Handling Missing Repeated Outcome Measurements in Clinical Research: Models, Myths, and Best Practices [Multiple imputation, MI]

Introduction

Repeated outcome measurements are common in longitudinal clinical studies—tracking symptoms, biomarkers, or functional scores across time. However, incomplete follow-up is equally common, creating analytical challenges that can distort treatment effects, underestimate variability, or introduce bias.

Handling these missing repeated measures requires more than plugging gaps—it calls for model-based strategies that respect time structure, subject-level correlations, and assumptions about missingness. This article explores and contrasts key approaches: complete case analysis, Last Observation Carried Forward (LOCF), linear mixed-effects modeling, and Multiple Imputation (MI), highlighting best practices and trade-offs.

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Understanding Repeated Measures Data Structure

Wide vs Long Format

• Wide format stores each repeated measure as a separate column (e.g., QoL0, QoL12, QoL24).

• Long format stacks timepoints vertically with identifiers for subject and time (e.g., id, visit, QoL).

Long format is more suitable for modeling techniques that account for time trends and intra-individual correlation.

📌 Clinical Tip: Always reshape into long format before applying multilevel models or MI packages designed for longitudinal data.

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Method 1: Complete Records Analysis

How It Works

• Retains only individuals with no missing values at any measurement time point.

• Simplifies analysis but leads to biased estimates when data are not Missing Completely at Random (MCAR).

Limitations

• Information loss: High attrition of sample size, especially in longer follow-up studies.

• Selection bias: Patients who complete all follow-ups may differ systematically (e.g., healthier, more adherent).

Example: In a 12-month follow-up study with 4 assessments, only 30% of patients may have complete data. Analyzing only these individuals may inflate treatment effects if the healthiest patients are overrepresented.

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Method 2: Last Observation Carried Forward (LOCF)

How It Works

• Fills in missing values by repeating the last available observation.

• Assumes stability of the measured outcome over time beyond the last known value.

Pitfalls

• Unrealistic assumption: Clinical trajectories (e.g., recovery, disease progression) rarely remain static.

• Variance distortion: Artificially reduces variability, leading to overconfident confidence intervals.

• Bias risk: Can either under- or overestimate effects depending on outcome trends.

⚠️ LOCF may be tempting due to simplicity, but it is neither conservative nor liberal—just misleading under most conditions.

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Method 3: Linear Mixed-Effects Models (LMMs)

Why It Works

LMMs account for:

• Intra-individual correlation (e.g., repeated scores within each patient),

• Unequal time intervals,

• Missingness under MAR assumptions—valid if missingness depends only on observed data.

Statistical Mechanics

• Estimate fixed effects (population-level trends) and random effects (subject-level deviations).

• Fit via Maximum Likelihood (ML) or Restricted Maximum Likelihood (REML).

Key Feature: LMMs use all available data—patients with partial follow-up contribute information without being dropped.

🔍 Secret Insight: A landmark study showed that using MI in addition to LMMs yielded no extra benefit for outcome estimation if the model was already properly specified.

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Method 4: Multiple Imputation for Repeated Measures

Expanding the Toolkit

Multiple Imputation (MI) can also be applied to longitudinal data, but requires extra caution:

• Format: Long format is preferred.

• Structure: Time dependency and within-subject clustering must be addressed.

• Challenge: MI under independent assumptions ignores the within-subject correlation.
  

Advanced Package: mimix in Stata

• Based on mi impute mvn, the mimix package imputes time-series structured missing outcomes in long format.

• Allows imputation across treatment arms, enabling sensitivity analysis under alternative missingness assumptions.
  

Scenarios Supported

1. Missing at Random (MAR) – Default; assumes dropout unrelated to unmeasured values after conditioning on observed data.

2. Jump to Reference (J2R) – Imputes missing values based on control arm trajectory post-dropout.

3. Copy Reference (CR) – Assumes treatment effect ceases and the subject follows the reference group thereafter.

4. Copy Increments in Reference (CIR) – Adds the average increment in the control group to the last observed value.

5. Last Mean Carried Forward (LMCF) – Assumes flat trajectory at the last group-level mean.

📊 Clinical Application: In an asthma trial, MAR-based MI projected optimistic FEV1 recovery in the treatment arm, while J2R and CIR suggested a more conservative trajectory—critical when interpreting treatment durability.

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Comparing the Approaches: Strengths & Caveats

Method	Uses All Data	Respects Time	Handles Correlation	Assumption Robustness	Ideal For
Complete Records	❌	❌	❌	MCAR only	Preliminary checks
LOCF	❌	❌	❌	Implausible	Rare cases (e.g., plateau outcomes)
LMM	✅	✅	✅	MAR	Primary analysis
MI (mimix, etc.)	✅	✅	✅ (if configured)	MAR + sensitivity	Sensitivity checks, policy impact

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Conclusion

Handling missing repeated outcome measurements isn’t just a technical necessity—it’s a design integrity safeguard. Choosing the right approach depends on:

• Your assumptions about missingness (MCAR vs MAR vs MNAR),

• The complexity of your longitudinal structure, and

• The inferential weight of your missing data.

Linear mixed-effects models should be your primary go-to for analysis. MI methods—especially mimix—are powerful for sensitivity scenarios, allowing you to probe how results might shift under different assumptions about dropout behavior.

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Key Takeaways

• Complete case and LOCF are inadequate in most longitudinal clinical settings.

• LMMs offer robust handling of partial data under MAR.

• Multiple Imputation, when used correctly, can strengthen sensitivity analyses and clinical interpretations.

• mimix enables scenario modeling (e.g., Jump to Reference) that reflects patient behavior post-protocol deviation.