Frailty Modeling of the Bimodal Age-Incidence of Hodgkin Lymphoma in the Nordic Countries
ABSTRACT The bimodality of the age-incidence curve of Hodgkin lymphoma (HL) has been ascribed to the existence of subgroups with distinct etiologies. Frailty models can be usefully applied to age-incidence curves of cancer to aid the understanding of biological phenomena in these instances. The models imply that for a given disease, a minority of individuals are at high risk, compared with the low-risk majority.
Frailty modeling is applied to interpret HL incidence on the basis of population-based cancer registry data from the five Nordic countries for the period 1993 to 2007. There were a total of 8,045 incident cases and 362,843,875 person-years at risk in the study period.
A bimodal frailty analysis provides a reasonable fit to the age-incidence curves, employing 2 prototype models, which differ by having the sex covariate included in the frailty component (model 1) or in the baseline Weibull hazard (model 2). Model 2 seemed to fit better with our current understanding of HL than model 1 for the male-to-female ratio, number of rate-limiting steps in the carcinogenic process, and proportion of susceptibles; whereas model 1 performed better related to the heterogeneity in HL among elderly males.
The present analysis shows that HL age-incidence data are consistent with a bimodal frailty model, indicating that heterogeneity in cancer susceptibility may give rise to bimodality at the population level, although the individual risk remains simple and monotonically increasing by age.
Frailty modeling adds to the existing body of knowledge on the heterogeneity in risk of acquiring HL.
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ABSTRACT: Modeling of cancer hazards at age deals with a dichotomous population, a small part of which (the fraction at risk) will get cancer, while the other part will not. Therefore, we conditioned the hazard function, (), the probability density function (pdf), (), and the survival function, (), on frailty α in individuals. Assuming α has the Bernoulli distribution, we obtained equations relating the unconditional (population level) hazard function, (), cumulative hazard function, (), and overall cumulative hazard, , with the (), (), and () for individuals from the fraction at risk. Computing procedures for estimating (), (), and () were developed and used to fit the pancreatic cancer data collected by SEER9 registries from 1975 through 2004 with the Weibull pdf suggested by the Armitage-Doll model. The parameters of the obtained excellent fit suggest that age of pancreatic cancer presentation has a time shift about 17 years and five mutations are needed for pancreatic cells to become malignant.Cancer informatics 02/2013; 12:67-81. DOI:10.4137/CIN.S8063
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ABSTRACT: At present, carcinogenic models imply that all individuals in a population are susceptible to cancer. These models either ignore a fall of the cancer incidence rate at old ages, or use some poorly identifiable parameters for its accounting. In this work, a new heuristic model is proposed. The model assumes that, in a population, only a small fraction (pool) of individuals is susceptible to cancer and decomposes the problem of the carcinogenic modeling on two sequentially solvable problems: (i) determination of the age-specific hazard rate in individuals susceptible to cancer (individual hazard rate) from the observed hazard rate in the population (population hazard rate); and (ii) modelling of the individual hazard rate by a chosen "up" of the theoretical hazard function describing cancer occurrence in individuals in time (age). The model considers carcinogenesis as a failure of individuals susceptible to cancer to resist cancer occurrence in aging and uses, as the theoretical hazard function, the three-parameter Weibull hazard function, often utilized in a failure analysis. The parameters of this function, providing the best fit of the modeled and observed individual hazard rates (determined from the population hazard rates), are the outcomes of the modeling. The model was applied to the pancreatic cancer data. It was shown that, in the populations stratified by gender, race and the geographic area of living, the modeled and observed population hazard rates of pancreatic cancer occurrence have similar turnovers at old ages. The sizes of the pools of individuals susceptible to this cancer: (i) depend on gender, race and the geographic area of living; (ii) proportionally influence the corresponding population hazard rates; and (iii) do not influence the individual hazard rates. The model should be further tested using data on other types of cancer and for the populations stratified by different categorical variables.PLoS ONE 06/2014; 9(6):e100087. DOI:10.1371/journal.pone.0100087 · 3.53 Impact Factor
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ABSTRACT: The Armitage-Doll model with random frailty can fail to describe incidence rates of rare cancers influenced by an accelerated biological mechanism at some, possibly short, period of life. We propose a new model to account for this influence. Osteosarcoma and Ewing sarcoma are primary bone cancers with characteristic age-incidence patterns that peak in adolescence. We analyze Surveillance, Epidemiology and End Result program incidence data for whites younger than 40 years diagnosed during the period 1975-2005, with an Armitage-Doll model with compound Poisson frailty. A new model treating the adolescent growth spurt as the accelerated mechanism affecting cancer development is a significant improvement over that model. We also model the incidence rate conditioning on the event of having developed the cancers before the age of 40 years and compare the results with those predicted by the Armitage-Doll model. Our results support existing evidence of an underlying susceptibility for the two cancers among a very small proportion of the population. In addition, the modeling results suggest that susceptible individuals with a rapid growth spurt acquire the cancers sooner than they otherwise would have if their growth had been slower. The new model is suitable for modeling incidence rates of rare diseases influenced by an accelerated biological mechanism. Copyright © 2012 John Wiley & Sons, Ltd.Statistics in Medicine 12/2012; 31(28). DOI:10.1002/sim.5441 · 2.04 Impact Factor