Institut für Medizinische Biometrie und Statistik (IMBI)

Dozent:	Prof. Dr. Wilhelm Sauerbrei; Edwin Kipruto
Beginn:	Mittwoch, 21.01.2026
Ende:	Mittwoch, 11.02.2026
Uhrzeit:	14.15 - 17.30 Uhr
Ort:	Hörsaal, Stefan-Meier-Str. 26
VLVZ:	04LE58V-IMBI-StatRegRep-FA
Kommentar:	Language: English 4 days, 8 blocks (90 minutes). 5 blocks regression models, 1 block reporting, 2 blocks discussion of analyses from students. Registration required, deadline 08 January 2026. Please send an email to (Prof. Dr. Wilhelm Sauerbrei) giving: Name, surname, Department and Instution, student (y/n)

Inhalt:

Multivariable regression models are widely used in all areas of science in which empirical data are analyzed. In this lecture, we will discuss key issues of building various types of regression models such as linear regression, logistic regression, and models for survival data (Cox proportional hazards model).

We will concentrate on two components: variable selection to identify the subset of “important” variables, and identification of possible non-linearity in continuous variables. Many researchers assume a linear function for continuous variables, which may be problematic if the assumption is incorrect. This may prevent the detection of stronger effects or cause the effects to be mismodeled.

 Ad hoc ‘traditional’ approaches to variable selection have been in use for over 5 decades. Similarly, methods for determining functional forms for continuous variables were proposed many years ago. Meanwhile, many alternative approaches to address these two challenges have been developed, but knowledge of their properties and meaningful comparisons between them are scarce. We will provide an overview of variable selection procedures and discuss some open issues (Sauerbrei et al., 2020).

The multivariable fractional polynomial (MFP) approach (Royston and Sauerbrei, 2008; https://mfp.imbi.uni-freiburg.de/node/13) combines variable and functional form selection simultaneously. It is a relatively simple approach which can be understood without advanced training in statistical modeling. We will discuss key issues of MFP in details. Recently, a new R package, mfp2, was published, which implements the MFP approach. This package will be used to demonstrate MFP modelling in practice (Kipruto et al., 2023). At the end of day 3, we will provide a dataset to all participants to apply what they have learned. On day 4, we will discuss the analyses of this dataset.

In addition, we will briefly discuss the importance of good reporting, which helps in understanding the relevant steps of an analysis (Sauerbrei et al. 2023).  Participants should have a basic knowledge of linear regression models.

 

References

Variable Selection and MFP

Binder H., Sauerbrei W. (2010): Adding local components to global functions for continuous covariates in multivariable regression modeling. Statistics in Medicine, 29: 800-817.

Carlin, J. B., & Moreno‐Betancur, M. (2025). On the uses and abuses of regression models: a call for reform of statistical practice and teaching. Statistics in Medicine, 44(13-14), e10244.

Chatfield, C. (2002): Confessions of a pragmatic statistician, The Statisticican 51: 1-20.

Heinze, G., Baillie, M., Lusa, L., Sauerbrei, W., Schmidt, C.O., Harrell, F.E., Huebner, M. (2024). Regression without regrets –initial data analysis is a prerequisite for multivariable regression. BMC Medical Research Methodology 24. https://doi.org/10.1186/s12874-024-02294-3

Kipruto E, Sauerbrei W (2022) Comparison of variable selection procedures and investigation of the role of shrinkage in linear regression-protocol of a simulation study in low-dimensional data. PLOS ONE 17(10): e0271240. https://doi.org/10.1371/journal.pone.0271240

Kipruto, E., Kammer, M., Royston, P., & Sauerbrei, W (2023). mfp2: Multivariable Fractional Polynomial Models with Extensions. R package version 1.0.0, <https://CRAN.R-project.org/package=mfp2>.

