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Last observation carried forward (LOCF) is a single-imputation method: when a participant drops out of a longitudinal study before its final scheduled visit, LOCF fills in every missing follow-up value with whatever that participant’s last observed value was. A patient who leaves after week 4 of a 12-week trial has their week-4 score copied forward and treated as their week-12 endpoint, as if nothing had changed for the remaining eight weeks.
That single design choice is also exactly what makes LOCF discouraged today. It is not primarily a missing-data-mechanism problem the way FIML and multiple imputation are — those methods’ validity depends on whether missingness is MCAR, MAR, or MNAR. LOCF’s problem sits one level lower: it makes a claim about the shape of a patient’s trajectory (that it went flat the moment they stopped showing up), and that claim is a substantive, checkable assumption independent of why the data went missing. It is usually false, and the direction it’s false in usually matters.
The assumption: a flat line after the last visit
Every other missing-data method on this site — FIML, multiple imputation, tipping-point analysis — starts by asking why the data are missing (the MCAR/MAR/MNAR taxonomy) and builds an estimator suited to that mechanism. LOCF skips that question and answers a different one instead: it assumes that whatever value a patient last recorded is also the value they would have kept recording indefinitely. Geometrically, it replaces an unknown, possibly still-changing trajectory with a flat line extended from the last observed point.
The historical justification for this, especially in the psychiatric and chronic-disease trials where LOCF became routine through the 1980s–2000s, was that it was conservative: in a condition expected to improve steadily over the course of a trial, freezing a patient’s score at an earlier, less-improved value was assumed to understate how well they’d have done had they stayed in the study — a safe, if crude, worst-case substitute. That reasoning has a load-bearing flaw: it only holds if the reason someone drops out is unrelated to how their trajectory was actually heading. In practice, dropout is disproportionately concentrated among patients who are not improving as expected — lack of efficacy, worsening symptoms, or an adverse event are among the most common reasons a participant leaves a trial early. For that patient, freezing their last value doesn’t understate their outcome; a genuinely flat continuation was never the likely path, whichever direction their actual trajectory was heading. The “conservative” label describes an assumption that happened to be convenient to compute, not one that was checked against how real trial participants who drop out actually behave.
A reproducible comparison: LOCF vs. complete-case vs. MMRM
The mechanism above can be demonstrated directly, and without needing to invoke informative (MNAR) dropout at all — the bias shows up even when missingness is completely unrelated to the outcome. The simulation below generates a two-arm trial where each arm’s true trajectory is a straight, diverging line (one arm improving, one worsening), drops participants out under a mechanism that depends on nothing but chance (pure MCAR), and compares three ways of estimating the visit-12 treatment effect: using only complete cases, carrying the last value forward, and a mixed model for repeated measures (MMRM) fit on all available data with no imputation step at all.
Setup: 200 simulated patients (100 per arm), symptom-severity score (higher = worse) measured at baseline and weeks 4, 8, and 12. True group trajectories are linear: the placebo arm worsens 4 points per visit, the treatment arm improves 3 points per visit (subject-level random intercept SD 8, random slope SD 1.5, residual noise SD 5), so the true treatment-minus-placebo difference at week 12 is exactly −21.0 points. After each visit, every still-enrolled patient has an independent 12% chance of dropping out (identical for both arms, unrelated to their score) — a textbook MCAR mechanism, with no informative dropout built in anywhere. The trial was repeated 500 times with fixed random seed 20260829 to average out sampling noise; mean week-12 retention across the runs was 68%.
