Nonstationary Gaussian Process Regression for Evaluating Repeated Clinical Laboratory Tests

Abstract

Sampling repeated clinical laboratory tests with appropriate timing is challenging because the latent physiologic function being sampled is in general nonstationary. When ordering repeated tests, clinicians adopt various simple strategies that may or may not be well suited to the behavior of the function. Previous research on this topic has been primarily focused on cost-driven assessments of oversampling. But for monitoring physiologic state or for retrospective analysis, undersampling can be much more problematic than oversampling. In this paper we analyze hundreds of observation sequences of four different clinical laboratory tests to provide principled, data-driven estimates of undersampling and oversampling, and to assess whether the sampling adapts to changing volatility of the latent function. To do this, we developed a new method for fitting a Gaussian process to samples of a nonstationary latent function. Our method includes an explicit estimate of the latent function's volatility over time, which is deterministically related to its nonstationarity. We find on average that the degree of undersampling is up to an order of magnitude greater than oversampling, and that only a small minority are sampled with an adaptive strategy.