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Abstract:
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Trend and biomarker data often feature changing amounts of variability over time. For example, in U.S. cancer incidence data, there may be several years of flat or slowly increasing cancer incidence followed by a sharp spike in cases because of a new risk factor or a change in screening protocols. Existing methods struggle to accommodate this change in variance and may oversmooth the spike while adding excess variability to the linear or flat portions of the trend. For this setting, we propose horseshoe process regression, which places a Bayesian shrinkage horseshoe process prior on the first derivative of the function to be fit. We implement horseshoe process regression in Stan and evaluate its performance by simulation. Compared to other common smoothing approaches, we find that horseshoe process regression performs extremely well for fitting functions that exhibit sharp increases, while performing comparably to other comparators when fitting smooth functions without sharp increases. We demonstrate the use of horseshoe process regression to model U.S. cancer incidence data from the Surveillance, Epidemiology, and End Results (SEER) Program.
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