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Additional file 1.

Additional file 1. Web supplement.

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.

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

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