Last Observation Carried Forward: Why It's Outdated

Introduction

Missing outcome measurements are common in longitudinal clinical trials. Patients may discontinue treatment, withdraw from the study, miss visits, experience adverse events, lose follow-up, or simply fail to provide a measurement at a scheduled assessment.

Historically, one of the most common approaches for dealing with a missing longitudinal outcome was Last Observation Carried Forward, usually abbreviated LOCF.

The idea is simple: if the outcome is missing at a later visit, use the patient's most recent observed value as though it were their value at the missing visit.

For example, suppose a patient's observed measurements are:

LOCF replaces both missing measurements with 55.

This sounds conservative and convenient. But there is a fundamental problem: the patient's last observed value is not necessarily a reasonable prediction of what their outcome would have been at the later visits.

What Exactly Is LOCF?

Suppose patient \(i\) has measurements at visits \(1,\ldots,T\), but their outcome becomes missing after visit \(k\).

LOCF defines every subsequent missing value as:

In other words, the outcome is assumed to remain exactly constant after the patient's last observed measurement.

If the last observed value was 55, then LOCF assumes:

This creates a flat trajectory after dropout.

Why Was LOCF So Popular?

LOCF became popular partly because it was easy to understand and easy to implement.

It offered several apparent advantages:

• No missing values remained in the analysis dataset.
• Standard statistical procedures could be applied to the completed dataset.
• The method was computationally simple.
• It avoided explicit modeling of the missing-data mechanism.
• It appeared conservative in many settings.
• It was easy to explain in a statistical analysis plan.

In an era when longitudinal statistical modeling was less accessible, these features were attractive.

But simplicity is not the same thing as validity.

LOCF Is Not a Missing-Data Model

A critical conceptual distinction is that LOCF is an imputation rule, not a scientifically justified model of why data are missing.

Suppose a patient discontinues treatment because their disease is worsening.

LOCF does not model that worsening. Instead, it freezes the patient's outcome at the last observed value.

Similarly, suppose another patient discontinues because they have achieved a substantial improvement and no longer wish to attend clinic. LOCF again freezes the outcome at the last observed value.

The method therefore treats very different dropout mechanisms in essentially the same mechanical way.

The Hidden Assumption: No Change After Dropout

The most obvious assumption behind LOCF is:

for every later time point \(t>k\).

This says that, conditional on the patient's last observed value, their expected future outcome remains exactly unchanged.

That is an extremely strong assumption.

Clinical outcomes frequently change over time because of:

• Disease progression
• Treatment response
• Treatment discontinuation
• Adverse events
• Concomitant treatment
• Natural disease history
• Regression toward the mean
• Time-dependent treatment effects

There is generally no reason to assume that a patient's outcome would remain perfectly flat after their final observed visit.

A Simple Example of the Problem

Consider a patient whose disease score improves over time:

LOCF assumes:

But suppose the patient's underlying trajectory would have continued to:

LOCF would systematically underestimate the patient's improvement.

Now imagine the opposite trajectory, where the patient's disease worsens after Week 12. LOCF would then overestimate their outcome.

Why LOCF Can Bias the Treatment Effect

Suppose a randomized trial compares treatment \(A\) with treatment \(B\). Let the final outcome be \(Y_T\).

The treatment effect might be defined as:

If missing outcomes are replaced using LOCF, the estimated treatment effect becomes based partly on artificial values:

If dropout patterns differ between treatment groups, LOCF can distort the difference between groups.

For example, suppose patients receiving treatment \(A\) tend to discontinue after improving, while patients receiving treatment \(B\) tend to discontinue because their disease worsens.

The two groups may have very different unobserved trajectories.

LOCF does not account for that distinction.

LOCF Can Create Artificial Data

An important conceptual problem is that LOCF turns a missing measurement into a value that looks observed.

Consider:

The analysis dataset now contains four values of 55.

But only one of those four measurements was actually observed.

The other three are assumptions.

LOCF Can Artificially Reduce Variability

Suppose several patients discontinue at different times. LOCF creates repeated identical values after each patient's dropout.

This can produce artificial patterns such as:

• Long stretches of perfectly flat trajectories
• Repeated identical values across multiple visits
• Reduced apparent within-patient variability
• Distorted covariance structures

These properties may be very different from the actual biological process.

The problem becomes particularly important when the analysis depends on the longitudinal covariance structure.

