Quantifying the Change of Melanoma Incidence by Breslow Thickness

Melanoma incidence has increased throughout the world over the past 25 years. A surrogate for the severity of melanoma is the Breslow thickness of the lesions. Data on melanoma, including Breslow thickness, were collected in 1978–1980 and 1988–1990 from the Tasmania Tumor Registry. We use a density ratio model to quantify the change of melanoma by Breslow thickness. In this model, the ratio of two densities is assumed to have a known form up to a parameter, but the underlying densities are not modeled. This model includes the length bias sampling model as a special case. The Kolmogorov–Smirnov test statistic is used to test the correctness of the density ratio model. Model-based cumulative distribution estimation is studied. Methodology developed in this article is applied to the Tasmania Tumor Registry data.