Do you know your total cholesterol (TC) number?

Total cholesterol (TC) measurements are subject to errors primarily because of temporal variations in cholesterol levels within each individual. These errors make it difficult to estimate the proportion of study subjects with true (error-free) TC in a specific range, an extremely important parameter to policy makers in health care management. To properly address this issue, it is key to accurately estimate the distribution function of the true TC, which typically deviates from the normal distribution. To better approximate the distribution function of the true TC, we propose a constrained maximum likelihood estimator based on a mixture-of-normals model. A simulation study illustrates that the proposed estimator performs better than an estimator based on the normality assumption that is frequently used in the literature to address the same issue. Finally, the proposed estimator is applied to data from a study, and its performance is once again compared with that of an estimator based on the normality assumption.