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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.

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 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.)

Multivariable regression models can link a potentially large number of variables to various kinds of outcomes, such as continuous, binary, or time-to-event endpoints. Selection of important variables and selection of the functional form for continuous covariates are key parts of building such models but are notoriously difficult due to several reasons. Caused by multicollinearity between predictors and a limited amount of information in the data, (in)stability can be a serious issue of models selected. For applications with a moderate number of variables, resampling-based techniques have been developed for diagnosing and improving multivariable regression models. Deriving models for high-dimensional molecular data has led to the need for adapting these techniques to settings where the number of variables is much larger than the number of observations. Three studies with a time-to-event outcome, of which one has high-dimensional data, are used to illustrate several techniques. Investigations at the covariate level and at the predictor level are seen to provide considerable insight into model stability and performance. While some areas are indicated where resampling techniques for model building still need further refinement, our case studies illustrate that these techniques can already be recommended for wider use.

When global techniques, based on fractional polynomials (FPs), are employed for modeling potentially nonlinear effects of several continuous covariates on a response, accessible model equations are obtained. However, local features might be missed. Therefore, a procedure is introduced, which systematically checks model fits, obtained by the multivariable fractional polynomial (MFP) approach, for overlooked local features. Statistically significant local polynomials are then parsimoniously added. This approach, called MFP + L, is seen to result in an effective control of the Type I error with respect to the addition of local components in a small simulation study with univariate and multivariable settings. Prediction performance is compared with that of a penalized regression spline technique. In a setting unfavorable for FPs, the latter outperforms the MFP approach, if there is much information in the data. However, the addition of local features reduces this performance difference. There is only a small detrimental effect in settings where the MFP approach performs better. In an application example with children's respiratory health data, fits from the spline-based approach indicate many local features, but MFP + L adds only few significant features, which seem to have good support in the data. The proposed approach may be expected to be superior in settings with local features, but retains the good properties of the MFP approach in a large number of settings where global functions are sufficient.

In medical research, continuous variables are often converted into categorical variables by grouping values into two or more categories. We consider in detail issues pertaining to creating just two groups, a common approach in clinical research. We argue that the simplicity achieved is gained at a cost; dichotomization may create rather than avoid problems, notably a considerable loss of power and residual confounding. In addition, the use of a data-derived 'optimal' cutpoint leads to serious bias. We illustrate the impact of dichotomization of continuous predictor variables using as a detailed case study a randomized trial in primary biliary cirrhosis. Dichotomization of continuous data is unnecessary for statistical analysis and in particular should not be applied to explanatory variables in regression models., (Copyright 2005 John Wiley & Sons, Ltd.)

In epidemiology and clinical research, there is often a proportion of unexposed individuals resulting in zero values of exposure, meaning that some individuals are not exposed and those exposed have some continuous distribution. Examples are smoking or alcohol consumption. We will call these variables with a spike at zero (SAZ). In this paper, we performed a systematic investigation on how to model covariates with a SAZ and derived theoretical odds ratio functions for selected bivariate distributions. We consider the bivariate normal and bivariate log normal distribution with a SAZ. Both confounding and effect modification can be elegantly described by formalizing the covariance matrix given the binary outcome variable Y. To model the effect of these variables, we use a procedure based on fractional polynomials first introduced by Royston and Altman (1994, Applied Statistics 43: 429-467) and modified for the SAZ situation (Royston and Sauerbrei, 2008, Multivariable model-building: a pragmatic approach to regression analysis based on fractional polynomials for modelling continuous variables, Wiley; Becher et al., 2012, Biometrical Journal 54: 686-700). We aim to contribute to theory, practical procedures and application in epidemiology and clinical research to derive multivariable models for variables with a SAZ. As an example, we use data from a case-control study on lung cancer. [ABSTRACT FROM AUTHOR]

Objectives: We illustrate a recently proposed two-step bootstrap model averaging (bootstrap MA) approach to cope with model selection uncertainty. The predictive performance is investigated in an example and in a simulation study. Results are compared to those derived from other model selection methods.Methods: In the framework of the linear regression model we use the two-step bootstrap MA, which consists of a screening step to eliminate covariates thought to have no influence on the response, and a model-averaging step. We also apply the full model, variable selection using backward elimination based on Akaike's Information Criterion (AIC), the Bayes Information Criterion (BIC) and the bagging approach. The predictive performance is measured by the mean squared error (MSE) and the coverage of confidence intervals for the true response.Results: We obtained similar results for all approaches in the example. In the simulation the MSE was reduced by all approaches in comparison to the full model. The smallest values are obtained for bootstrap MA. Only the bootstrap MA and the full model correctly estimated the nominal coverage. The backward elimination procedures led to substantial underestimation and bagging to an overestimation of the true coverage. The screening step of bootstrap MA eliminates most of the unimportant factors.Conclusion: The new bootstrap MA approach shows promising results for predictive performance. It increases practical usefulness by eliminating unimportant factors in the screening step. [ABSTRACT FROM AUTHOR]

Objectives: In fitting regression models, data analysts must often choose a model based on several candidate predictor variables which may influence the outcome. Most analysts either assume a linear relationship for continuous predictors, or categorize them and postulate step functions. By contrast, we propose to model possible non-linearity in the relationship between the outcome and several continuous predictors by estimating smooth functions of the predictors. We aim to demonstrate that a structured approach based on fractional polynomials can give a broadly satisfactory practical solution to the problem of simultaneously identifying a subset of 'important' predictors and determining the functional relationship for continuous predictors.Methods: We discuss the background, and motivate and describe the multivariable fractional polynomial (MFP) approach to model selection from data which include continuous and categorical predictors. We compare our results with those from other approaches in examples. We present a small simulation study to compare the functional form of the relationship obtained by fitting fractional polynomials and splines to a single predictor variable.Results: We illustrate the advantages of the MFP approach over standard techniques of model construction in two real example datasets analyzed with logistic and Cox regression models, respectively. In the simulation study, fractional polynomial models had lower mean square error and more realistic behaviour than comparable spline models.Conclusions: In many practical situations, the MFP approach can satisfy the aim of finding models that fit the data well and also are simple, interpretable and potentially transportable to other settings. [ABSTRACT FROM AUTHOR]

A common strategy within the framework of regression models is the selection of variables with possible predictive value, which are incorporated in the regression model. Two recently proposed methods, Breiman's Garotte (BREIMAN, 1995) and Tibshirani's Lasso (TIBSHIRANI, 1996) try to combine variable selection and shrinkage. We compare these with pure variable selection and shrinkage procedures. We consider the backward elimination procedure as a typical variable selection procedure and as an example of a shrinkage procedure an approach of VAN HOUWELINGEN and LE CESSIE (1990). Additionally an extension of van Houwelingens and le Cessies approach proposed by SAUERBREI (1999) is considered. The ordinary least squares method is used as a reference. With the help of a simulation study we compare these approaches with respect to the distribution of the complexity of the selected model, the distribution of the shrinkage factors, selection bias, the bias and variance of the effect estimates and the average prediction error. [ABSTRACT FROM AUTHOR]

Describes a method of building multivariable prognostic and diagnostic models based on the transformation of the continuous predictors by using fractional polynomial regression functions. Steps involved in the derivation of the method.