On the use of statistical models of within-person variation in long-term studies of healthy individuals.

Abstract

Two statistical models for forecasting from very short time series have been applied to serial data from 162 participants in a health monitoring program. One model assumes stationary (“homeostatic”) variability over time with statistically independent observations: the other model presumes nonstationary (“random walk”) variation with a high degree of autocorrelation between observations. The data consist of results from 14 biochemical and seven hematological tests in blood collected on several successive weeks during each of four or more annual examinations of the subjects. Based on the average week-to-week variation in a given individual during the first three sampling periods, forecast ranges for the mean of every analyte measured during the fourth period in that individual were calculated from the two models. The random-walk model was better at detecting trends (at the 5% level of significance) during the first four sampling periods, with an average sensitivity of 56%, close to that predicted from theory. The stationary model was more adept at detecting a sudden nonrandorn change from the past record. When both models were used together, about 63% of the highest decile of nontrend changes were detected. We present tabulations of the magnitudes of observed trends and of the larger non-trend changes so that the probable clinical usefulness of detecting such changes may be assessed.