Using the outcome for imputation of missing predictor values was preferred.
OBJECTIVE
Epidemiologic studies commonly estimate associations between predictors (risk factors) and outcome. Most software automatically exclude subjects with missing values. This commonly causes bias because missing values seldom occur completely at random (MCAR) but rather selectively based on other (observed) variables, missing at random (MAR). Multiple imputation (MI) of missing predictor values using all observed information including outcome is advocated to deal with selective missing values. This seems a self-fulfilling prophecy.


METHODS
We tested this hypothesis using data from a study on diagnosis of pulmonary embolism. We selected five predictors of pulmonary embolism without missing values. Their regression coefficients and standard errors (SEs) estimated from the original sample were considered as "true" values. We assigned missing values to these predictors--both MCAR and MAR--and repeated this 1,000 times using simulations. Per simulation we multiple imputed the missing values without and with the outcome, and compared the regression coefficients and SEs to the truth.


RESULTS
Regression coefficients based on MI including outcome were close to the truth. MI without outcome yielded very biased--underestimated--coefficients. SEs and coverage of the 90% confidence intervals were not different between MI with and without outcome. Results were the same for MCAR and MAR.


CONCLUSIONS
For all types of missing values, imputation of missing predictor values using the outcome is preferred over imputation without outcome and is no self-fulfilling prophecy.
Moons
Karel G M
KG
Julius Center for Health Sciences and General Practice, University Medical Center, Utrecht, P.O. Box 80035, 3508 GA Utrecht, The Netherlands. K.G.M.Moons@umcutrecht.nl
Donders
Rogier A R T
RA
Stijnen
Theo
T
Harrell
Frank E
FE
D000328:Adult; D000367:Age Factors; D000368:Aged; D015982:Bias; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D017063:Outcome Assessment, Health Care; D011183:Postoperative Complications; D011655:Pulmonary Embolism / Q000175:diagnosis* / Q000209:etiology; D012307:Risk Factors; D012984:Software