Last Observation Carried Forward

A missing data method substituting a participant's most recent value for all subsequent missing time points, assuming their condition stayed unchanged.

Source: Molenberghs & Kenward 2007

Last observation carried forward fills a participant's missing later values by repeating their most recent recorded value, carrying it forward to every subsequent time point they missed. This rests on the questionable assumption that the person's condition stayed exactly as it was when last measured, which is often false for progressive diseases. Once common in trials, it is now widely criticised for the bias it introduces, and multiple imputation is generally preferred. Freezing the last value onward is its method. Little and Rubin (2002) discuss this.

Source: Little & Rubin 2002

Last observation carried forward is criticised because its assumption that a participant's outcome stays unchanged after dropout is often unrealistic, since conditions typically change over time, so carrying the last value forward can bias the results in either direction and understate the uncertainty by treating imputed values as known. So last observation carried forward is criticised for resting on an implausible constancy assumption that can distort estimates and give falsely precise inference, which is why it is now generally discouraged as a primary analysis in favour of principled methods such as multiple imputation or mixed models that make more reasonable assumptions and properly reflect the uncertainty in the missing data.

Source: Molenberghs & Kenward 2007

Last observation carried forward assumes that a participant's outcome remains unchanged from their last observed value onward, so that the missing later measurements would have equalled the last one recorded. This is a strong and often unrealistic assumption, since outcomes usually change over time, whether improving or worsening. So last observation carried forward rests on the assumption of no change after the last observation, which rarely holds in practice, and this is the source of its potential bias, since if participants would in fact have improved or deteriorated, carrying the last value forward misrepresents their outcomes and can systematically distort the estimated treatment effect.

Source: Molenberghs & Kenward 2007

The alternatives to last observation carried forward include principled methods such as multiple imputation, which imputes plausible values reflecting uncertainty; mixed models for repeated measures and other likelihood-based methods, which use all available data validly under the missing at random assumption; and reference-based imputation approaches for specific settings. So rather than carrying the last value forward, the alternatives handle missing data with methods that make more reasonable assumptions and properly reflect the uncertainty, which is why multiple imputation and mixed models are generally preferred, with last observation carried forward now largely avoided as a primary analysis and, at most, used as a sensitivity analysis.

Source: Molenberghs & Kenward 2007

Last observation carried forward was widely used in the past for analysing longitudinal trials with dropout, valued for its simplicity and once accepted, sometimes on the belief that it was conservative. Its limitations have since led to its decline. So last observation carried forward was historically common in trial analysis but is now generally discouraged, since its constancy assumption is unrealistic and its supposed conservatism is not guaranteed, which is why regulatory and methodological guidance has shifted toward principled missing data methods, leaving last observation carried forward as an approach to be avoided for primary analyses and used, if at all, only in sensitivity analyses.

Source: Molenberghs & Kenward 2007