arXiv subjects

Willi Sauerbrei

Publications and source records attributed to Willi Sauerbrei.

7 recordsLinked to original sources

arXiv2026

Methods for adjusting for covariate measurement error in flexible modelling of functional form: results of a blinded, controlled neutral comparison simulation study

Covariate measurement error is pervasive in epidemiological research and distorts estimated exposure-outcome associations, yet correction methods have been studied almost exclusively under linear modelling assumptions. Their behaviour when the underlying association is non-linear and is itself estimated with flexible regression, remains poorly characterised. We report a blinded, multi-stage neutral comparison simulation study, conducted within the STRATOS initiative, evaluating measurement error correction coupled with flexible modelling of functional form. Six families of correction methods (pointwise and coefficient-based Simulation Extrapolation [SIMEX], Bayesian inference on the logit and risk scales, Multiple Imputation [MI], and Regression Calibration [RC]) were each combined with B-splines (BS), penalised splines (PS), fractional polynomials (FP), and natural splines (NS), yielding 23 analytic methods. Methods were applied to case-control data generated under five functional forms (J-shape, linear, two threshold models, and saturation) across simulated datasets spanning varying sample sizes, replication substudy sizes, error magnitudes, and error distributions, with classical additive error and a replication substudy for error calibration. Performance was assessed by the log mean squared error of the estimated function over the central 95 % of the exposure distribution. Pointwise SIMEX was the most accurate and most robust approach overall, followed by Bayesian methods and RC when paired with PS, FP, or NS; MI performed less well, and Bayesian estimation with unpenalised BS performed worst. PS, FP, and NS were near-equivalent, whereas BS was consistently inferior. No single method dominated across all scenarios, underscoring the value of sensitivity analyses.

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arXiv2026

Methods for adjusting for covariate measurement error in flexible modelling of functional form: designing a blinded, controlled neutral comparison simulation study

This article describes the design of a neutral comparison study in the context of empirical studies where the interest is in learning the functional relationship between a continuous errorprone exposure variable and a binary outcome. The performance of combinations of measurement error correction methods and flexible regression modeling techniques was compared using a simulation study. The project involved four independent teams, one devoted to data generation and evaluation, the other three to specific methods of measurement error correction (Simulation-Extrapolation, Regression-Calibration and Multiple imputation, Bayesian method). The study was conducted in three successive stages. In Stage 1, the first team simulated five datasets differing only by the true exposure-outcome functional form and distribution of true exposure. Furthermore, the implementation of flexible modeling methods (B-splines, P-splines, and fractional polynomials) was standardized. The three methods teams, blinded to the underlying data generation process, created the codes to implement their methods, and provided their results to the first team who evaluated them. These codes were then used by this team in the next Stages of the project. In Stage 2, the team simulated 150 additional datasets where other design parameters varied while using the same five exposureoutcome functions. Stage 3 consisted of simulating independent replications of each of the 150 scenarios considered in Stage 2 to quantify the sampling variance of the estimates. This work emphasizes the relevance of neutral comparison studies to fairly evaluate statistical methods aimed at addressing a complex analytical challenge, and demonstrates their feasibility through a large collaborative project.

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arXiv2025

Evaluating treatment effects on longitudinal outcomes with attrition due to death: Methods for a two-dimentional estimand with a case study in Quality of Life

When longitudinal outcomes are evaluated in mortal populations, their non-existence after death complicates the analysis and its causal interpretation. Where popular methods often merge longitudinal outcome and survival into one scale or otherwise try to circumvent the problem of mortality, some highly relevant questions require survival to be acknowledged as a unique condition. "\textit{What are my chances of survival}" and "\textit{What can I expect for my condition while still alive}" reflect the intrinsically two-dimensional outcome of survival and longitudinal outcome while-alive. We define a two-dimensional causal while-alive estimand for a point exposure and compare two methods for estimation in an observational setting. Regression-Standardization models survival and the observed longitudinal outcome before standardizing the latter to a target population weighted by its estimated survival. Alternatively, Inverse Probability of Treatment and Censoring Weighting weights the observed outcomes twice, to account for censoring and differences in baseline-case-mix. Both approaches rely on the same causal identification assumptions, but require different models to be correctly specified. With its potential to extrapolate, Regression-Standardization is more efficient when all assumptions are met. We show finite sample performance in a simulation study and apply the methods to a case study on quality of life in oncology.

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arXiv2025

A categorization of performance measures for estimated non-linear associations between an outcome and continuous predictors

In regression analysis, associations between continuous predictors and the outcome are often assumed to be linear. However, modeling the associations as non-linear can improve model fit. Many flexible modeling techniques, like (fractional) polynomials and spline-based approaches, are available. Such methods can be systematically compared in simulation studies, which require suitable performance measures to evaluate the accuracy of the estimated curves against the true data-generating functions. Although various measures have been proposed in the literature, no systematic overview exists so far. To fill this gap, we introduce a categorization of performance measures for evaluating estimated non-linear associations between an outcome and continuous predictors. This categorization includes many commonly used measures. The measures can not only be used in simulation studies, but also in application studies to compare different estimates to each other. We further illustrate and compare the behavior of different performance measures through some examples and a Shiny app.

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arXiv2022

Exhuming nonnegative garrote from oblivion using suitable initial estimates- illustration in low and high-dimensional real data

The nonnegative garrote (NNG) is among the first approaches that combine variable selection and shrinkage of regression estimates. When more than the derivation of a predictor is of interest, NNG has some conceptual advantages over the popular lasso. Nevertheless, NNG has received little attention. The original NNG relies on least-squares (OLS) estimates, which are highly variable in data with a high degree of multicollinearity (HDM) and do not exist in high-dimensional data (HDD). This might be the reason that NNG is not used in such data. Alternative initial estimates have been proposed but hardly used in practice. Analyzing three structurally different data sets, we demonstrated that NNG can also be applied in HDM and HDD and compared its performance with the lasso, adaptive lasso, relaxed lasso, and best subset selection in terms of variables selected, regression estimates, and prediction. Replacing OLS by ridge initial estimates in HDM and lasso initial estimates in HDD helped NNG select simpler models than competing approaches without much increase in prediction errors. Simpler models are easier to interpret, an important issue for descriptive modelling. Based on the limited experience from three datasets, we assume that the NNG can be a suitable alternative to the lasso and its extensions. Neutral comparison simulation studies are needed to better understand the properties of variable selection methods, compare them and derive guidance for practice.

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arXiv2022

Effects of Influential Points and Sample Size on the Selection and Replicability of Multivariable Fractional Polynomial Models

The multivariable fractional polynomial (MFP) procedure combines variable selection with a function selection procedure (FSP). For continuous variables, a closed test procedure is used to decide between no effect, linear, FP1 or FP2 functions. Influential observations (IPs) and small sample size can both have an impact on a selected fractional polynomial model. In this paper, we used simulated data with six continuous and four categorical predictors to illustrate approaches which can help to identify IPs with an influence on function selection and the MFP model. Approaches use leave-one or two-out and two related techniques for a multivariable assessment. In seven subsamples we also investigated the effects of sample size and model replicability. For better illustration, a structured profile was used to provide an overview of all analyses conducted. The results showed that one or more IPs can drive the functions and models selected. In addition, with a small sample size, MFP might not be able to detect non-linear functions and the selected model might differ substantially from the true underlying model. However, if the sample size is sufficient and regression diagnostics are carefully conducted, MFP can be a suitable approach to select variables and functional forms for continuous variables.

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arXiv2019

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

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.

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