Last modified: 4/17/25
ANESTHESIOLOGY
Missing Data Part 1: Types of Missing Data
Rubin (1976) described three missing data mechanisms that inform assumptions for missing data
methods:
1,2
1. Missing Not at Random (MNAR) The missing values of a variable are related to the values
of that variable itself, even after controlling for other variables.
1,2
Example: When data are missing on mean arterial blood pressure (MAP) and only
the people with low MAP values have missing observations for this variable. A
problem with the MNAR mechanism is that it is impossible to verify that values are
MNAR without knowing the missing values.
3
2. Missing at Random (MAR) The missing and observed values might have systematic
differences, but these can entirely be explained by other observed variables.
3
This
assumption cannot be confirmed, because we cannot test whether the probability of
missing on a variable is solely a function of other measured covariates.
2
Example: If mean arterial blood pressure (MAP) data are missing at random,
conditional on age and sex, the distributions of missing and observed MAP values
will be similar among people of the same age and sex.
This assumption cannot be confirmed, because we cannot test whether the
probability of missing on a variable is solely a function of other measured
covariates.
3. Missing Completely at Random (MCAR) The missing observations are a random subset of
all observations.
2
Thus, the missing and observed values will have similar distributions.
2
Example: Data are missing for patients because they were not recorded/lost.
This hypothesis can be tested by separating the missing and complete cases and
assessing patients’ characteristics in each group.
Final Notes:
- There are well-developed statistical techniques to ‘complete’ the data under the MCAR,
MAR, and MNAR assumptions.
2
- There is no consensus how much missing data is “too much.” Generally, complete case
analysis is believed to be biased if missingness is more than 20% overall.
3
- Methods for handling missing data can vary based on whether a study is pragmatic or
exploratory.
4
- In some cases, it may be useful to compare covariates between complete and not
complete cases.
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Last modified: 4/17/25
References
1. Allison, PD. (2009). Missing Data. SAGE handbook of Quantitative Methods in Psychology.
Thousand Oaks, CA.
2. Graham, JW. (2009). Missing Data Analysis: Making it Work in the Real World. Annu. Rev.
Psychol. 60:549-576.
3. Bhaskaran, K & Smeeth, L (2014). What is the difference between missing completely at
random and missing at random? International Journal of Epidemiology. 1336-1339. Doi:
10.1093/ije/dyu080.
4. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data (2nd ed.). Hoboken,
NJ: John Wiley & Sons.