LOCF and Longitudinal Clinical Trials

Modern clinical trials frequently collect repeated outcomes such as:

• Blood pressure
• HbA1c
• Depression scores
• Lung function
• Pain scores
• Functional assessments
• Biomarkers
• Quality-of-life measurements

These measurements contain information about the patient's trajectory over time.

LOCF discards much of that structure by replacing an entire future trajectory with a single historical measurement.

LOCF Does Not Properly Address MAR or MNAR

Modern missing-data analyses distinguish among mechanisms such as:

• Missing completely at random (MCAR)
• Missing at random (MAR)
• Missing not at random (MNAR)

These concepts concern the relationship between missingness, observed data, and unobserved outcomes.

LOCF does not establish that the data are MCAR.

It does not establish that the data are MAR.

And it does not provide a principled model of MNAR behavior.

The missing-data mechanism concerns how the probability of missingness relates to observed and unobserved outcomes.

LOCF simply assigns values after missingness occurs.

Those are fundamentally different tasks.

MCAR Does Not Rescue LOCF

Even if missingness were completely at random, LOCF would not automatically become the preferred analysis.

Under MCAR:

The missingness mechanism is independent of the observed and unobserved outcomes.

But this does not imply that the last observed value is a valid estimate of the missing future value.

MCAR may justify certain complete-case approaches under particular models. It does not justify freezing every patient's trajectory at their last measurement.

LOCF Does Not Mean "Conservative"

One of the most persistent misconceptions is: LOCF is conservative.

That statement is not generally true.

Whether LOCF biases a treatment effect toward or away from the null depends on the relationship among:

• The direction of treatment effects
• The timing of dropout
• The amount of missing data
• The relationship between dropout and outcome
• The trajectory of the outcome
• The missingness mechanism

In one trial, LOCF might reduce an estimated treatment effect. In another, it might exaggerate one.

A Numerical Example of Potential Bias

Suppose the true mean trajectories are:

The true final treatment difference is:

Now suppose treatment patients who discontinue at Week 12 are assigned their Week 12 value of 52 under LOCF. Their Week 16 value becomes:

The treatment effect is then pulled toward the null compared with the hypothetical Week 16 outcome of 46.

But if dropout occurred preferentially among patients whose outcomes would have worsened, the direction of the resulting bias could be different.

LOCF Can Distort the Timing of Treatment Effects

Longitudinal treatment effects often evolve over time.

For example, a drug might have:

• Small effects at Week 4
• Moderate effects at Week 8
• Large effects at Week 12
• A plateau after Week 16

LOCF effectively assumes that a patient who disappears after Week 8 has the same outcome at Week 12, Week 16, and beyond as they had at Week 8.

That assumption ignores the time-varying nature of treatment response.

LOCF Is Particularly Problematic When Dropout Is Informative

Suppose patients discontinue because their disease is getting worse.

The missing future outcomes are therefore likely related to the reason the outcomes became missing.

This is a form of potentially informative dropout.

LOCF does not model the worsening. Instead, it holds the outcome fixed.

Consequently, LOCF can make the post-dropout trajectory look more stable than it actually would have been.

Why Modern Methods Are Different

Modern longitudinal methods generally try to use the information that was actually observed rather than replacing every missing outcome with a copied value.

Two major approaches are:

• Mixed models for repeated measures (MMRM)
• Multiple imputation (MI)

These methods can incorporate baseline measurements, treatment group, intermediate outcomes, visit effects, treatment-by-visit interactions, and other relevant covariates.

MMRM: Model the Observed Longitudinal Data

A typical MMRM models the outcome as a function of treatment, visit, and their interaction.

A simplified model is:

The model estimates the treatment effect at each visit while accounting for correlation among repeated observations from the same patient.

Crucially, the model does not require the analyst to create an artificial flat trajectory after dropout.

Why MMRM Can Use Incomplete Patient Records

Consider a patient with:

An MMRM does not need to convert the missing Week 12 and Week 16 values into 55.

The observed baseline, Week 4, and Week 8 measurements still contribute information to estimation of the model parameters.

The resulting treatment comparison is based on a model for the observed data and its covariance structure.

The Typical MMRM Model

For a continuous longitudinal endpoint, a common model specification includes:

• Treatment
• Visit
• Treatment-by-visit interaction
• Baseline covariate
• Baseline-by-visit interaction when appropriate
• A repeated-measures covariance structure

For example:

The treatment effect at visit \(j\) is obtained from the appropriate treatment-by-visit contrast.

