Analysis of a marker for cancer of the thyroid with a limit of detection

Limit of detection (LoD) is a common problem in the analysis of data generated by instruments that cannot detect very small concentrations or other quantities, resulting in left-censored measurements. Methods intended for data that are not subject to this problem are often difficult to modify for censoring. We adapt the simulation-extrapolation method, devised originally for fitting models with measurement error, to dealing with LoD in conjunction with a mixture analysis. The application relates the levels of thyroglobulin in individuals with cancer of the thyroid before and after treatment with radioactive iodine I–131. We conclude that the fitted mixture components correspond to levels of effectiveness of the treatment.