In Reply

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 would like to express our gratitude for the two valuable additions to our article, with which we agree wholeheartedly. Our decision not to address these aspects is primarily a result of the word count limitations and the aim of the series to convey information in a way that is as non-technical and accessible as possible; consequently, we had to omit certain methodological details.

When it comes to missing values resulting from measurements below the limit of quantification or detection (left-censoring), the methodological scope can be broadened even further. Several methods are available that can handle missing values resulting from other mechanisms in a valid manner. Of particular note here are the standard methods of survival analysis, where the values are usually right-censored and, in some cases, truncated. In an even broader sense, all methods of causal inference are statistical methods in which counterfactual observations are treated as missing values.

If the missing at random (MAR) assumption is met, the maximum likelihood principle provides valid estimators for the model parameters without the need to explicitly impute missing values. In addition, it is possible to use Bayesian methods where missing values themselves are considered parameters to be estimated. They are then estimated together with the actual model parameters. An accessible, general introduction to Bayesian methods has recently been published in this series (2).

Lastly, we fully support the call for transparent and detailed documentation of the imputation models used. We further regard the publication by Sterne et al. as a key guideline (3).

DOI: 10.3238/arztebl.m2026.0045

For the authors

Dr. PH Alexander Lang

Deutsches Diabetes-Zentrum für Diabetes-Forschung

Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany

Conflict of interest

The authors of both contributions declare no conflict of interest.

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. Gerß JWO, Vonthein R: Introduction to bayesian statistics: Part 36 of a series on the evaluation of scientific publications. Dtsch Arztebl Int 2025; 122: 271–6

3. Sterne JA, White IR, Carlin JB, et al.: Multiple imputation for missing data in epidemiological and clinical research: Potential and pitfalls. BMJ 2009; 338: b2393