Statistical resolutions for large variabilities in hair mineral analysis

Measuring biomaterials is usually subject to error. Measurement errors are classified into either random errors or biases. Random errors can be well controlled using appropriate statistical methods. But, biases due to unknown, unobserved, or temporary causes, may lead to biased conclusions. This study describes a verification method to examine whether measurement errors are random or not and to determine efficient statistical methods. 1. How can we ascertain the reliability of measurements? 2. How can we assess and control the variability of measurements? 3. How do we efficiently determine associations between hair minerals and exposures? 4. How can we concisely present the reference values? Since hair minerals all have distinctive natures, it would be unproductive to examine each mineral individually to find significant and consistent answers that apply to all minerals. To surmount this difficulty, we used one simple model for all minerals to explore quantitative answers. Hair mineral measurements of six-year-old children were analyzed based on the statistical model. The analysis verified that most of the measurements were reliable, and their inter-individual variations followed two-parameter distributions. These results allow for sophisticated study designs and efficient statistical methods to examine the effects of various kinds of exposures on hair minerals.