Multiple imputation for an incomplete covariate that is a ratio.

Area of Science:

• Biostatistics
• Statistical Modeling
• Data Analysis

Background:

• Multiple imputation is used for missing data in regression covariates.
• Ratios of variables are common covariates, but their imputation requires careful consideration.
• Existing methods for imputing ratios may introduce bias depending on data characteristics.

Purpose of the Study:

• To evaluate different multiple imputation strategies for ratio variables used as covariates.
• To compare 'passive' imputation (imputing components then calculating ratio) versus 'active' imputation (imputing ratio directly).
• To assess the impact of imputation model choice on regression analysis results, particularly concerning the ratio's denominator variation.

Main Methods:

• Two real-world datasets were used, involving body mass index and cholesterol ratios.
• Sensitivity analyses were performed comparing various multiple imputation models.
• A simulation study was conducted to systematically investigate bias under different conditions.
• Fully Bayesian joint models were explored but found computationally infeasible.

Main Results:

• Results were similar across imputation models in the first dataset.
• In the second dataset, results were sensitive to the imputation model choice, influenced by the denominator's coefficient of variation.
• Passive imputation without log-transformation showed a risk of downward bias when the denominator's coefficient of variation exceeded 0.1.

Conclusions:

• The choice of imputation method for ratio covariates significantly impacts regression results, especially when the denominator has high variability.
• Active imputation or passive imputation after log-transformation are generally preferred methods.
• Careful consideration of the ratio's denominator characteristics is essential for robust statistical inference.