Complete Case Analysis

Complete case analysis, also called listwise deletion, is a statistical approach that includes only participants who have complete data for all variables of interest in the analysis, excluding anyone with any missing values. While simple to implement, this approach reduces statistical power whenever cases are excluded, and it can introduce bias when the data are not missing completely at random.

Missing data are ubiquitous in research. Participants skip survey questions, drop out of studies, or have missing laboratory values. How researchers handle missing data directly affects the validity and generalizability of their findings. Complete case analysis is the default approach in most statistical software and is used, often without deliberate choice, in a large proportion of published studies. Understanding its assumptions and limitations is essential for every researcher, because using it inappropriately can lead to biased estimates and incorrect conclusions.

In complete case analysis, the analyst examines the dataset and identifies all participants who have at least one missing value on any variable included in the analysis. These participants are excluded entirely, and the analysis proceeds using only the subset of participants with complete data on all relevant variables.

The validity of complete case analysis depends on the mechanism of missingness. Data can be missing completely at random (MCAR), meaning that the probability of being missing is unrelated to any observed or unobserved data. Under MCAR, complete case analysis produces unbiased estimates but with reduced precision due to the smaller sample size. Data can be missing at random (MAR), meaning that the probability of being missing is related to observed variables but not to the missing values themselves, after conditioning on observed data. Under MAR, complete case analysis can be biased. Data can be missing not at random (MNAR), meaning that the probability of being missing depends on the unobserved values themselves. Under MNAR, all standard approaches, including multiple imputation, can be biased.

In practice, MCAR is a strong assumption that rarely holds. If participants with more severe disease are more likely to have missing outcome data, for example, the complete case analysis will overrepresent participants with milder disease, biasing the results. The more variables included in the analysis, the larger the proportion of participants likely to be excluded due to missingness on at least one variable.

Complete case analysis is appropriate when the proportion of missing data is very small (e.g., less than 5%), when data are plausibly MCAR, and when the loss of sample size does not meaningfully reduce statistical power. It is also acceptable as one component of a sensitivity analysis, compared with results from methods such as multiple imputation. It is generally not appropriate as the main analysis when the proportion of missing data is substantial, when the data are likely MAR or MNAR, or when the characteristics of participants with missing data differ from those with complete data. One exception applies to regression models: if the chance of being a complete case does not depend on the outcome once the covariates are taken into account, complete case analysis can still give unbiased regression estimates, even when the data are not MCAR.

A common mistake is using complete case analysis by default without examining the extent and mechanism of missing data. Researchers should always report the proportion of missing data, compare the characteristics of complete and incomplete cases, and justify their chosen approach. Another error is failing to recognize that complete case analysis on a multivariable model excludes participants who are missing on any variable, which can dramatically reduce the sample size when many variables are involved, even if each individual variable has only modest missingness.

Researchers sometimes also incorrectly assume that complete case analysis is always conservative (biased toward the null). Depending on the missing data mechanism, it can bias results in either direction. Finally, treating complete case analysis and multiple imputation as interchangeable without understanding their different assumptions can lead to inappropriate method selection. Multiple imputation is generally preferred when data are plausibly MAR and missing data are not trivial, but it is not automatically better: it rests on its own assumptions, including a correctly specified imputation model.

A longitudinal study of 1,200 patients with chronic kidney disease measures six variables at five time points. By year five, 340 patients (28%) have at least one missing value across the 30 data points. Complete case analysis retains only 860 patients. Comparison reveals that excluded patients had higher baseline creatinine levels, more comorbidities, and were older than included patients, indicating that the data are not MCAR. The researchers conduct both complete case analysis and multiple imputation using 50 imputed datasets, finding that the complete case analysis gives a rate of disease progression 15% lower than the multiple imputation analysis, consistent with the exclusion of the sickest patients, who were also the most likely to have missing follow up data.