Concept Architecture
Concept
Theoretically, Listwise Deletion is a complete-case method for handling missing data in which an observation is excluded from an analysis whenever it has a missing value for any variable required by that analysis. The method produces a dataset containing only fully observed cases and yields unbiased parameter estimates when data are missing completely at random. It exists as a simple and transparent approach to missing-data management, although it can reduce statistical power and introduce bias when the missingness mechanism is not completely random.
Mathematically, Listwise Deletion is represented by restricting estimation to observations for which the missingness indicators equal zero for every variable included in the model. The resulting estimator is calculated from the complete-case subset rather than the original sample. Under missing completely at random, the complete cases constitute a random subsample of the target population; otherwise, the retained sample may differ systematically from the excluded observations.
In practice, Listwise Deletion is implemented by identifying records with one or more missing values across the variables required for a particular analysis and excluding those records before estimation. In health economics, it may be applied in regression analyses, trial-based economic evaluations and observational studies involving costs, utilities, clinical outcomes and covariates. Analysts should report the number and characteristics of excluded observations and assess whether multiple imputation, likelihood-based estimation or sensitivity analysis is more appropriate.
Purpose
Used to create a complete analytical dataset by excluding observations with missing values, enabling standard statistical procedures to be applied without directly imputing unobserved data.
Mathematical Formulae
Primary Formula
I? = ????? (1 ? R??)
where:
- I? = 1 if observation i is complete for all p variables and 0 otherwise
- R?? = 1 if variable j is missing for observation i and 0 otherwise
- p = number of variables required for the analysis
The complete-case sample is:
S? = {i : I? = 1}
Supporting Formulae
Complete-case sample size:
n? = ????� I?
Complete-case mean:
x?? = (1/n?) ? ????� I?x?
Complete-case Ordinary Least Squares estimator:
??? = (X??X?)??X??Y?
Related Mathematical Methods
- Complete-Case Analysis
- Multiple Imputation
- Maximum Likelihood Estimation
- Inverse Probability Weighting
- Missing Completely at Random
- Missing at Random
- Sensitivity Analysis
Example
A trial-based economic evaluation includes 500 participants and requires complete information on treatment allocation, total cost, EQ-5D utility, age and baseline disease severity.
Forty participants have at least one missing value across these variables.
The complete-case sample size is:
n? = 500 ? 40 = 460
The cost-effectiveness analysis is therefore conducted using 460 participants. Before interpreting the results, the analyst compares treatment allocation, age and baseline severity between included and excluded participants. Material differences would indicate that Listwise Deletion may have introduced selection bias and that a multiple-imputation analysis should be considered.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| COUNTBLANK | =COUNTBLANK(B2:F2) | Count missing values across the variables required for each participant. |
| IF | =IF(COUNTBLANK(B2:F2)=0,"Include","Exclude") | Identify complete cases for the economic analysis. |
| FILTER | =FILTER(B2:F501,G2:G501="Include") | Extract the complete-case dataset in supported Excel versions. |
| COUNTIF | =COUNTIF(G2:G501,"Include") | Calculate the number of observations retained after deletion. |
| AVERAGEIF | =AVERAGEIF(G2:G501,"Include",D2:D501) | Calculate a mean cost or utility using complete cases only. |
VBA (Optional)
A VBA routine can identify incomplete records, create a complete-case analysis dataset and produce a summary of retained and excluded observations.
Sources
- Little RJA, Rubin DB. Statistical Analysis with Missing Data. Wiley.
- Carpenter JR, Kenward MG. Multiple Imputation and Its Application. Wiley.
- National Research Council. The Prevention and Treatment of Missing Data in Clinical Trials. National Academies Press.
- Sterne JAC, White IR, Carlin JB, et al. Multiple Imputation for Missing Data in Epidemiological and Clinical Research: Potential and Pitfalls. BMJ. 2009;338:b2393.
- Faria R, Gomes M, Epstein D, White IR. A Guide to Handling Missing Data in Cost-Effectiveness Analysis Conducted within Randomised Controlled Trials. Pharmacoeconomics. 2014;32(12):1157?1170.
- NICE. Health Technology Evaluation Manual.
Related Concepts (2)
Library
Publications
1
Bayesian Methods in Health Economics — Gianluca Baio, 1st Edition ed., 2012 (Chapman & Hall / CRC Press)
An overview of Bayesian statistical methods for the analysis of health economic data, covering economic evaluation concepts, statistical cost-effectiveness analysis, Bayesian computation and MCMC, and applied health economic evaluation.
BookView source →
Frequently Asked Questions (6)
What is listwise deletion?
A missing data method excluding any observation with a missing value on any variable in an analysis, using only complete cases.
Source: Rubin 1976
Which records does listwise deletion drop from an analysis?
Listwise deletion drops from an analysis any individual who is missing a value on any of the variables involved, keeping only those with complete data on all of them. This is simple and gives a single consistent sample, but it can discard a great deal of information when missingness is scattered, and it biases results unless the missing data are unrelated to the outcome. Where much is missing, the surviving complete cases may poorly represent the whole. Keeping only wholly complete records is its rule. Little and Rubin (2002) describe this.
Source: Little & Rubin 2002
When is listwise deletion valid?
Listwise deletion is generally valid, giving unbiased estimates, only when the data are missing completely at random, meaning that whether a value is missing is unrelated to any observed or unobserved variables, so the complete cases are a representative subset. When missingness depends on the data, the complete cases can be unrepresentative and the analysis biased. So listwise deletion is valid mainly under the strong missing completely at random assumption, which often does not hold, since missingness is frequently related to the variables involved, meaning that in many settings listwise deletion can distort estimates, which is why more principled methods are usually preferred.
Source: Rubin 1976
What are the disadvantages of listwise deletion?
The disadvantages of listwise deletion include the loss of information and reduced sample size, sometimes substantially, when many cases have some missing data, which lowers precision; and the potential for bias when the data are not missing completely at random, since the excluded cases may differ systematically from those retained. So listwise deletion can be inefficient and biased, discarding usable partial data and giving unrepresentative results unless missingness is completely at random, which is why it is often not the preferred approach, and methods such as multiple imputation or maximum likelihood, which use the available partial data, are generally recommended instead.
Source: Rubin 1976
How does listwise deletion differ from available case analysis?
Listwise deletion excludes any case with a missing value on any variable in the analysis, using a single consistent set of complete cases throughout, while available case analysis, or pairwise deletion, uses all cases with the data needed for each specific calculation, so different calculations may use different subsets. So the two differ in whether the sample is fixed to fully complete cases or varies by calculation, with listwise deletion giving a consistent but smaller sample and available case analysis retaining more data at the cost of consistency, and both rely on the missing completely at random assumption to avoid bias, being simpler but less sound than principled methods.
Source: Rubin 1976
What are the alternatives to listwise deletion?
The alternatives to listwise deletion include multiple imputation, which fills in missing values with plausible estimates reflecting uncertainty; maximum likelihood and mixed model methods, which use all available data validly under the missing at random assumption; and other principled approaches. So rather than discarding incomplete cases, the alternatives make use of the partial data and rest on more reasonable assumptions, which is why multiple imputation and likelihood-based methods are generally preferred over listwise deletion, since they retain information, reduce bias when data are missing at random, and properly reflect the uncertainty from the missing data, with listwise deletion reserved for situations where its assumptions are plausible.
Source: Rubin 1987
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 18 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/listwise-deletion
- Term code
- HE-ES-SA-104
Stable URI · Machine-readable · Resolvable · CC BY 4.0