# Publications

Please find below the full references of all papers mentioned. They are linked to the publishers' websites and PubMed if available where you will find (nearly) all abstracts.

Some papers are freely available.

Papers are listed in a categorized manner.

To give a better overview we refer to some papers in more than one category.

# Fractional polynomials

Ambler, G. and Royston, P. (2001): Fractional polynomial model selection procedures: investigation of Type I error rate, Journal of Statistical Computation and Simulation 69: 89–108. DOI

Becher, H., Lorenz, E., Royston, P. and Sauerbrei, W. (2012): Analysing covariates with spike at zero: a modified FP procedure and conceptual issues. Biometrical Journal 54 (5): 686–700. PubMed DOI

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

Royston, P. (2014): A smooth covariate rank transformation for use in regression models with a sigmoid dose-response function, Stata Journal 14: 329 – 341. Publisher

Royston, P. and Altman, D. G. (1994): Regression using fractional polynomials of continuous covariates: parsimonious parametric modelling (with discussion), Applied Statistics 43(3): 429–467. DOI

Royston, P. and Altman, D. G. (1997): Approximating statistical functions by using fractional polynomial regression, The Statistician 46: 411–422. DOI

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

Royston, P. and Sauerbrei, W. (2016): mfpa: extension of mfp using the acd covariate transformation for enhanced parametric multivariable modelling. Stata Journal 16(1): 72-87.

Royston, P., Sauerbrei, W. and Becher, H. (2010): Modelling continuous exposures with a ‘spike’ at zero: a new procedure based on fractional polynomials. Statistics in Medicine, 29: 1219-1227. PubMed DOI

Sauerbrei, W. and Royston, P. (2010): Continuous Variables: To Categorize or to Model? In: Reading, C. (Ed.): The 8th International Conference on Teaching Statistics- Data and Context in statistics education: Towards an evidence based society. International statistical Institute, Voorburg. Full Text from Publisher

# Variable selection

Augustin, N., Sauerbrei, W. and Schumacher, M: (2005): The practical utility of incorporating model selection uncertainty into prognostic models for survival data. Statistical Modelling, 5:95-118. DOI

Buchholz, A., Holländer, N. and Sauerbrei, W. (2008): On properties of predictors derived with a two-step bootstrap model averaging approach – A simulation study in the linear regression model. Computational Statistics and Data Analysis, 52:2778-2793. DOI

De Bin R., Janitza S., Sauerbrei W., Boulesteix A.L. (2016): Subsampling versus bootstrapping in resampling-based model selection for multivariable regression. Biometrics, 72(1): 272-280. DOI

Royston, P. and Sauerbrei, W. (2003): Stability of multivariable fractional polynomial models with selection of variables and transformations: a bootstrap investigation. Statistics in Medicine, 22:639 – 659. PubMed DOI

Sauerbrei, W. (1999): The use of resampling methods to simplify regression models in medical statistics, Applied Statistics, 48:313-329. DOI

Sauerbrei, W., Boulesteix, A.-L. and Binder, H. (2011): Stability investigations of multivariable regression models derived for low and high dimensional data. Journal of Biopharmaceutical Statistics, 21:1206-1231. PubMed DOI

Sauerbrei, W., Buchholz, A., Boulesteix, A.-L. and Binder, H. (2015): On stability issues in deriving multivariable regression models. Biometrical Journal, 57:531-555. PubMed DOI

Sauerbrei, W., Holländer, N. and Buchholz, A. (2008): Investigation about a screening step in model selection. Statistics and Computing, 18:195-208. DOI

Sauerbrei, W. and Schumacher, M. (1992): A Bootstrap Resampling Procedure for Model Building: Application to the Cox Regression Model, Statistics in Medicine, 11: 2093-2109. DOI

Shmueli, G. (2010). To explain or to predict?, Statistical Science 3, 289–310. DOI

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

Van Houwelingen, J. C. and Le Cessie, S. (1990): Predictive value of statistical models, Statistics in Medicine 9: 1303–1325. DOI

# MFP

Binder, H., Sauerbrei, W. and Royston, P. (2011): Multivariable model-building with continuous covariates: 1. Performance measures and simulation design, FDM-Preprint 105, University of Freiburg.

Binder, H., Sauerbrei, W. and Royston, P. (2011): Multivariable model-building with continuous covariates: 2. Comparison between splines and fractional polynomials, FDM-Preprint 106, University of Freiburg.