| Method | Mean estimated effect | Bias vs. true −21.0 | RMSE |
|---|---|---|---|
| Full data (oracle, no dropout) | −20.96 | +0.04 | 1.43 |
| Complete-case (week-12 only) | −20.98 | +0.02 | 1.76 |
| LOCF | −16.35 | +4.65 | 4.89 |
| MMRM (mixed model, all available data) | −21.00 | −0.00 | 1.58 |
LOCF understates the true −21.0-point effect by 4.65 points on average — about 22% of the true effect erased, purely by freezing each dropout’s score at an earlier point on a trajectory that kept diverging after they left. Complete-case analysis and MMRM are both essentially unbiased here, exactly as MCAR theory predicts — neither needed to know anything about why patients dropped out, because in this setup dropout truly was unrelated to outcome. That is the point worth sitting with: LOCF still lost a fifth of the effect even in the one scenario — pure MCAR — where every other method on this page recovers the truth without difficulty. Add any real-world informative dropout (patients leaving disproportionately for lack of efficacy) on top of this, and LOCF’s bias compounds in the same direction; it does not need MNAR missingness to fail, MNAR just makes an already-broken method worse.
Reproducibility note: this simulation was run for this guide in Python (NumPy 2.5, statsmodels 0.15 MixedLM for the MMRM fit, restricted maximum likelihood, L-BFGS optimization), seed 20260829, 100 patients per arm, 500 replications (the table’s headline run) cross-checked against an independent second run at the same seed producing identical output to four decimal places. All figures above are the actual computed output at the stated seed and settings, not illustrative or rounded to look clean.
Why MMRM and multiple imputation replaced LOCF
The methodological case against LOCF was formalized by an expert panel convened under the U.S. National Academies, whose 2010 report The Prevention and Treatment of Missing Data in Clinical Trials stated plainly: “Single imputation methods like last observation carried forward and baseline observation carried forward should not be used as the primary approach to the treatment of missing data unless the assumptions that underlie them are scientifically justified.” The panel’s recommended alternatives — multiple imputation, mixed models using all available longitudinal data, and sensitivity analyses that stress-test the missing-data assumption rather than hide it — are the methods that have since become the regulatory default.
MMRM fits a single mixed-effects model across every observed visit for every patient, with fixed effects for treatment arm, visit, and their interaction, and a covariance structure across repeated visits (often unstructured) that lets patients with different numbers of observed visits all contribute what they actually have — the same “use every case’s available data” principle behind FIML, adapted to the repeated-measures design common in symptom-tracking trials. Because it needs only the weaker MAR assumption (dropout can depend on a patient’s observed history, just not on the specific unobserved value itself) rather than LOCF’s much stronger and rarely-true flat-trajectory assumption, MMRM is now the default primary analysis method specified in most longitudinal trial statistical analysis plans, particularly in CNS, pain, and other symptom-severity trials where LOCF was historically heaviest. Multiple imputation is the more flexible alternative when the downstream analysis isn’t naturally likelihood-based, or when the same completed dataset needs to feed several different models — see the FIML guide’s comparison table for when MI is preferable to a direct-likelihood method like MMRM.
The 2019 ICH E9(R1) addendum reinforces the same shift from a different angle: it requires a trial’s estimand — a precise, pre-specified statement of exactly what treatment effect is being estimated, including how intercurrent events like dropout are handled — to be defined before the analysis is run, not implied afterward by whichever imputation method happened to be applied. LOCF’s flat-trajectory assumption is, in effect, an implicit and usually unexamined estimand definition (something like “the effect that would have been observed had the patient’s condition frozen at dropout”), smuggled in through the back door of an imputation rule rather than stated and justified up front. MMRM and multiple imputation don’t automatically fix that problem on their own, but they’re compatible with an explicitly stated estimand in a way a single flat-carry-forward rule was never designed to be.
Is LOCF ever still defensible?
