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Developing Calibration Weights and Standard-Error Estimates for a Survey of Drug-Related Emergency-Room Visits

Keywords: Frame variable, response model, prediction model, finite population correction, SUDAAN

Like many establishment surveys, the Drug Abuse Warning Network (DAWN) is based on a stratified random sample drawn from a complete frame containing a single measure of size for each population unit, in this case a hospital with an emergency department. Many DAWN sampled hospitals are selected with certainty, but all sampled hospitals share the possibility of unit nonresponse. This paper describes a two-step calibration-weighting scheme for the hospitals in the DAWN respondent sample. The first step adjusts for unit nonresponse. The second increases the statistical efficiency of most estimators of interest. Both use the measure of size and other useful auxiliary variables contained on the frame. Although many survey variables are roughly a linear function of the measure of size, response is better modeled as a function of the log of that measure. Consequently the log of size is a calibration variable in the nonresponse-adjustment step, while the measure of size itself is a calibration variable in the second calibration step. Nonlinear calibration procedures, implemented using SUDAAN® 11, are employed in both steps. SUDAAN 11 has been designed to produce linearization-based standard-error estimates when there is a single calibration-weighting step but not two. We show with 2010 DAWN data that using a one-step routine when there are in fact two calibration-weighting steps can, after appropriately adjusting the finite-population correct in some sense, produce standard-error estimates that tend to be slightly conservative.