Kipruto, E., Sauerbrei, W. (2022). Exhuming nonnegative garrote from oblivion using suitable initial estimates-illustration in low and high-dimensional real data. arXiv preprint arXiv:2210.15592. https://doi.org/10.48550/arXiv.2210.15592

Kipruto, E., Sauerbrei, W. (2024). Post‐Estimation Shrinkage in Full and Selected Linear Regression Models in Low‐Dimensional Data Revisited. Biometrical Journal 66. https://doi.org/10.1002/bimj.202300368

Kipruto, E., Sauerbrei, W. (2025). Unravelling Similarities and Differences Between Non-Negative Garrote and Adaptive Lasso: A Simulation Study in Low- and High-Dimensional Data. Stats 8, 70. https://doi.org/10.3390/stats8030070

Kipruto, Edwin, and Willi Sauerbrei. (2025). Evaluating Prediction Performance: A Simulation Study Comparing Penalized and Classical Variable Selection Methods in Low-Dimensional Data Applied Sciences 15, no. 13: 7443. https://doi.org/10.3390/app15137443

Perperoglou A, Sauerbrei W, Abrahamowicz M, Schmid M on behalf of TG2 of the STRATOS initiative (2019): A review of spline function procedures in R, BMC Medical Research Methodology, 19:46 doi: 10.1186/s12874-019-0666-3

Royston, P., Ambler, G., Sauerbrei, W. (1999): ‘The use of fractional polynomials to model continuous risk variables in epidemiology’ International Journal of Epidemiology, 28:964-974.

Royston, P., Sauerbrei, W. (2007): Improving the robustness of fractional polynomial models by preliminary covariate transformation: a pragmatic approach. Computational Statistics and Data Analysis, 51: 4240-4253.

Royston, P., & Sauerbrei, W. (2008). Multivariable model-building: a pragmatic approach to regression anaylsis based on fractional polynomials for modelling continuous variables. John Wiley & Sons

Sauerbrei, W. (1999): ‘The use of resampling methods to simplify regression models in  medical statistics’, Applied Statistics, 48:313-329. https://doi.org/10.1111/1467-9876.00155

 

Sauerbrei, W., Kipruto, E., Balmford, J. (2023). Effects of Influential Points and Sample Size on the Selection and Replicability of Multivariable Fractional Polynomial Models. Diagnostic and Prognostic Research, 7(1):7.

Sauerbrei, W., Meier-Hirmer, C., Benner, A., Royston, P. (2006): Multivariable regression model building by using fractional polynomials: description of SAS, STATA and R programs. Computational Statistics and Data Analysis, 50: 3464-3485.

Sauerbrei, W., Perperoglou, A., Schmid, M., Abrahamowicz, M., Becher, H., Binder, H., ... & TG2 of the STRATOS initiative (2020). State of the art in selection of variables and functional forms in multivariable analysis—outstanding issues. Diagnostic and prognostic research, 4, 1-18.

Sauerbrei W, Perperoglou A, Schmid M, Abrahamowicz M, Becher H, Binder H, Dunkler D, Harrell Jr. FE, Royston P, Heinze G for TG2 of the STRATOS initiative (2020). State of the art in selection of variables and functional forms in multivariable analysis - outstanding issues. Diagnostic and Prognostic Research, 4:3, 1-18. DOI: 10.1186/s41512-020-00074-3

Sauerbrei, W. and Royston, P. 2016. Multivariable Fractional Polynomial Models. Wiley StatsRef: Statistics Reference Online.  1–8. DOI: 10.1002/9781118445112.stat07861

Sauerbrei, W., Royston, P. (1999): ‘Building multivariable prognostic and diagnostic models: Transformation of the predictors by using fractional polynomials’. Journal of the Royal Statistical Society, A. 162:71-94; Corrigendum (2002), 165: 339-400.

Sauerbrei, W., Royston, P., Binder H (2007): Selection of important variables and determination of functional form for continuous predictors in multivariable model building. Statistics in Medicine, 26: 5512-5528.

Sauerbrei, W., Royston, P., Bojar, H., Schmoor, C., Schumacher, M. and the German Breast Cancer Study Group (GBSG) (1999): ‘Modelling the effects of standard prognostic factors in node positive breast cancer’, British Journal of Cancer, 79: 1752-1760.

Sauerbrei, W., Royston, P., & Kipruto, E. (2025). Multivariable Fractional Polynomial Models and Extensions. In International Encyclopedia of Statistical Science (pp. 1609-1616). Berlin, Heidelberg: Springer Berlin Heidelberg.