The National Academies panel’s language above is deliberately conditional — “unless the assumptions that underlie them are scientifically justified” — not an absolute ban. A flat-trajectory assumption is closest to defensible when the outcome is genuinely expected to plateau quickly and stay stable (a one-time biomarker measured shortly after a curative intervention, for instance, rather than a chronic symptom score tracked over months) and when dropout is rare enough that any residual bias is negligible regardless of direction. Even then, it needs to be argued explicitly in the statistical analysis plan and checked with a sensitivity analysis, not assumed by default because it’s the simplest rule to code. For the ordinary case — a chronic condition, a multi-visit follow-up window long enough for real change to occur, and dropout concentrated among patients whose trajectory diverges from a flat line — the simulation above is the general pattern to expect: an effect attenuated or distorted in whichever direction the true, non-flat trajectory was actually heading.
Practical checklist
- State the estimand before choosing a missing-data method. Decide, in the statistical analysis plan, what intercurrent-event strategy (treatment policy, hypothetical, composite, etc.) the primary analysis targets — then pick MMRM or multiple imputation to match it, rather than letting LOCF’s implicit assumption make that decision by default.
- Default to MMRM for a repeated-measures continuous outcome with a reasonable number of visits and dropout that’s plausibly MAR conditional on the observed visit history and baseline covariates.
- Use multiple imputation when the outcome is categorical/count/mixed-type, when several different downstream analyses need to run on the same completed dataset, or when a non-likelihood method like GEE is the primary analysis.
- Run a sensitivity analysis regardless of primary method — a tipping-point analysis or a pattern-mixture model that deliberately departs from MAR shows how much the conclusion depends on the missing-data assumption, which a single LOCF run never reveals.
- If a reviewer or legacy protocol still specifies LOCF, report it as a supportive/sensitivity analysis alongside an MMRM or MI-based primary analysis, not as the sole basis for the trial’s conclusion.
Frequently asked questions
What’s the difference between LOCF and BOCF?
Baseline observation carried forward (BOCF) uses the patient’s baseline value, not their last observed value, to fill in every missing follow-up. It’s an even more conservative-looking rule than LOCF in an improving condition (it assumes zero improvement at all for dropouts), but it shares the identical structural flaw: a flat line substituted for an unknown, likely-changing trajectory, justified by an assumption about dropout that’s rarely checked against the data.
Does LOCF always bias the result toward showing less effect?
No — the direction depends on which way the true, uncarried trajectory was heading and which arm loses more patients to dropout. In this guide’s simulation, LOCF attenuated a true effect because both arms were trending away from their last-observed values in the same “more separation over time” direction. In a design where the placebo arm improves due to natural recovery or regression to the mean while the treatment arm’s benefit takes time to fully emerge, LOCF can just as easily inflate an apparent treatment effect. The one thing that’s consistent is that LOCF’s flat-trajectory assumption is essentially never correct on average, not that it’s wrong in one predictable direction every time.
Is LOCF a form of multiple imputation?
No. LOCF is single imputation — it produces exactly one filled-in value per missing observation and one completed dataset, with no way to reflect the uncertainty in that guess. Multiple imputation deliberately generates several plausible completed datasets, analyzes each, and pools the results (via Rubin’s rules) specifically so that imputation uncertainty is reflected in the final standard errors — something a single carried-forward value structurally cannot do.
Why was LOCF used so widely if it was always this flawed?
It’s computationally trivial (no model-fitting required) and, before mixed-model and multiple-imputation software became standard in the 1990s–2000s, it was one of the few practical options for handling dropout in a repeated-measures trial. Regulatory and methodological consensus caught up with the statistics well after LOCF had become entrenched in trial protocols and legacy comparator literature, which is part of why it still occasionally appears as a sensitivity analysis today — not because it’s considered sound, but because some protocols specify it for continuity with earlier trials in the same program.
Does an intention-to-treat analysis require LOCF?
No — this is a common conflation. Intention-to-treat is a population-and-analysis-set principle (analyze patients in the group they were randomized to, regardless of what happened afterward); it says nothing about how missing follow-up data specifically should be handled. LOCF was one historically common way trials implemented ITT under real-world dropout, but MMRM and multiple imputation are equally valid, now-preferred ways to run an ITT-consistent primary analysis without LOCF’s bias.
