This note compares multiple imputation and listwise deletion using simulations that focus on data missing not at random (MNAR). Both approaches are known to produce biased estimates under MNAR; the simulations investigate how their relative performance changes across realistic scenarios.

📊 How the Simulations Were Set Up

• Simulated datasets generated under MNAR mechanisms.
• Scenarios varied the strength of correlation between fully observed variables and variables with missing values, including cases where those correlations were very strong so the data were nearly “missing at random.”
• Performance was evaluated on bias, efficiency, and interval coverage for common estimands.

🔍 Key Findings

• Multiple imputation frequently produced more biased estimates than listwise deletion when the data were MNAR.
• Multiple imputation also tended to be less efficient (larger variance) and to have worse coverage than listwise deletion in these MNAR scenarios.
• These patterns held even with very strong correlations between observed and partially observed variables, i.e., situations that are nearly missing at random.
• Importantly, both methods remain biased under MNAR; the comparison indicates relative performance, not unbiased recovery.

⚖️ Why This Matters

• When the true data-generating process is unknown, comparing results from multiple imputation and listwise deletion requires caution: apparent improvements from imputation can be misleading under MNAR.
• Practitioners should be aware that strong auxiliary correlations do not guarantee that multiple imputation will outperform simple casewise deletion if MNAR mechanisms are present.

📌 Bottom Line

• Under MNAR, multiple imputation can underperform listwise deletion on bias, efficiency, and coverage, so researchers should not assume imputation always improves inference when missingness mechanisms are uncertain.