Nonparametric Bayesian Multiple Imputation for Missing Data Due to Mid-study Switching of Measurement Methods

Investigators often change how variables are measured during the middle of data collection, for example in hopes of obtaining greater accuracy or reducing costs. The resulting data comprise sets of observations measured on two (or more) different scales, which complicates interpretation and can create bias in analyses that rely directly on the differentially measured variables. We develop approaches for handling mid-study changes in measurement for settings in the absence of calibration data, i.e., no subjects are measured on both (all) scales, based on multiple imputation. This setting creates a seemingly insurmountable problem for multiple imputation: since the measurements never appear jointly, there is no information in the data about ∗Lane F. Burgette is an Associate Statistician at the RAND Corporation, Arlington, VA 22202-5050 ([email protected]) and Jerome P. Reiter ([email protected]) is Mrs. Alexander Hehmeyer Associate Professor, Department of Statistical Science, Duke University, Durham, NC 27708-0251. The authors wish to thank Howard Chang, Sharon Edwards, Marie Lynn Miranda, Geeta Swamy, three anonymous referees, an Associate Editor, and the Editor for helpful comments. L.F. Burgette was a Postdoctoral Research Associate in the Department of Statistical Science at Duke University when this research was conducted. This research was funded by Environmental Protection Agency grant R833293.