Last Observation Carried Forward

Rationale

When participants drop out of longitudinal studies (i.e., ones that collect data at two or more time points), two different problems are introduced. First, the sample size of the study is reduced, which might decrease the power of the study, that is, its ability to detect a difference between groups when one actually exists. This problem is relatively easy to overcome by initially enrolling more participants than are actually needed to achieve a desired level of power, although this might result in extra cost and time. The second problem is a more serious one, and it is predicated on the belief that people do not drop out of studies for trivial reasons. Patients in trials of a therapy might stop coming for return visits if they feel they have improved and do not recognize any further benefit to themselves from continuing their participation. More often, however, participants drop out because they do not experience any improvement in their condition, or they find the side effects of the treatment to be more troubling than they are willing to tolerate. At the extreme, the patients might not be available because they have died, either because their condition worsened or, in rare cases, because the “treatment” actually proved to be fatal. Thus, those who remain in the trial and whose data are analyzed at the end reflect a biased subset of all those who were enrolled. Compounding the difficulty, the participants might drop out of the experimental and comparison groups at different rates, which biases the results even more. [Page 687]Needless to say, the longer the trial and the more follow-up visits or interviews that are required, the worse the problem of attrition becomes. In some clinical trials, drop-out rates approach 50% of those who began the study.

LOCF is a method of data imputation, or “filling in the blanks,” for data that are missing because of attrition. This allows the data for all participants to be used, ostensibly solving the two problems of reduced sample size and biased results. The method is quite simple, and consists of replacing all missing values of the dependent variable with the last value that was recorded for that particular participant. The justification for using this technique is shown in Figure 1, where the left axis represents symptoms, and lower scores are better. If the effect of the treatment is to reduce symptoms, then LOCF assumes that the person will not improve any more after dropping out of the trial. Indeed, if the person discontinues very early, then there might not be any improvement noted at all. This most probably underestimates the actual degree of improvement experienced by the patient and, thus, is a conservative bias; that is, it works against the hypothesis that the intervention works. If the findings of the study are that the treatment does work, then the researcher can be even more confident of the results. The same logic applies if the goal of treatment is to increase the score on some scale; LOCF carries forward a smaller improvement.

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