*These two FDM-Preprints give some more details about issues presented in the following paper:*

Binder, H., Sauerbrei, W. and Royston, P. (2013): Comparison between splines and fractional polynomials for multivariable model building with continuous covariates: a simulation study with continuous response, Statistics in Medicine. 32:2262-2277. PubMed DOI

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

Royston, P. and Sauerbrei, W. (2003): Stability of multivariable fractional polynomial models with selection of variables and transformations: a bootstrap investigation. Statistics in Medicine, 22:639 – 659. PubMed DOI

Royston, P. and Sauerbrei, W. (2005): Building multivariable regression models with continuous covariates in clinical epidemiology, with an emphasis on fractional polynomials. Methods of Information in Medicine, 44: 561-571. PubMed

Royston, P. and Sauerbrei, W. (2016): mfpa: extension of mfp using the acd covariate transformation for enhanced parametric multivariable modelling. Stata Journal 16(1): 72-87.

Sauerbrei, W. and 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. DOI

Sauerbrei, W. and Royston, P. (2011): Multivariable Fractional Polynomial Models, in: Lovric, M. (Ed.): International Encyclopedia of Statistical Science, Springer Berlin, p.899-902. Publisher

**Sauerbrei, W. and Royston, P. (2016). Multivariable Fractional Polynomial Models. Wiley StatsRef: Statistics Reference Online. 1–8. DOI**

Sauerbrei, W., Royston, P. and 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. PubMed DOI

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. PubMed DOI

Sauerbrei, W. and Royston, P. (2017): The Multivariable Fractional Polynomial Approach, with Thoughts about Opportunities and Challenges in Big Data. In: Hans-Joachim Mucha (Ed.)Big data clustering: Data preprocessing, variable selection, and dimension reduction. WIAS Report 29, Berlin: 36-54. PDF

Sauerbrei W, Abrahamowicz M, Altman DG, le Cessie S and Carpenter J on behalf of the STRATOS initiative. (2014): STRengthening Analytical Thinking for Observational Studies: the STRATOS initiative. Statistics in Medicine, 33: 5413-5432. DOI

# Interactions

### 1.MFPI

Altman, D.G., Lausen, B., Sauerbrei, W. and Schumacher, M. (1994): Dangers of using ‘Optimal’ cutpoints in the evaluation of prognostic factors. Journal of the National Cancer Institute, 86: 829-835. PubMed DOI

Bonetti, M. and Gelber, R.D. (2000): A graphical method to assess treatment–covariate interactions using the Cox model on subsets of the data, Statistics in Medicine 19: 2595–2609. PubMed DOI

Kasenda, B., Sauerbrei, W., Royston, P. and Briel, M. (2014): Investigation of continuous effect modifiers in a meta-analysis on higher versus lower PEEP in patients requiring mechanical ventilation - protocol of the ICEM study. Systematic Reviews, 3:46. PubMed DOI

Kasenda B., Sauerbrei W., Royston P., Mercat A., Slutsky AS., Cook D., Guyatt GH., Brochard L., Richard JCM., Stewart TE., Meade M., Briel M. (2016): Multivariable fractional polynomial interaction to investigate continuous effect modifiers in a meta-analysis on higher versus lower PEEP for patients with ARDS. BMJ Open; 6:e011148. DOI

Royston, P., Altman, D.G. and Sauerbrei, W. (2006): Dichotomizing continuous predictors in multiple regression: a bad idea. Statistics in Medicine, 25: 127-141. PubMed DOI

Royston, P. and Sauerbrei, W. (2004): A new approach to modelling interactions between treatment and continuous covariates in clinical trials by using fractional polynomials. Statistics in Medicine, 23:2509-2525. PubMed DOI

Royston, P. and Sauerbrei, W. (2008): Interactions between treatment and continuous covariates – a step towards individualizing therapy (Editorial).JCO, 26:1397-1399. Reply to a letter JCO, 26:3814-15. PubMed DOI

Royston, P. and Sauerbrei, W. (2013): Interaction of treatment with a continuous variable: simulation study of significance level for several methods of analysis. Statistics in Medicine, 32(22):3788-3803. PubMed DOI

Royston, P. and Sauerbrei, W. (2014): Interaction of treatment with a continuous variable: simulation study of power for several methods of analysis. Statistics in Medicine, 33: 4695-4708, PubMed DOI

Royston, P., Sauerbrei, W. and Ritchie, A. (2004): Is treatment with interferon-alpha effective in all patients with metastatic renal carcinoma? A new approach to the investigations of interactions. British Journal of Cancer, 90: 794-799. PubMed DOI

