Missing data

Inspect missingness and handle it: complete-case or multiple imputation

Published

July 2, 2026

Warning

Under development.

Register data almost always have missing values. Some are structural (a variable was not collected in all years) - that is not random, so think about why a value is missing before you handle it. Two common approaches: use only complete rows (complete-case), or multiple imputation.

Note

The code examples use generic path and variable names. Adapt them to your project. naniar and mice must be installed in your R environment on DST.

Inspect missingness

Start by seeing where and how much is missing.

library(naniar)                            # overview of missing data

df <- readRDS("path/to/analysis.rds")      # analysis-ready dataset

miss_var_summary(df)                       # table: count and proportion missing per variable
gg_miss_var(df)                            # the same as a figure
vis_miss(df)                               # a "map" of where in the dataset values are missing

Approach 1: complete-case

Many R functions drop rows with NA themselves (listwise deletion). It is simple, but can give bias and loss of power if the data are not missing completely at random.

df_complete <- na.omit(df)                 # keep only rows with no NA at all (use deliberately)

Approach 2: multiple imputation (mice)

mice stands for Multivariate Imputation by Chained Equations and is the most widely used R package for multiple imputation (mice on CRAN). The idea is to fill in the missing values several times, fit your model on each completed dataset, and combine the results, so the uncertainty from the imputation itself is counted.

library(mice)                              # md.pattern(), mice(), with(), pool()

md.pattern(df)                             # which variables are missing TOGETHER? (patterns), not just how much

# --- STEP 1: fill in the gaps (impute) ---
# mice() builds the IMPUTATION model and makes m complete datasets. By default it uses
# ALL columns in df to predict each variable with gaps. This is NOT your analysis - it
# only fills in the missing values.
# m = number of imputed datasets. You choose it yourself. Rule of thumb: at least as
# many as the percentage of rows with at least one gap (if e.g. 30% of rows are
# incomplete => set m around 30). Today 20-50 is typical; more m => more stable, but
# slower.
imp <- mice(df, m = 20, seed = 123)        # seed = fixed number => reproducible (same idea as matching, see 10a)

# --- STEP 2: run YOUR analysis on each completed dataset ---
# Here YOU choose the ANALYSIS model (your research question): which variables go in is
# set in glm() - not in mice(). with() runs the same glm() on EACH of the 20 datasets.
fit <- with(imp,
            glm(outcome ~ exposure + age, family = binomial))

# --- STEP 3: combine the results into one ---
pool(fit) %>% summary()                    # combine the 20 estimates into one result (Rubin's rules, see below)

complete(imp, 1)                           # the first completed dataset, if you want to inspect it

How does it find the values?

For each variable with missing values, mice builds a regression model that predicts the variable from the other variables. A missing value is not filled in with a single “best guess”, but with a random draw from the predicted distribution. That is why the 20 datasets differ.

“Chained equations” describes how mice handles several variables with gaps at once: it takes them one at a time, imputes the first from the others, moves on to the next and now uses the just-filled first variable as well, and so on. It runs several rounds through (the chain) until the variables are imputed consistently from one another.

Imputation affects both the estimate and the confidence interval. The estimate is the average across the 20 datasets. The confidence interval is built on Rubin’s rules, the standard method for combining results from several imputed datasets (Rubin 1987): it adds the spread between the datasets on top of the model’s own uncertainty. The more the imputed values disagree from dataset to dataset, the larger that contribution, and the wider the confidence interval. That is exactly the point: if there is little in the observed data to impute from, the uncertainty should reflect it.

When can you use it?

Imputation makes most sense when a non-trivial share of the data is missing and complete-case would either be biased or waste too many rows. If complete-case is already unbiased (see the regression case below), the main gain from imputation is power, not correctness.

mice rests on the MAR assumption (missing at random). MAR does not mean the gaps are pure chance. It means that the reason a value is missing lies in something you have measured, not in the missing value itself.

Analogy: suppose older patients more often skip a question. As long as you have age recorded, this is no problem - within each age group, those missing the answer resemble those who answered, and mice can fill in from the observed ones. The gap is due to age (which you have), not the missing answer itself. The assumption cannot be tested in the data, only judged on substantive grounds.

  • Missing covariates: the classic use. Here, include the outcome in the imputation model. It sounds backwards, but it is necessary: leave the outcome out and you pull the covariate-outcome association artificially toward null. Including the outcome adds no extra assumption, it simply respects the association you will later estimate.
  • Missing exposure: here it is more uncertain. In principle exposure can be imputed like any other variable, but it is more fragile, and whether it is defensible at all depends heavily on the situation and on how well the exposure can be predicted from the other data. Seek specific guidance before doing it.
  • Missing outcome: here imputation gains least. If you impute only the outcome from the same variables already in the analysis model, you typically end up with the same result as complete-case. A real gain requires extra auxiliary variables that predict the outcome. An alternative is inverse probability weighting (IPCW), see IP weighting.
Important

The MAR assumption is what matters, not the percentage. mice only corrects bias if missingness is MAR: that the reason a value is missing lies in the observed data. If a variable is missing precisely because of the value that is missing (for example, the sickest patients never get it measured), the data are MNAR (missing not at random), and then mice can introduce its own bias and give false precision. MAR cannot be tested in the data, only judged on substantive grounds.

This is why imputation is not automatically better than just accepting some missing:

  • Under MCAR (missing completely at random) complete-case is already unbiased, just less efficient.
  • In a regression model, complete-case is in fact unbiased when missingness does not depend on the outcome given the covariates, even when it is not MCAR. (Analysing only the observed means conditioning on being observed; this creates bias only when being observed depends on both exposure/covariates and outcome - that is, a collider.)
  • mice is only as good as the imputation model you give it. Pick the wrong variables to predict the missing values, and the filled-in values, and hence your result, will be wrong too. mice invents no information; it only exploits the associations that are already in the data.
Important

How much missing is okay? There is no real percentage threshold (5% / 10% / 40% are rules of thumb with no foundation). What matters is the mechanism and how well the missing values can be predicted from the rest. In practice: always report how much is missing per variable (STROBE), treat results with high missingness (roughly >40-50% on a key variable) as sensitivity / hypothesis-generating, and run complete-case and mice side by side as a sensitivity analysis. If they point the same way, you stand on firmer ground.

Warning

This is only a very short introduction to imputation. The page shows how to run mice in practice, not when it is substantively defensible. Learn the underlying theory (MAR/MCAR/MNAR, choosing the imputation model, number of imputations, diagnostics) elsewhere, for example:

Analysing the imputed dataset belongs to Phase 13 - Analysis.

TipFurther information

Further depth in The Epidemiologist R Handbook:

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