Analyzing Coarsened and Missing Data by Imputation Methods

Statistics in Medicine, vol. 44, pp. e70032

Abstract

ABSTRACT In various missing data problems, values are not entirely missing, but are coarsened. For coarsened observations, instead of observing the true value, a subset of values ‐ strictly smaller than the full sample space of the variable ‐ is observed to which the true value belongs. In our motivating example for patients with endometrial carcinoma, the degree of lymphovascular space invasion (LVSI) can be either absent, focally present, or substantially present. For a subset of individuals, however, LVSI is reported as being present, which includes both non‐absent options. In the analysis of such a dataset, difficulties arise when coarsened observations are to be used in an imputation procedure. To our knowledge, no clear‐cut method has been described in the literature on how to handle an observed subset of values, and treating them as entirely missing could lead to biased estimates. Therefore, in this paper, we evaluated the best strategy to deal with coarsened and missing data in multiple imputation. We tested a number of plausible ad hoc approaches, possibly already in use by statisticians. Additionally, we propose a principled approach to this problem, consisting of an adaptation of the SMC‐FCS algorithm (SMC‐FCS: Coarsening compatible), that ensures that imputed values adhere to the coarsening information. These methods were compared in a simulation study. This comparison shows that methods that prevent imputations of incompatible values, like the SMC‐FCS method, perform consistently better in terms of a lower bias and RMSE, and achieve better coverage than methods that ignore coarsening or handle it in a more naïve way. The analysis of the motivating example shows that the way the coarsening information is handled can matter substantially, leading to different conclusions across methods. Overall, our proposed SMC‐FCS method outperforms other methods in handling coarsened data, requires limited additional computation cost and is easily extendable to other scenarios.

Authors 7

1. Lars L. J. van der Burg corresponding Aachen

   Leiden University Medical Center

   Affiliation as printed

   Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

2. Stefan Böhringer Aachen

   Leiden University Medical Center

   Affiliation as printed

   Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

3. Jonathan William Bartlett

   London School of Hygiene & Tropical Medicine

   Affiliation as printed

   London School of Hygiene and Tropical Medicine London UK

4. Tjalling Bosse Aachen Department of Pathology Leiden University Medical Center Leiden The Netherlands

   Leiden University Medical Center

   Affiliation as printed

   Department of Pathology Leiden University Medical Center Leiden The Netherlands

5. Nanda Horeweg Aachen Department of Radiation Oncology Leiden University Medical Center Leiden The Netherlands

   Leiden University Medical Center

   Affiliation as printed

   Department of Radiation Oncology Leiden University Medical Center Leiden The Netherlands

6. Liesbeth C. de Wreede Aachen

   Leiden University Medical Center · Deutsche Knochenmarkspenderdatei

   Affiliation as printed

   Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

   DKMS Dresden/Tübingen Germany

7. Hein Putter Aachen

   Leiden University · Leiden University Medical Center

   Affiliation as printed

   Biomedical Data Sciences Leiden University Medical Center Leiden The Netherlands

   Mathematical Institute Leiden University Leiden The Netherlands