Latent class modeling approaches for assessing diagnostic error without a gold standard: With applications to p53 immunohistochemical assays in bladder tumors

Improved characterization of tumors for purposes of guiding treatment decisions for cancer patients will require that accurate and reproducible assays be developed for a variety of tumor markers. No gold standards exist for most tumor marker assays. Therefore, estimates of assay sensitivity and specificity cannot be obtained unless a latent class model-based approach is used. Our goal in this article is to estimate sensitivity and specificity for p53 immunohistochemical assays of bladder tumors using data from a reproducibility study conducted by the National Cancer Institute Bladder Tumor Marker Network. We review latent class modeling approaches proposed by previous authors, and we find that many of these approaches impose assumptions about specimen heterogeneity that are not consistent with the biology of bladder tumors. We present flexible mixture model alternatives that are biologically plausible for our example, and we use them to estimate sensitivity and specificity for our p53 assay example. These mixture models are shown to offer an improvement over other methods in a variety of settings, but we caution that, in general, care must be taken in applying latent class models.