A Generalized Beta Model for the Age Distribution of Cancers: Application to Pancreatic and Kidney Cancer

Abstract

The relationships between cancer incidence rates and the age of patients at cancer diagnosis are a quantitative basis for modeling age distributions of cancer. The obtained model parameters are needed to build rigorous statistical and biological models of cancer development. In this work, a new mathematical model, called the Generalized Beta (GB) model is proposed. Confidence intervals for parameters of this model are derived from a regression analysis. The GB model was used to approximate the incidence rates of the first primary, microscopically confirmed cases of pancreatic cancer (PC) and kidney cancer (KC) that served as a test bed for the proposed approach. The use of the GB model allowed us to determine analytical functions that provide an excellent fit for the observed incidence rates for PC and KC in white males and females. We make the case that the cancer incidence rates can be characterized by a unique set of model parameters (such as an overall cancer rate, and the degree of increase and decrease of cancer incidence rates). Our results suggest that the proposed approach significantly expands possibilities and improves the performance of existing mathematical models and will be very useful for modeling carcinogenic processes characteristic of cancers. To better understand the biological plausibility behind the aforementioned model parameters, detailed molecular, cellular, and tissue-specific mechanisms underlying the development of each type of cancer require further investigation. The model parameters that can be assessed by the proposed approach will complement and challenge future biomedical and epidemiological studies.

A novel Approach for Analysis of the Log-Linear Age-period-Cohort Model: Application to Lung Cancer Incidence

“…First primary, microscopically confirmed LC cases from the SEER9 database for patients with known gender and race were considered to be “filtered” data, whereas the cases where such filtering was not performed were considered to be “raw” data. We used only filtered data that are more reliable and homogeneous than raw data 5,16. The incidence rates, I ( t ), expressed per 100,000 persons and age-adjusted by the direct method to the 2000 United States standard population,17 and their standard errors, SE , were utilized.…”

Peak and decline in cancer incidence, mortality, and prevalence at old ages

“…Age-specific models of carcinogenesis generally are based on incidence or mortality data limited to those aged <85 years. 23 With several exceptions, including the beta model 23 and the generalized beta model, 38 such models project increasing cancer rates throughout adulthood. Certainly, models that do not agree with the data must be modified or rejected.…”

Basic Equations and Computing Procedures for Frailty Modeling of Carcinogenesis: Application to Pancreatic Cancer Data

“…3 Modeling of cancer hazards in aging requires the use of a theoretical hazard function and, when frailty is assumed, a frailty distribution function. As hazard functions, linear functions, 1 exponential functions, 4 beta-functions, 5,6 and some other functions have been used. 7 As frailty, the gamma-distribution, compound Poisson distribution, power-variance distribution, as well as other distributions, have been utilized.…”