Multiple linear regression modeling with values below a lower limit of quantification – a statistical method comparison

TL;DR

This paper compares statistical methods for handling values below a detection limit in multiple linear regression models, providing guidance for researchers dealing with censored data.

Contribution

The study provides a novel comparison of statistical methods for left-censored data in multiple linear regression settings.

Findings

The two compartment model performed best for independent variables with low collinearity.

Tobit model showed lowest bias for dependent variables with up to 80% censoring.

Abstract

Missing values occur in almost all real-world medical data. Sometimes, more information is available for the missing values due to technical measurement limits. This was also the case for some sports medical data set where several laboratory measurements below a lower limit of quantification (LLOQ) were faced and supposed to be used in a multiple linear regression model. When studying the literature, the problem arises in several disciplines (environmental epidemiology, pharmacokinetic studies etc.) and different statistical methods are suggested. However, only very limited work on a method comparison is available, especially in the multivariable linear regression settting.

Therefore, we compare statistical methods for addressing values below a LLOQ in multiple linear regression modeling by a simulation study. We consider both the case that the variable below the LLOQ is among one of the independent variables and that it is the dependent variable in the regression model. We also vary different underlying assumptions, such as distributions, sample sizes, proportions of missing values, correlations, or linearity assumptions.

Overall, the two compartment model showed the best performance in terms of bias and coverage when the LLOQ occurred in the independent variable and no big collinearity issue was present. When the variable subject to the LLOQ is the dependent variable, tobit showed the lowest bias and highest coverage for censoring proportions up to 0.8.

When facing a data set with values below a lower limit of quantification and a multiple linear regression model is chosen as analysis model, a conscious choice for dealing with those left-censored data should be made. In this article, we provide guidance on the performance of different established methods.

The online version contains supplementary material available at 10.1186/s12874-026-02770-y.

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