Multiple Imputation Takes a Different Approach

Multiple imputation explicitly creates several plausible completed datasets rather than a single deterministic completed dataset.

For each imputed dataset:

1. Missing values are replaced using a statistical imputation model.
2. The planned analysis is performed.
3. The resulting estimate and variance are stored.

This is repeated \(M\) times.

The results are then combined using Rubin's rules.

where \(Q_m\) is the estimate from imputed dataset \(m\).

The within-imputation variance is:

and the between-imputation variance is:

The total variance is then:

This additional uncertainty reflects the fact that the missing values are not known with certainty.

LOCF vs. Multiple Imputation

LOCF vs. MMRM

LOCF and the Intent-to-Treat Principle

Another reason LOCF became popular was its apparent connection to the intent-to-treat principle.

The reasoning was sometimes:

"Everyone randomized should be included, so we need to fill in their missing outcomes."

But these are separate concepts.

LOCF Does Not Solve Estimand Problems

A modern clinical trial analysis should begin by asking: What treatment effect are we actually trying to estimate?

This is an estimand question.

For example, investigators may be interested in:

• The treatment effect regardless of treatment discontinuation
• The effect while patients remain on treatment
• The effect if treatment had not been discontinued
• The treatment policy effect including subsequent therapy

LOCF does not define these scientific questions.

It merely specifies what number should be inserted when an observation is missing.

A scientifically meaningful estimand should therefore precede the missing-data method.

The Most Important Shift: From "Fill the Gap" to "Model the Question"

Older approaches often asked:

"How can we fill in the missing observations?"

Modern approaches increasingly ask:

"What treatment effect do we want to estimate, and what assumptions are required to estimate it from the observed data?"

That shift is one of the most important developments in modern clinical trial statistics.

LOCF Can Be Especially Problematic With Differential Dropout

Suppose dropout rates are:

The missingness patterns are clearly different.

If patients who discontinue have different expected outcomes from patients who remain, then simply copying the last observed value can create differential distortion between treatment groups.

This can be particularly serious when dropout is related to efficacy or tolerability.

Why "Last Observation" May Be the Wrong Observation

Even the phrase "last observation" can be misleading.

A patient might have:

• A temporary response at their last visit
• A transient adverse event
• A measurement affected by an acute illness
• A value unusually high or low because of random variation
• A trajectory that was changing rapidly

The last observed value may therefore be a poor predictor of the missing future outcome.

Regression Toward the Mean

Suppose a patient's final observed value is unusually extreme.

Future observations might naturally move closer to the patient's typical level even if there were no treatment effect.

LOCF freezes the extreme value indefinitely.

This can produce systematic distortion when dropout tends to occur following extreme observations.

LOCF Can Distort Standard Errors

LOCF does not only affect point estimates. It can also affect the estimated variability and therefore:

• Standard errors
• Confidence intervals
• Test statistics
• P-values

The problem arises because imputed values are often treated as though they were known observations.

But an imputed value contains uncertainty.

If that uncertainty is ignored, inferential procedures can become miscalibrated.

Why a Single Imputation Is Usually Insufficient

Suppose the missing outcome could plausibly be:

LOCF chooses one value based entirely on the last observation.

Multiple imputation instead acknowledges that several values may be plausible and propagates that uncertainty into the final inference.

LOCF and Sensitivity Analysis

Does this mean LOCF should never appear in a clinical trial analysis? Not necessarily.

There is an important distinction between using LOCF as a primary missing-data method and using it as an exploratory or sensitivity analysis.

A historical LOCF analysis may sometimes be informative as a deliberately simple alternative analysis.

However, its assumptions should be explicitly acknowledged.

LOCF Should Not Be Used Automatically

The correct question is not:

"Which imputation method should we use?"

The better sequence is:

A Better Workflow for Longitudinal Clinical Trials

A modern missing-data strategy should generally include several components.

1. Describe the Missingness

Report missing observations by:

• Treatment group
• Visit
• Reason for missingness
• Patient discontinuation status
• Important baseline characteristics

2. Investigate Reasons for Dropout

Distinguish among:

• Lack of efficacy
• Adverse events
• Withdrawal of consent
• Protocol deviations
• Administrative reasons
• Loss to follow-up

3. Define the Estimand

Specify exactly what treatment effect is being estimated.

4. Select the Primary Analysis

For many continuous longitudinal endpoints, an appropriately specified MMRM may be a strong candidate.

