Estimating genomic category probabilities from fluorescent in situ hybridization counts with misclassification

Fluorescent in situ hybridization (FISH) is used in many medical settings to identify the genetic or chromosomal abnormality characterizing a disease. FISH techniques may be used to classify a sample of a patient's cells into genomic categories, one or more of which is associated with the disease. The clinical goal is to determine whether there is a positive proportion of diseased cells in the patient, or to estimate this proportion. Unfortunately, such data are often subject to classification error inherent in FISH methodology. However, when additional data are available from cells of known type, typically from normal subjects, this information may be combined with the patient's data to perform the desired inference while correcting for misclassification. We provide a method for estimating the proportions of cells of each category and testing whether a particular proportion is positive in each of several patients when such background data are available. Our approach is to model the misclassification probabilities, jointly to estimate the model parameters and each patient's cell type proportions by using maximum likelihood and to use this to obtain likelihood ratio tests and confidence intervals. The method is applied to blood cell count data from chronic myelogenous leukaemia patients, where FISH is used to identify the chromosomal translocation characterizing the disease.