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# Fallacies of last observation carried forward analyses.

^{1}.

### Author information

- 1
- The Biostatistics Center, The George Washington University, Rockville, MD, USA jml@bsc.gwu.edu.

### 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.

© The Author(s) 2015.

#### KEYWORDS:

Last observation carried forward; imputation; missing data

- PMID:
- 26400875
- PMCID:
- PMC4785044
- DOI:
- 10.1177/1740774515602688

- [Indexed for MEDLINE]