for choosing the required complexity. To compare model selection approaches, we perform a simulation study in the linear regression context based on a data structure intended to reflect realistic biomedical data. We vary the sample size, variance explained and complexity parameters for model selection. We consider 15 variables. A sample size of 200 (1000) and R(2)  = 0.2 (0.8) is the scenario with the smallest (largest) amount of information. For assessing performance, we consider prediction error, correct and incorrect inclusion of covariates, qualitative measures for judging selected functional forms and further novel criteria. From limited information, a suitable explanatory model cannot be obtained. Prediction performance from all types of models is similar. With a medium amount of information, MFP performs better than splines on several criteria. MFP better recovers simpler functions, whereas splines better recover more complex functions. For a large amount of information and no local structure, MFP and the spline procedures often select similar explanatory models., (Copyright © 2012 John Wiley & Sons, Ltd.)