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Author: dr. ir. N van Geloven
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• What types of missing values are there?
• Can a GLM handle missing values?
• How do a mixed model and a GEE analysis account for missing values?
• For what percentage of my patients does the data need to be complete to justify imputation?
• Which program is best to use for imputing my missing data?
• References
• Additional resources

In general, three types of missing values are distinguished:

• MCAR - missing completely at random: Here it is assumed that the missing values are entirely random, so there is no reason to assume that higher or lower values are missing more often than other values. In other words: the missing-data process is independent of the outcome and of all other observed or unobserved patient characteristics. MCAR is present, for example, when follow-up data are missing because the measurement device was unavailable on the day the patient concerned had their follow-up visit.
• MAR - missing at random: Here it is assumed that the missing values are not random, but can depend on, for example, the level of previous observations or other known (patient) characteristics. In other words: the missing-data process depends on observed earlier measurements or known patient characteristics. For example, when patients with a poor outcome at the first follow-up visits are more inclined to drop out of the study than patients with a good outcome at earlier visits.
• Informative dropout / missing not at random: Here it is assumed that the missing values are not random and are influenced by processes that are not observed. In other words: the missing-data process depends on (as yet) unobserved measurements or unknown patient characteristics. For example, in a diagnostic setting where patients who spontaneously improve after the index test is performed no longer show up for the gold standard test, so that the final disease status remains unknown.

I want to use a general linear model (GLM) on a database. I have understood that if you have missing values, you cannot perform this analysis and therefore need to impute the data. Is this correct?

You can indeed run a GLM when you have missing values, but it will then only include the patients who have no missing values. It is therefore important to know for what percentage of your patients the data are incomplete. If this is a very small proportion, and the patients with missing values are expected to be fully comparable to patients without missing values (MCAR), you can simply apply a GLM. If not, you could perhaps impute the data or switch to another model that can better handle missing values (for example a mixed model in the case of repeated measures).

I have heard that a mixed model and a GEE analysis can already automatically handle missing values/drop-out. What method is precisely applied here, and does this also 'correct' for selective drop-out (missing at random (MAR))?

With an assumed missing-at-random mechanism, you are saying that there are -observed- variables that are predictive of the missingness. If these variables are included in a mixed model / GEE, then this is indeed accounted for. So it is important that the relevant variables are included in the model. Sometimes this is straightforward: when the assumption is that the measurements at T1 predict the missingness of the measurements at T2, then the predictive variable T1 is already in the model anyway, and this is thus indeed accounted for 'automatically'. However, if there are also other predictors — for example, women drop out more often than men — then the variable sex does need to be added to the model as a predictor to account for this. Note: if the (unobserved, but existing) value at T2 itself predicts the missingness at T2, then this is a case of 'not at random' missingness, and such a model cannot correct for that.

Unfortunately there is no single percentage that can be given that still makes imputation valid. See the list of additional resources at the bottom of this page for information on the (im)possibilities of (multiple) imputation.

In SPSS there is the option of using multiple imputation methods (go to Analyze -> Multiple Imputation). The 'SPSS Missing Values add-on' also offers multiple imputation when using earlier versions. The difference between single and multiple imputation is, in short: with single imputation you impute the data once, in one way, and use the resulting dataset in your analysis. With multiple imputation methods, you impute multiple times and account for the uncertainty in the imputed values.

Furthermore, packages such as Stata, S-Plus, SAS and R (for example mice or Hmisc) all have routines for multiple imputation.

1. White IR, Royston P, Wood AM. Multiple imputation using chained equations: Issues and guidance for practice. Statist. Med., 30: 377–399. DOI:10.1002/sim.4067

• National Research Council. The Prevention and Treatment of Missing Data in Clinical Trials. The National Academies Press, 2010.

• The European Medicines Agency’s (EMA’s) guideline on missing data in confirmatory clinical trials came into force on 1 January 2011.

• Treatment of missing data, website by David C. Howell

• Donders AR, van der Heijden GJ, Stijnen T, Moons KG. Review: a gentle introduction to imputation of missing values. J Clin Epidemiol. 2006 Oct;59(10):1087-91.

• Clark TG, Altman DG. Developing a prognostic model in the presence of missing data: an ovarian cancer case study. J Clin Epidemiol. 2003 Jan;56(1):28-37.

• Van Buuren, Stef. Flexible imputation of missing data. Second edition. CRC press, 2018. Link to the full online version of the book on the author's website.

• Multiple Imputation: 5 Recent Findings that Change How to Use It - article from The Analysis Factor.

• Rekenen met ontbrekende gegevens. RCA Rippe, M den Heijer, S le Cessie. Ned Tijdschr Geneeskd. 2013;157:A5539.

• Sterne JA, White IR, Carlin JB, Spratt M, Royston P, Kenward MG, Wood AM, Carpenter JR. Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls. BMJ. 2009 Jun 29;338:b2393.

• Vergouwe Y, Royston P, Moons KG, Altman DG. Development and validation of a prediction model with missing predictor data: a practical approach. J Clin Epidemiol. 2010 Feb;63(2):205-14.

• Moons KG, Donders RA, Stijnen T, Harrell FE Jr. Using the outcome for imputation of missing predictor values was preferred. J Clin Epidemiol. 2006 Oct;59(10):1092-101

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