For other estimands and data structures, multiple imputation or other methods may be appropriate.

5. Conduct Sensitivity Analyses

Evaluate whether conclusions are robust to plausible departures from the primary missing-data assumptions.

MMRM Example in SAS

A common MMRM implementation for a continuous endpoint can be specified with PROC MIXED.

proc mixed data=analysis;
    class usubjid treatment visit;

    model change =
        baseline
        treatment
        visit
        treatment*visit
        baseline*visit
        / ddfm=kr solution;

    repeated visit /
        subject=usubjid
        type=un;

    lsmeans treatment*visit /
        diff cl;
run;

The exact model specification should depend on the endpoint, estimand, covariates, covariance structure, and trial protocol.

MMRM Example in R

An MMRM can also be implemented in R using appropriate mixed-model or specialized longitudinal-analysis packages.

A simplified example using nlme is:

library(nlme)

fit <- lme(
  change ~ baseline +
    treatment * visit +
    baseline * visit,
  random = ~ 1 | usubjid,
  correlation = corSymm(form = ~ visit | usubjid),
  weights = varIdent(form = ~ 1 | visit),
  data = analysis
)

summary(fit)

For production clinical-trial work, the precise implementation should match the planned estimand, covariance assumptions, visit structure, and inferential requirements.

Multiple Imputation Example in R

A simplified multiple-imputation workflow can be implemented with packages such as mice.

library(mice)

imp <- mice(
  analysis,
  m = 50,
  method = "pmm",
  seed = 12345
)

fit <- with(
  imp,
  lm(
    outcome ~ treatment + baseline
  )
)

pooled <- pool(fit)

summary(pooled)

This is only a conceptual example. The imputation model should be aligned with the longitudinal structure and analysis model rather than selected merely because predictive mean matching is convenient.

LOCF vs. MMRM vs. Multiple Imputation

Reference-Based Imputation

Modern sensitivity analyses sometimes explicitly specify what should happen after a patient discontinues.

For example, a reference-based approach might assume that after treatment discontinuation, the patient's subsequent trajectory behaves more like the control group.

The important difference from LOCF is that the assumption is explicitly connected to a clinical scenario.

Rather than saying: "the patient's outcome remains exactly equal to their last measurement," the analyst might ask: "What would the treatment group's post-discontinuation trajectory look like if it followed the control trajectory?"

This makes the sensitivity assumption scientifically interpretable.

Jump to Reference

One example of a reference-based sensitivity assumption is jump to reference.

Under this assumption, after treatment discontinuation, the patient's future outcomes are modeled according to the reference arm.

Conceptually:

This is very different from LOCF.

LOCF assumes no change. Jump to reference assumes a particular clinically interpretable change.

Copy Reference

Another reference-based assumption is to preserve the treatment advantage observed at discontinuation while allowing subsequent change to follow the reference trajectory.

Conceptually:

where \(k\) is the discontinuation visit.

The exact implementation can be more sophisticated, but the conceptual point is important: the analyst explicitly states what is assumed to happen after intercurrent events.

LOCF and Sensitivity Analysis: A Better Perspective

Instead of asking whether LOCF is "conservative," consider asking:

• What post-dropout trajectory does LOCF assume?
• Is that trajectory clinically plausible?
• How does it differ from the primary MAR assumption?
• Would the conclusion change under that assumption?

This turns LOCF from a supposed default solution into an explicit sensitivity scenario.

What Does "Outdated" Really Mean?

Calling LOCF outdated does not mean that every historical analysis using LOCF was necessarily invalid.

The method was widely used because it was simple, transparent, and practical for the statistical tools available at the time.

The problem is that modern clinical-trial methodology provides substantially better ways to handle longitudinal incomplete data.

Today, an analyst should generally be able to explain:

• What estimand is being targeted
• Why observations are missing
• What assumptions are being made
• How those assumptions affect inference
• Why the selected primary method is appropriate
• How sensitivity analyses address departures from those assumptions

Common Misconceptions About LOCF

1. "LOCF is conservative." Not necessarily. The direction of bias depends on the data-generating and missingness mechanisms.
2. "LOCF preserves the intent-to-treat population." Including all randomized patients and imputing missing outcomes are separate issues.
3. "LOCF assumes missing completely at random." No. LOCF is an imputation rule and does not establish an MCAR mechanism.
4. "LOCF is unbiased because the last value was actually observed." The last value was observed, but the copied future values were not.
5. "LOCF is equivalent to an MMRM." It is not. MMRM estimates longitudinal trajectories and covariance from the observed data.
6. "Multiple imputation simply guesses the missing values." Multiple imputation represents uncertainty by generating multiple plausible datasets under an explicit imputation model.
7. "If LOCF and MMRM give similar results, the problem is solved." Agreement is reassuring but does not prove that either method's assumptions are correct.
8. "A low percentage of missing data makes LOCF harmless." Even a relatively small amount of informative dropout can matter if the missing observations are systematically related to treatment response.

