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.