Improving disparity estimates for rare racial/ethnic groups with trend estimation and Kalman filtering: an application to the National Health Interview Survey.

Eliminating racial/ethnic health disparities is a major federal policy goal; however, most national health surveys have limited ability to assess the health of racial/ethnic population subgroups (e.g., national origin subgroups of Hispanic ethnicity or Asian race) (Waksberg, Levine, and Marker 2000) or to measure progress toward those goals. The National Health Interview Survey (NHIS), the primary source of information on the nation's health (U.S. Department of Health and Human Services 2007), has been successfully used for innovative analyses in small areas (e.g., Long, Graves, and Zuckerman 2007) and can support simple analyses for racial/ethnic subgroups; sample sizes are insufficient for detailed analyses of subgroups other than Mexican Americans using traditional techniques. The Census 2000 and the American Community Survey provide sufficient sample sizes for accurate estimates for American Indians/Alaska Natives (AI/AN) and Asian national origin subgroups, but neither collects much data on health. In a time of limited survey budgets but pressing policy needs, the need to increase accuracy without generating additional costs cannot be overstated. Several approaches to combining data have been used to make estimates about the health of racial/ethnic populations. One approach is to “borrow strength” from larger groups (Rao 2003), that is, to combine direct estimates based on the data collected from the exact population of interest with indirect estimates based on related data, such as data from other geographic areas, subgroups, or time periods. While indirect estimates may contain bias if the related data differ systematically from the data of interest, in combination with direct estimates they can often improve overall accuracy by substantially decreasing the variance of a combined estimator.1 Borrowing strength from other geographic areas, often known as small-area estimation, is useful when one is trying to estimate in smaller geographic areas (e.g., Mendez-Luck et al. 2007), but of limited use for national estimates. Borrowing from other racial/ethnic groups by incorporating the overall population prevalence into weighted estimates can improve the precision of estimates for smaller racial/ethnic groups (which typically have smaller sample sizes in general national surveys), but because the overall population mean is dominated by non-Hispanic whites and other larger groups, this approach biases estimators of between-group health differences toward zero, underestimating the disparities between them. Such a bias directly confounds policy questions of interest. Combining multiple years of data within racial/ethnic subgroups (borrowing strength over time) can improve estimates without systematically underestimating differences. Simply averaging past and current years to estimate the present prevalence can introduce substantial bias if the prevalence changes over time, as obesity and diabetes have recently. What is needed is a method that improves the accuracy of prevalence estimates and means for national racial/ethnic groups in the most recent year for which data are available (hereafter referred to as the “current” year) that (a) does not systematically under- or overestimate differences between groups and (b) allows for time trends. We describe an alternative method for improving estimates for small population subgroups, based on the Kalman filter. This approach “borrows strength” across years—combining estimates from multiple years, but giving the greatest weight to the current year. The Kalman filter (Kalman 1960), which originated as a recursive computational algorithm to estimate the state of a process and “filter” out “noise” (as opposed to signal) in engineering applications, provides a general set of tools applicable to a variety of nonengineering settings. It views a survey estimate as a noisy measure of an underlying population mean that is influenced by its own past values. Treating present values as “updates” from the past allows us to smooth the estimate of the present using the past. In particular, it provides an optimal means for combining data across years to capture under a statistical model: (a) autocorrelated time-varying means for each racial/ethnic group that transition smoothly across years; (b) individual variance within these groups around the means (Blight and Scott 1973; Binder and Dick 1989; Lind 2005;); and (c) errors in the estimates of the annual group means resulting from sampling individuals from the group population. For estimating disparities, more general recommendations by the National Center for Health Statistics (NCHS) suggest using the difference between a given group (e.g., AI/AN or Chinese) and the group with the most salutary level of a given outcome among those groups with a relative standard error (RSE) of <10 percent for that outcome (Keppel, Pearcy, and Klein 2004). Such an approach ensures that the reference group is itself well estimated and that the error in disparity estimates involving rare racial/ethnic groups such as AI/AN and Chinese in the present application is primarily a function of the error in the estimates for these rare groups themselves. However, relatively small sample sizes for both AI/AN and Chinese American subgroups mean that simple 1-year direct estimates for both have RSEs exceeding the recommended maximum of 30 percent for several health outcomes. We use data from AI/AN and Chinese American samples in the NHIS to demonstrate the utility of the modified Kalman filter (MKF) for health-disparities research. Each group (1) represents percent of the U.S. population, (2) has been identified as a distinct subgroup in NHIS data for a number of years, and (3) has about 200 observations annually.