A Practical Decision Framework

When LOCF May Still Appear

Despite its limitations, LOCF can still appear in:

• Historical clinical-trial analyses
• Legacy analysis specifications
• Exploratory analyses
• Simple descriptive summaries
• Predefined sensitivity analyses
• Educational examples illustrating poor imputation assumptions

Its presence should not automatically be interpreted as evidence that an analysis is wrong.

The more important question is: What role does LOCF play, and are its assumptions appropriate for that role?

What a Modern Statistical Analysis Plan Should Say

A modern SAP should generally avoid language such as:

"Missing values will be replaced using LOCF."

That statement provides almost no information about the scientific rationale.

Instead, the SAP should describe:

• The estimand
• The primary analysis model
• The missing-data assumptions
• The treatment of intercurrent events
• The role of observed post-baseline data
• The sensitivity-analysis framework
• Any assumptions concerning post-discontinuation outcomes

Example SAP Language

A conceptual modern approach for a continuous longitudinal endpoint might state that the primary analysis will use an MMRM including treatment, visit, treatment-by-visit interaction, and prespecified baseline covariates, with an appropriate covariance structure for repeated observations.

The missing-data assumptions should then be stated explicitly, with sensitivity analyses assessing the robustness of the treatment comparison to plausible departures from those assumptions.

Why MMRM Is Often Preferred for Continuous Longitudinal Outcomes

MMRM has several advantages in this setting:

• It uses available repeated measurements without requiring LOCF.
• It models the covariance among repeated measurements.
• It allows treatment effects to vary by visit.
• It can adjust for baseline measurements.
• It naturally accommodates unequal numbers of observations per patient.
• Under appropriate assumptions, it can provide valid inference with incomplete longitudinal data.

The important qualification is: MMRM is not automatically unbiased simply because it is modern.

Its validity depends on model specification and missing-data assumptions.

MMRM Is Not a Magic Missing-Data Solution

A common overcorrection is to say: "LOCF is outdated, so use MMRM and the missing-data problem is solved."

That is also incorrect.

MMRM typically relies on assumptions such as a missing-at-random framework for the primary analysis.

If missingness depends on unobserved outcomes even after conditioning on observed information, sensitivity analyses may be required.

Thus:

The goal is to make the assumptions explicit, scientifically defensible, and test their influence on the conclusion.

A Useful Comparison of Assumptions

The Key Statistical Lesson

Every missing-data method makes assumptions.

The mistake is not necessarily making an assumption. The mistake is making a strong assumption without recognizing it.

LOCF hides a particularly strong assumption behind a very simple operation: copy the last number forward.

Modern methods make the assumptions more explicit and allow the analyst to evaluate their consequences.

A Compact Example

Suppose a patient has:

LOCF produces:

But a model-based analysis might estimate that, conditional on the patient's observed history and treatment group, the expected Week 12 outcome is:

The difference between 60 and 52 is precisely the type of uncertainty that LOCF ignores.

What If the Patient Would Have Worsened?

Suppose instead the conditional expected Week 12 outcome were:

LOCF would now underestimate the outcome.

This demonstrates why LOCF cannot inherently be labeled conservative.

Its bias depends on the direction of the unobserved trajectory relative to the last observed value.

Missing Data Should Be Treated as an Information Problem

A missing measurement means that information was not collected.

It does not mean that the patient's outcome stopped changing.

It also does not mean that the last measurement is the most likely future value.

The statistical task is therefore to extract as much valid information as possible from:

• Previous measurements
• Other visits
• Baseline characteristics
• Treatment assignment
• Other observed outcomes
• Reasons for discontinuation
• Patterns of missingness

Modern longitudinal methods are designed around this principle.

