Defining Reproducibility Statistics as a Function of the Spatial Covariance Structures in Biomarker Studies

The reproducibility of a biomarker plays a paramount role in determining whether it provides an accurate indication of the true underlying disease or risk status of an individual. When biomarker measurement involves obtaining samples of tissue at random from the organ of interest, sampling variability based on spatial effects can affect this reproducibility. This situation arises when a target organ, such as the prostate or esophagus, is evaluated by multiple random needle biopsies or when an excised organ is randomly sampled. We present a general approach toward estimating reproducibility in the presence of different variance-covariance structures needed to account for possible spatial or temporal variation and correlation. Specifically, we extend the work of previous authors involving applications of the concordance correlation coefficient (CCC) by allowing for different variance-covariance structures of the data. A general concordance correlation matrix representing pairwise concordance correlation coefficients is presented along with an overall concordance correlation coefficient both of which may be obtained from models assuming different variance-covariance structures. The overall concordance correlation coefficient provides a measure of the overall reproducibility and its validity relative to various assumed covariance structures can be assessed by examining commonly employed goodness-of-fit measures. We illustrate these methods to minichromosome maintenance protein 2 (MCM2) data coming from the prostate glands of seven subjects having prostate biopsies between 2002 and 2003.