Sauerbrei, W., Schumacher, M. (1992): ‘A Bootstrap Resampling Procedure for Model Building: Application to the Cox Regression Model’, Statistics in Medicine, 11: 2093-2109. https://doi.org/10.1002/sim.4780111607

Sekula, P., Steinbrenner, I., Schultheiss, U. T., Valveny, N., Rebora, P., Halabi, S., Cadarette S. M., Riley, R. D., Collins, G. S., Sauerbrei, W. & Gail, M. H. (2025). Design aspects for prognostic factor studies. BMJ open, 15(8), e095065. https://doi.org/10.1136/bmjopen-2024-095065

Ullmann, T., Heinze, G., Abrahamowicz, M., Perperoglou, A., Sauerbrei, W., Schmid, M., Dunkler, D., 2025. A Systematic Categorization of Performance Measures for Estimated Non‐Linear Associations Between an Outcome and Continuous Predictors. WIREs Computational Statistics 17. https://doi.org/10.1002/wics.70042

Van Houwelingen H.C., Sauerbrei W. (2013): Cross-validation, shrinkage and variable selection in linear regression revisited. Open Journal of Statistics, 3: 79-102.
DOI: 10.4236/ojs.2013.32011.

 

Reporting

Altman DG, McShane LM, Sauerbrei W, Taube SE (2012) Reporting recommendations for tumor marker prognostic studies (REMARK): explanation and elaboration. In: PLoS Med 9(5): E 1001216 and in BMC Med 10 (1), 51. DOI: 10.1016/j.ejca.2005.03.032.

Hayes, D. F., Sauerbrei, W., & McShane, L. M. (2023). REMARK guidelines for tumour biomarker study reporting: a remarkable history. British Journal of Cancer, 1-3. https://doi.org/10.1038/s41416-022-02046-4

Kempf E, de Beyer JA, Cook J, Holmes J, Mohammed S, Nguyên L, Simera I, Trivella M, Altman DG, Hopewell S, Moons KG, Porcher R, Reitsma J, Sauerbrei W, Collins GS (2018): Overinterpretation and misreporting of prognostic factor studies in oncology: A systematic review.; Br J Cancer; 119(10): 1288-1296; doi: 10.1038/s41416-018-0305-5

Mallett S., Timmer A., Sauerbrei W., Altman D.G. (2010): Reporting of prognostic studies of tumor markers: a review of published articels in relation to REMARK guidelines. British Journal of Cancer, 102:173-180. DOI: 10.1038/sj.bjc.6605462

McShane, L.M., Altman, D.G., Sauerbrei, W. (2005): Identification of clinically useful cancer prognostic factors: What are we missing? (Editorial). Journal of the National Cancer Institute, 97: 1023-1025.  https://doi.org/10.1093/jnci/dji193

McShane, L.M., Altman, D.G., Sauerbrei, W., Taube, S.E., Gion, M., Clark, G.M. for the Statistics Subcommittee of the NCI-EORTC Working on Cancer Diagnostics (2005): REporting recommendations for tumor MARKer prognostic studies (REMARK). Journal of the National Cancer Institute, 97: 1180-1184. Simultaneous Publication in Journal of Clinical Oncology, Nature Clinical Practice Oncology, European Journal of Cancer, British Journal of Cancer and reprints in other journals in 2006.  https://doi.org/10.1093/jnci/dji237

Sauerbrei, W. (2005). Prognostic Factors – Confusion caused by bad quality of design, analysis and reporting of many studies. In: Bier H. (ed). Current Research in Head and Neck Cancer. Advances in Oto-Rhino-Laryngology. Basel, Karger, 62:184-200. https://doi.org/10.1159/000082508

Sauerbrei W, Haeussler T, Balmford J, Huebner M. Structured reporting to improve transparency of analyses in prognostic marker studies. BMC medicine. 2022 Dec;20(1):1-9. https://doi.org/10.1186/s12916-022-02304-5

Sauerbrei W, Taube SE, McShane LM, Cavenagh MM, Altman DG (2018). Reporting Recommendations for Tumor Marker Prognostic Studies (REMARK): An Abridged Explanation and Elaboration. J Natl Cancer Inst. 110(8): 803-811. DOI: 10.1093/jnci/djy088

Sekula, P., Mallett, S., Altman, D.G., Sauerbrei, W. (2017): Did the reporting of prognostic studies of tumour markers improve since the introduction of REMARK guideline? A comparison of reporting in published articles. PLoS ONE;12(6):e0178531. doi: 10.1371/journal.pone.0178531