The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
Fallacies of last observation carried forward analyses
Open accessAbstract
Background: Last observation carried forward is a common statistical approach to the analysis of longitudinal repeated measures data where some follow-up observations may be missing. In a last observation carried forward analysis, a missing follow-up visit value is replaced by (imputed as) that subject’s previously observed value, that is, the last observation is carried forward. The combination of the observed and imputed data is then analyzed as though there were no missing data. Purpose: There have been numerous statistical demonstrations of faults of this approach. In 2012, the National Research Council’s Panel on Handling Missing Data in Clinical Trials issued a report that raised concerns with the use of last observation carried forward and described alternative methods that offer greater statistical validity. Nevertheless, the method persists, and its use is rampant. A search of the key word “last observation carried forward” using Google Scholar yielded “about 2480” published citations during 2014 alone, the overwhelming majority presenting the results of scientific studies. However, there has not been a simple explanation of the statistical deficiencies of last observation carried forward. Such a description is presented herein. Results: A simple repeated measures model is described for quantitative observations at two times (e.g. 1 and 2 years), with complete values at 1 year that are used to impute by last observation carried forward the missing values at 2 years under the missing completely at random assumption. This results in a mixture distribution of observed and imputed values at 2 years with mean and variance that are a function of the mixture of the 1- and 2-year distributions. The expressions show that last observation carried forward is only unbiased when the distribution of the observed values at 1 year is exactly equal to the distribution of the missing values at 2 years, the latter, of course, being unknown. Limitations: When the values at 2 years are not randomly missing, no simple expressions for the mean and variance of the mixture distribution are possible without additional unverifiable assumptions. Conclusion: All analyses using last observation carried forward are of questionable veracity, if not being outright specious (definition: appearing to be true but actually false). It is hoped that future studies will make a more vigorous attempt to minimize the amount of missing data and that more valid statistical analyses will be employed in cases where missing data occur. Last observation carried forward should not be employed in any analyses.
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In the citing paper
“LOCF is a common imputation method, but it has previously been criticized for overestimation of values as the true mean differences are not present when dropout rates differ between groups (Gueorguieva and Krystal, 2004; Lachin, 2016).”
From Internet-based treatment for vulvodynia (EMBLA) – Study protocol for a randomised controlled study (2021) · cites this paper as Lachin, 2016
Experimental — accuracy not yet measuredIn the citing paper
“Missing values were treated based on Last-Observation-Carried-Forward method (LOCF) (Lachin, 2016).”
From Effect of Probiotic Supplementation on Cognitive Function and Metabolic Status in Alzheimer's Disease: A Randomized, Double-Blind and Controlled Trial (2016) · cites this paper as Lachin, 2016
In the citing paper
“Simple imputation methods (eg, last observation carried forward) may seem appealing but are not advisable as they introduce bias and ignore the uncertainty induced by missing data, leading to confidence intervals that are too narrow.433”
From SPIRIT 2025 explanation and elaboration: updated guideline for protocols of randomised trials (2025) · cites this paper as [433]
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Cites
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Self-citationLinear Mixed Models in Practice
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Last Observation Carried Forward: A Crystal Ball?
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Cited by
Sorted by citations
Akbari, E., Asemi, Z., Daneshvar Kakhaki, R., Bahmani, F., Kouchaki, E., Tamtaji, O. R., Hamidi, G. A., & Salami, M. (2016) · Frontiers in Aging Neuroscience · doi:10.3389/fnagi.2016.00256 · Cited by 946
“LOCF ignores whether the participant’s condition was improving or deteriorating at the time of dropout, instead, it freezes outcomes at the values observed before dropout (i.e., last observation) (Lachin, 2016).”
BackgroundMethodGaertner, J., Siemens, W., Meerpohl, J. J., Antes, G., Meffert, C., Xander, C. J., Stock, S., Müeller, D., Schwarzer, G., & Becker, G. (2017) · BMJ · doi:10.1136/bmj.j2925 · Cited by 396
Thorsen-Meyer, H.-C., Nielsen, A. B., Nielsen, A. P., Kaas-Hansen, B. S., Toft, P., Schierbeck, J., Strøm, T., Chmura, P. J., Heimann, M., Dybdahl, L., et al. (2020) · The Lancet Digital Health · doi:10.1016/s2589-7500(20)30018-2 · Cited by 336
Razzaghi, R., Pourbagheri, H., Momen–Heravi, M., Bahmani, F., Shadi, J., Soleimani, Z., & Asemi, Z. (2016) · Journal of Diabetes and its Complications · doi:10.1016/j.jdiacomp.2016.06.017 · Cited by 210
CONSORT 2025 explanation and elaboration: updated guideline for reporting randomised trials
Hopewell, S., Chan, A.-W., Collins, G. S., Hróbjartsson, A., Moher, D., Schulz, K. F., Tunn, R., Aggarwal, R., Berkwits, M., Berlin, J. A., et al. (2025) · BMJ · doi:10.1136/bmj-2024-081124 · Cited by 205
Metadata
- Authors
- Lachin, J. M.
- Affiliations
- George Washington University (US)
- Corresponding author
- Lachin, John M
- ORCID
- Lachin, John M
- Venue
- Clinical Trials
- Publisher
- SAGE Publications
- Published
- 2015-09-22
- Volume
- 13
- Issue
- 2
- Pages
- 161-168
- ISSN
- 1740-7745 (ISSN-L)
- 1740-7753
- PMC
- PMC4785044
- OpenAlex
- W2134947937
- Cited by
- 328
- References
- 13
- Citations by year
- 2026: 42 · 2025: 46 · 2024: 52 · 2023: 34 · 2022: 40 · 2021: 24 · 2020: 30 · 2019: 17 · 2018: 15 · 2017: 15 · 2016: 11 · 2015: 1
- FWCI
- 12.46
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Clinical Trials (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of Diabetes and Digestive and Kidney Diseases (U01DK098246)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Keywords
- last observation carried forward, missing data, imputation, missing completely at random, bias, mixture distributions, repeated measures models, statistical validity
- MeSH terms
- Data Collection, Data Interpretation, Statistical, Follow-Up Studies, Longitudinal Studies, Research Design, Bias
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