Random draws from observed values for missing data: when do they support valid inference? A simulation study with a clinical illustration

Imputation methods that draw replacement values from a variable's admissible domain are attractive because they are simple and never produce structurally invalid values. This study asks when such draws support valid statistical inference. The Random-Draw Observation Framework (RDOF) is examined in three forms: the original Random-Draw Observation Imputation (ROI), which draws uniformly between the observed minimum and maximum; ROI-E, which draws from the empirical distribution of the observed values via the approximate Bayesian bootstrap; and Random-Draw Class Observation Imputation (RCOI-E), which applies the same draws within cells defined by a class variable and the analysis variables. We combine completed datasets using Rubin's rules and also assess the common practice of retaining the imputation with the smallest standard error (SE). In a pre-specified simulation study of 72 scenarios (six marginal distributions; MCAR, MAR and MNAR mechanisms; 30% and 60% missingness; strong and weak class variables; n = 340; 500 replications per scenario), uniform-range ROI attenuated the regression slope by 55–83% on average, and its 95% confidence intervals covered the true slope in no more than 16% of replications in any scenario (6% when averaged over distributions). Selecting the minimum-SE imputation understated the mean SE by up to 68% without reducing bias. RCOI-E never produced an invalid value and achieved 93–96% slope coverage at 30% missingness under all three mechanisms. Still, coverage fell to 85% at 60% MAR missingness and to 58% when the class variable was weakly informative. Predictive mean matching (PMM), which also imputes observed values, was more robust under MAR, whereas RCOI-E was comparable or slightly better under MCAR and MNAR. A resampling study of 270 complete clinical records (Statlog Heart data) reproduced these patterns: at 60% missingness, uniform-range ROI attenuated the slope of age on maximum heart rate by 71–74% and covered the true slope in at most 1% of replications, whereas RCOI-E and PMM kept coverage between 91% and 95%. Value-format preservation is therefore necessary but not sufficient: random-draw imputation supports valid inference only when the draws condition on the variables that drive the analysis and the missingness, and when the imputations are pooled rather than selected.