Smoothing across time in repeated cross-sectional data

Repeated cross-sectional samples are common in national surveys of health like the National Health Interview Survey (NHIS). Because population health outcomes generally evolve slowly, pooling data across years can improve the precision of current-year annual estimates of disease prevalence and other health outcomes. Pooling over time is particularly valuable in health disparities research, where outcomes for small groups are often of interest and pooling data across groups would bias disparity estimates. State-space modeling and Kalman filtering are appealing choices for smoothing data across time. However, filtering can be problematic when few time points are available, as is common with annual cross-sectional data. Problems arise because filtering relies on estimated variance components, which can be biased and imprecise when estimated with small samples, especially when estimated in tandem with linear trends. We conduct a simulation study showing that even when trends and variance components are estimated poorly, smoothing with these estimates can improve the mean squared error (MSE) of estimated health states for multiple racial/ethnic groups when the variance components are estimated with the pooled sample. We consider frequentist estimators with no trends, one common trend across groups, and separate trends for every group, as well as shrinkage estimators of trends through a Bayesian model. We show that the Bayesian model offers the greatest improvement in MSE, and that Bayesian Information Criterion (BIC)-based model averaging of the frequentist estimators with different trend assumptions performs nearly as well. We present empirical examples using the NHIS data.