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      State of the art in selection of variables and functional forms in multivariable analysis—outstanding issues

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          Abstract

          Background

          How to select variables and identify functional forms for continuous variables is a key concern when creating a multivariable model. Ad hoc ‘traditional’ approaches to variable selection have been in use for at least 50 years. Similarly, methods for determining functional forms for continuous variables were first suggested many years ago. More recently, many alternative approaches to address these two challenges have been proposed, but knowledge of their properties and meaningful comparisons between them are scarce. To define a state of the art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge, many outstanding issues in multivariable modelling remain. Our main aims are to identify and illustrate such gaps in the literature and present them at a moderate technical level to the wide community of practitioners, researchers and students of statistics.

          Methods

          We briefly discuss general issues in building descriptive regression models, strategies for variable selection, different ways of choosing functional forms for continuous variables and methods for combining the selection of variables and functions. We discuss two examples, taken from the medical literature, to illustrate problems in the practice of modelling.

          Results

          Our overview revealed that there is not yet enough evidence on which to base recommendations for the selection of variables and functional forms in multivariable analysis. Such evidence may come from comparisons between alternative methods. In particular, we highlight seven important topics that require further investigation and make suggestions for the direction of further research.

          Conclusions

          Selection of variables and of functional forms are important topics in multivariable analysis. To define a state of the art and to provide evidence-supported guidance to researchers who have only a basic level of statistical knowledge, further comparative research is required.

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          Most cited references89

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          Ridge Regression: Biased Estimation for Nonorthogonal Problems

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            Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

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              The Adaptive Lasso and Its Oracle Properties

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                Author and article information

                Contributors
                wfs@imbi.uni-freiburg.de
                Journal
                Diagn Progn Res
                Diagn Progn Res
                Diagnostic and Prognostic Research
                BioMed Central (London )
                2397-7523
                2 April 2020
                2 April 2020
                2020
                : 4
                : 3
                Affiliations
                [1 ]GRID grid.5963.9, Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, , University of Freiburg, ; Freiburg, Germany
                [2 ]Data Science and Artificial Intelligence AstraZeneca, Cambridge, UK
                [3 ]GRID grid.10388.32, ISNI 0000 0001 2240 3300, Department of Medical Biometry, Informatics and Epidemiology, Faculty of Medicine, , University of Bonn, ; Bonn, Germany
                [4 ]GRID grid.14709.3b, ISNI 0000 0004 1936 8649, McGill University Health Centre, , McGill University, ; Montreal, Canada
                [5 ]GRID grid.13648.38, ISNI 0000 0001 2180 3484, Institute for Medical Biometry and Epidemiology, , University Medical Center Hamburg-Eppendorf, ; Hamburg, Germany
                [6 ]GRID grid.22937.3d, ISNI 0000 0000 9259 8492, Section for Clinical Biometrics, Center for Medical Statistics, Informatics and Intelligent Systems, , Medical University of Vienna, ; Vienna, Austria
                [7 ]GRID grid.152326.1, ISNI 0000 0001 2264 7217, Department of Biostatistics, School of Medicine, , Vanderbilt University, ; Nashville, TN USA
                [8 ]GRID grid.83440.3b, ISNI 0000000121901201, MRC Clinical Trials Unit at UCL, Institute of Clinical Trials and Methodology, , University College London, ; London, UK
                Article
                74
                10.1186/s41512-020-00074-3
                7114804
                32266321
                bd6d20b2-f283-4bc2-bf23-894481f53c62
                © The Author(s) 2020

                Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

                History
                : 6 November 2019
                : 18 March 2020
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                © The Author(s) 2020

                descriptive modelling,methods for variable selection,spline procedures,fractional polynomials,categorisation,bias,shrinkage,empirical evidence,stratos initiative

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