Predicting high-risk cholesterol levels

Abstract

The pattern of longitudinal changes in cholesterol levels has important implications for screening policies and for understanding the role of cholesterol as a risk factor for coronary heart disease. We explored a variety of longitudinal models to predict changes in cholesterol over several years, emphasizing the probability that an individual will develop a cholesterol level that requires further diagnostic tests or treatment. The first question was whether measured cholesterol is Markovian. A chi-square statistic based on the bootstrap and motivated by the Chapman-Kolmogorov equations established that it is not. Related bootstrap-based tests indicate that the probability structure of measured cholesterol is not that of a low order autoregressive moving average (ARMA) model. We then tested several alternative models to predict future cholesterol levels from the pattern of previous measured values, using receiver-operating characteristic (ROC) curves to summarize the sensitivity and specificity of the resulting rules for predicting high risk values. One method was based on the Gaussian assumption that the logarithms of cholesterol levels are jointly Gaussian; a second was based on ordinary least squares regression; a third was based on logistic regression. We developed a bootstrap technique for finding confidence regions for points on the ROC curves. Bootstrap simulations were used in three different ways in computing the regions: one to bias correct each point on a curve, a second to find the bootstrap distribution of points for each threshold that defines a particular value of sensitivity and specificity, and a third to find the volume of the (ellipsoidal) regions. The results of our analyses suggest that the models can be used to identify subgroups of individuals who are unlikely to develop very high risk levels of cholesterol. The models also can be used to help formulate schedules for screening individuals.