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Cited by 328Statistical Methods and Bayesian InferenceStatistical Methods in Clinical TrialsStatistical Methods in Epidemiology

Fallacies of last observation carried forward analyses

Open access
Lachin, John M·2016·Clinical Trials
DOI 10.1177/1740774515602688PMC PMC4785044
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Abstract

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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  • LOCF has been criticized for overestimation of values when dropout rates differ between groups.

    “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

    The Two Sample Biases section (page unavailable) shows that LOCF can overestimate the true between-group mean difference, but it can also underestimate it. The analysis explicitly assumes the same fraction of missing values in both groups, so it does not establish the claim specifically for differing dropout rates. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • Missing values were treated based on the Last-Observation-Carried-Forward method.

    “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

  • Simple imputation methods (eg, last observation carried forward) introduce bias and ignore the uncertainty induced by missing data, leading to confidence intervals that are too narrow.

    “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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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
DOI
10.1177/1740774515602688
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
Licence
journals.sagepub.com/page/policies/text-and-data-mining-license (tdm)
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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