Sauerbrei, W., Royston, P. and Zapien, K. (2007): Detecting an interaction between treatment and a continuous covariate: a comparison of two approaches. Computational Statistics and Data Analysis, 51: 4054-4063. DOI

### 2.MFPT

Buchholz, A. (2010) Assessment of Time-Varying Long-Term Effects of Therapies and Prognostic Factors. Ph.D. Thesis, Technische Universität Dortmund, Dortmund. http://hdl.handle.net/2003/27342

Buchholz, A. and Sauerbrei, W. (2011): Comparison of procedures to assess non-linear and time- varying effects in multivariable models for survival data. Biometrical Journal, 53(2): 308–331. PubMed DOI

Buchholz, A., Sauerbrei, W. and Royston, P. (2014): A Measure for Assessing Functions of Time-Varying Effects in Survival Analysis. Open Journal of Statistics, 4, 977-998. DOI

Royston, P., Lambert, P.C. (2011): Flexible parametric survival analysis using Stata. Beyond the Cox model. College Station, TX: Stata Press. Publisher

Sauerbrei, W., Royston, P. and Look, M. (2007): A new proposal for multivariable modelling of time-varying effects in survival data based on fractional polynomial time-transformation. Biometrical Journal, 49: 453-473. PubMed DOI

# Meta-analysis

Blettner, M., Sauerbrei, W., Schlehofer, B., Scheuchenpflug, T. and Friedenreich, C. (1999): Traditional reviews, meta-analyses and pooled analyses in epidemiology, International Journal of Epidemiology, 28:1-9. PubMed DOI

Kasenda, B., Sauerbrei, W., Royston, P. and Briel, M. (2014): Investigation of continuous effect modifiers in a meta-analysis on higher versus lower PEEP in patients requiring mechanical ventilation - protocol of the ICEM study. Systematic Reviews, 3:46. PubMed DOI

Kasenda B., Sauerbrei W., Royston P., Mercat A., Slutsky AS., Cook D., Guyatt GH., Brochard L., Richard JCM., Stewart TE., Meade M., Briel M. (2016): Multivariable fractional polynomial interaction to investigate continuous effect modifiers in a meta-analysis on higher versus lower PEEP for patients with ARDS. BMJ Open; 6:e011148. DOI

Sauerbrei, W. and Royston, P. (2011): A new strategy for meta-analysis of continuous covariates in observational studies. Statistics in Medicine, 30(28):3341-3360. PubMed DOI

# Further papers

Binder, H., Sauerbrei, W. (2009): Stability analysis of an additive spline model for respiratory health data by using knot removal. Journal of the Royal Statistical Society, C (Applied Statistics), 58: 577-600. DOI

Dunkler, D., Sauerbrei, W. and Heinze, G. (2016): Global, Parameterwise and Joint Post-Estimation Shrinkage. Journal of Statistical Software, 69: 8. DOI

Sauerbrei, W. and Royston, P. (2007): Modelling to extract more information from clinical trials data: on some roles for the bootstrap. Statistics in Medicine, 26: 4989-5001. PubMed DOI

Schumacher, M., Holländer, N., Schwarzer, G., Binder, H. and Sauerbrei, W. (2012): Prognostic Factor Studies, in: Crowley, J. and Hoering, A., Handbook of Statistics in Clinical Oncology, Third Edition: Chapman and Hall/CRC, 415-470. Publisher

# Software

Benner, A. (2005): mfp: Multivariable fractional polynomials. R News, 5(2):20-23. PDF

Royston, P. (2014): A smooth covariate rank transformation for use in regression models with a sigmoid dose-response function. The Stata Journal, 14:329-341. Publisher

Royston, P. and Sauerbrei, W. (2007): Multivariable modelling with cubic regression splines: A principled approach. The Stata Journal, 7:45-70. Publisher

Royston, P. and Sauerbrei, W. (2009): Bootstrap assessment of the stability of multivariable models. The Stata Journal, 9:547-570. Publisher

Royston, P. and Sauerbrei, W. (2009): Two techniques for investigating interactions between treatment and continuous covariates in clinical trials. The Stata Journal, 9: 230-251. Publisher

Royston, P. and Sauerbrei, W. (2016): mfpa: extension of mfp using the acd covariate transformation of enhanced parametric multivariable modelling. The Stata Journal, 16: 72-87.

Sauerbrei, W., Meier-Hirmer, C., Benner, A. and 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. DOI