Review: a gentle introduction to imputation of missing values.
In most situations, simple techniques for handling missing data (such as complete case analysis, overall mean imputation, and the missing-indicator method) produce biased results, whereas imputation techniques yield valid results without complicating the analysis once the imputations are carried out. Imputation techniques are based on the idea that any subject in a study sample can be replaced by a new randomly chosen subject from the same source population. Imputation of missing data on a variable is replacing that missing by a value that is drawn from an estimate of the distribution of this variable. In single imputation, only one estimate is used. In multiple imputation, various estimates are used, reflecting the uncertainty in the estimation of this distribution. Under the general conditions of so-called missing at random and missing completely at random, both single and multiple imputations result in unbiased estimates of study associations. But single imputation results in too small estimated standard errors, whereas multiple imputation results in correctly estimated standard errors and confidence intervals. In this article we explain why all this is the case, and use a simple simulation study to demonstrate our explanations. We also explain and illustrate why two frequently used methods to handle missing data, i.e., overall mean imputation and the missing-indicator method, almost always result in biased estimates.
Donders
A Rogier T
AR
Center for Biostatistics, Utrecht University, Utrecht, The Netherlands. R.Donders@geo.uu.nl
van der Heijden
Geert J M G
GJ
Stijnen
Theo
T
Moons
Karel G M
KG
D015982:Bias; D003627:Data Interpretation, Statistical; D006801:Humans; D016015:Logistic Models; D012107:Research Design