A comparison of missing data approaches for linear regression with missing not at random outcome and predictors

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Observational health and longitudinal studies frequently have missing data.
• Missingness often depends on unobserved data, violating the missing at random assumption.
• Existing methods for missing not at random (MNAR) data typically assume predictors are fully observed.

Purpose of the Study:

• To compare methods for handling MNAR data in linear regression when both outcomes and predictors have missing values.
• To evaluate the performance of various imputation and modeling techniques under complex MNAR scenarios.

Main Methods:

• Extensive simulations were conducted to assess different approaches.
• Methods evaluated include complete-case analysis, multiple imputation (MAR and MNAR), Heckman selection models, imputation stacking, and random indicator imputation.
• Sensitivity analyses were performed using real-world data from the Betula study.

Main Results:

• No single method consistently provided unbiased estimates or nominal coverage across all simulated MNAR scenarios.
• Not-at-random fully conditional specification (NAR FCS) demonstrated straightforward implementation and near-nominal coverage when sensitivity parameters were accurately specified.
• Sensitivity analyses are crucial for understanding the impact of MNAR assumptions on results.

Conclusions:

• Addressing MNAR data in both outcomes and predictors requires careful consideration of modeling assumptions.
• NAR FCS offers a practical approach, but its reliability depends on accurate sensitivity parameter specification.
• The relationship between longitudinal memory decline and brain structure in aging remained robust across various MNAR conditions.