Missing Values Below the Detection Limit

Letter to the Editor regarding the article Missing Values in Empirical Research: Theory and Practice Part 39 of a Series on Evaluation of Scientific Publications by Edyta Schaefer, Alexander Lang, Katharina Piedboeuf-Potyka, and Oliver Kuss in issue 3/2026

We very much appreciate that the authors have addressed the important issue of missing values in the Series on Evaluation of Scientific Publications (1). One aspect, however, deserves to be looked at more closely: missing values due to measurements below the limit of quantification or detection, so-called left-censored observations. “Missing not at random“ (MNAR) structures are particularly common in epidemiological studies in occupational and environmental medicine.

The statement that MNAR data inherently introduce systematic bias in multiple imputation requires refinement in this context: Bias only occurs if the mechanism underlying the missing values is unaccounted for in the imputation model. This is why the first step in multiple imputation (2) is of particular importance. At this point, all available information should be used to arrive at imputed values that are plausible to the greatest extent possible. For example, if the imputations of left-censored observations are performed using a Tobit-based approach, the resulting estimators are unbiased, as shown by various simulation studies in the literature (2). To ensure scientific transparency, authors should describe both the boundary conditions and the actual imputation method used.

It should also be noted that multiple imputation is not the only valid option for addressing missing observations. Bayesian methods also provide a statistically valid way to account for missing or censored values (3). In addition, there are other methods available that account for missing or censored observations directly in the estimation, such as Cox‑based models, Tobit regression and methods based on the expectation–maximization (EM) algorithm. The crucial point is that researchers clearly state how the statistical analysis method handled missing observations.

DOI: 10.3238/arztebl.m2026.0044

Dipl.-Stat. Anne Lotz, Prof. Dr. med. Thomas Behrens

Institut für Prävention und Arbeitsmedizin der Deutschen Gesetzlichen Unfallversicherung, Institut der Ruhr-Universität Bochum, Bochum, Germany

References

1. Schaefer E, Lang A, Piedboeuf-Potyka K, Kuss O: Missing values in empirical research: Theory and practice. Part 39 of a series on the evaluation of scientific publications. Dtsch Arztebl Int 2026; 123: 71–6

2. Lubin JH, Colt JS, Camann D, et al.: Epidemiologic evaluation of measurement data in the presence of detection limits. Environ Health Perspect 2004; 112: 1691–6

3. Erler NS, Rizopoulos D, van Rosmalen J, Jaddoe VW, Franco OH, Lesaffre EM: Dealing with missing covariates in epidemiologic studies: A comparison between multiple imputation and a full Bayesian approach. Stat Med 2016; 35: 2955–74.