Reporting Recommendations

When reporting a longitudinal clinical-trial analysis, consider reporting:

• Number and percentage of missing observations by visit
• Number and percentage of patients who discontinue
• Reasons for discontinuation
• Missingness patterns by treatment group
• Primary estimand
• Primary analysis model
• Missing-data assumptions
• Sensitivity analyses
• Impact of alternative assumptions on the treatment estimate

Simply stating "LOCF was used for missing observations" provides little insight into whether the resulting inference is scientifically credible.

Common Analyst Mistakes

1. Using LOCF because it is easy. Ease of implementation is not a statistical justification.
2. Calling LOCF conservative. The direction of bias depends on the data-generating process.
3. Equating LOCF with ITT. The analysis population and missing-data method are separate concepts.
4. Ignoring dropout reasons. Reasons for missingness can contain important information about the outcome.
5. Ignoring the longitudinal trajectory. Repeated measurements contain information that LOCF largely discards.
6. Using only one missing-data method. Sensitivity analysis is important when conclusions depend on unobserved outcomes.
7. Assuming MMRM is assumption-free. It is not. Its validity depends on model and missing-data assumptions.
8. Using an imputation model unrelated to the analysis. The imputation model should be scientifically and statistically compatible with the estimand and analysis.
9. Failing to distinguish observed from imputed data. Imputed values represent assumptions, not newly observed facts.

Modern Missing-Data Workflow

What Should Be in the Statistical Analysis Plan?

A robust SAP for a longitudinal endpoint should specify:

• The estimand
• Primary endpoint definition
• Analysis population
• Baseline definition
• Visit windows
• Primary statistical model
• Covariates
• Treatment-by-visit interactions
• Covariance structure
• Degrees-of-freedom method when relevant
• Missing-data assumptions
• Handling of intercurrent events
• Primary estimand-specific contrast
• Sensitivity analyses
• Any reference-based assumptions
• Any tipping-point or MNAR analyses

The phrase "LOCF will be used" should generally not be the entirety of the missing-data strategy.

LOCF in Historical Perspective

LOCF is important to understand because it appears frequently in older clinical-trial literature, legacy programs, and interviews.

A statistician working with historical datasets may encounter variables such as:

AVAL_LOCF
CHG_LOCF
BASELINE_LOCF
WEEK12_LOCF

Understanding what those variables mean is important.

But recognizing that a dataset contains LOCF-derived values is different from believing that LOCF is still the preferred approach for modern primary analyses.

Interview Question: Why Is LOCF Outdated?

A strong interview answer is:

LOCF: The Five Things to Remember

The Most Important Concept

The fundamental problem with LOCF is not that copying a number forward is mathematically complicated. It is that the copied number represents an assumption about an outcome that was never observed.

When a patient drops out after Week 8, their Week 12 outcome is unknown. LOCF replaces that unknown with the Week 8 value.

But there is no general statistical law saying:

The patient's outcome might have improved. It might have worsened. It might have fluctuated. It might have followed the control trajectory. It might have followed the treatment trajectory. It might have responded differently depending on why the patient discontinued.

Modern missing-data methodology does not eliminate this uncertainty. Instead, it makes the uncertainty and assumptions explicit.

References

Little, R.J.A. & Rubin, D.B. (2019). Statistical Analysis with Missing Data. 3rd ed. Wiley.

Mallinckrodt, C.H., Lin, Q., Molenberghs, G., et al. (2014). Recent developments in the prevention and treatment of missing data in clinical trials. Therapeutic Innovation & Regulatory Science.

Mallinckrodt, C.H., Lane, P.W., Schnell, R.R., Peng, Y., Molenberghs, G. & Carroll, R.J. (2008). Recommendations for the primary analysis of continuous endpoints in longitudinal clinical trials. Pharmaceutical Statistics.

Mallinckrodt, C.H., Clark, W.S. & David, S.R. (2001). Accounting for dropout bias using mixed-effects models. Journal of Biopharmaceutical Statistics.

Molenberghs, G. & Kenward, M.G. (2007). Missing Data in Clinical Studies. Wiley.

National Research Council (2010). The Prevention and Treatment of Missing Data in Clinical Trials. National Academies Press.

ICH (2019). ICH E9(R1): Addendum on Estimands and Sensitivity Analysis in Clinical Trials to the Guideline on Statistical Principles for Clinical Trials.

Little, R.J., D'Agostino, R., Cohen, M.L., et al. (2012). The prevention and treatment of missing data in clinical trials. New England Journal of Medicine, 367, 1355–1360.