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 based on multiple imputation for handling mid-study changes in measurement for settings without calibration data, that is, no subjects are measured on both (all) scales. This setting creates a seemingly insurmountable problem for multiple imputation: since the measurements never appear jointly, there is no information in the data about their association. We resolve the problem by making an often scientifically reasonable assumption that each measurement regime accurately ranks the samples but on differing scales, so that, for example, an individual at the qth percentile on one scale should be at about the qth percentile on the other scale. We use rank-preservation assumptions to develop three imputation strategies that flexibly transform measurements made in one scale to measurements made in another: a Markov chain Monte Carlo (MCMC)-free approach based on permuting ranks of measurements, and two approaches based on dependent Dirichlet process (DDP) mixture models for imputing values conditional on covariates. We use simulations to illustrate conditions under which each strategy performs well, and present guidance on when to apply each. We apply these methods to a study of birth outcomes in which investigators collected mothers' blood samples to measure levels of environmental contaminants. Midway through data ascertainment, the study switched from one analytical lab to another. The distributions of blood lead levels differ greatly across the two labs, suggesting that the labs report measurements according to different scales. We use nonparametric Bayesian imputation models to obtain sets of plausible measurements on a common scale, and estimate quantile regressions of birth weight on various environmental contaminants.