Weibull-like Model of Cancer Development in Aging

Mathematical modeling of cancer development is aimed at assessing the risk factors leading to cancer. Aging is a common risk factor for all adult cancers. The risk of getting cancer in aging is presented by a hazard function that can be estimated from the observed incidence rates collected in cancer registries. Recent analyses of the SEER database show that the cancer hazard function initially increases with the age, and then it turns over and falls at the end of the lifetime. Such behavior of the hazard function is poorly modeled by the exponential or compound exponential-linear functions mainly utilized for the modeling. In this work, for mathematical modeling of cancer hazards, we proposed to use the Weibull-like function, derived from the Armitage-Doll multistage concept of carcinogenesis and an assumption that number of clones at age t developed from mutated cells follows the Poisson distribution. This function is characterized by three parameters, two of which (r and λ) are the conventional parameters of the Weibull probability distribution function, and an additional parameter (C0) that adjusts the model to the observational data. Biological meanings of these parameters are: r—the number of stages in carcinogenesis, λ—an average number of clones developed from the mutated cells during the first year of carcinogenesis, and C0—a data adjustment parameter that characterizes a fraction of the age-specific population that will get this cancer in their lifetime. To test the validity of the proposed model, the nonlinear regression analysis was performed for the lung cancer (LC) data, collected in the SEER 9 database for white men and women during 1975–2004. Obtained results suggest that: (i) modeling can be improved by the use of another parameter A- the age at the beginning of carcinogenesis; and (ii) in white men and women, the processes of LC carcinogenesis vary by A and C0, while the corresponding values of r and λ are nearly the same. Overall, the proposed Weibull-like model provides an excellent fit of the estimates of the LC hazard function in aging. It is expected that the Weibull-like model can be applicable to fit estimates of hazard functions of other adult cancers as well

Web tool for estimating the cancer hazard rates in aging.

A computational approach for estimating the overall, population, and individual cancer hazard rates was developed. The population rates characterize a risk of getting cancer of a specific site/type, occurring within an age-specific group of individuals from a specified population during a distinct time period. The individual rates characterize an analogous risk but only for the individuals susceptible to cancer. The approach uses a novel regularization and anchoring technique to solve an identifiability problem that occurs while determining the age, period, and cohort (APC) effects. These effects are used to estimate the overall rate, and to estimate the population and individual cancer hazard rates. To estimate the APC effects, as well as the population and individual rates, a new web-based computing tool, called the CancerHazard@Age, was developed. The tool uses data on the past and current history of cancer incidences collected during a long time period from the surveillance databases. The utility of the tool was demonstrated using data on the female lung cancers diagnosed during 1975-2009 in nine geographic areas within the USA. The developed tool can be applied equally well to process data on other cancer sites. The data obtained by this tool can be used to develop novel carcinogenic models and strategies for cancer prevention and treatment, as well as to project future cancer burden

Estimation of Hazard Functions in the Log-Linear Age-Period-Cohort Model: Application to Lung Cancer Risk Associated with Geographical Area

An efficient computing procedure for estimating the age-specific hazard functions by the log-linear age-period-cohort (LLAPC) model is proposed. This procedure accounts for the influence of time period and birth cohort effects on the distribution of age-specific cancer incidence rates and estimates the hazard function for populations with different exposures to a given categorical risk factor. For these populations, the ratio of the corresponding age-specific hazard functions is proposed for use as a measure of relative hazard. This procedure was used for estimating the risks of lung cancer (LC) for populations living in different geographical areas. For this purpose, the LC incidence rates in white men and women, in three geographical areas (namely: San Francisco-Oakland, Connecticut and Detroit), collected from the SEER 9 database during 1975–2004, were utilized. It was found that in white men the averaged relative hazard (an average of the relative hazards over all ages) of LC in Connecticut vs. San Francisco-Oakland is 1.31 ± 0.02, while in Detroit vs. San Francisco-Oakland this averaged relative hazard is 1.53 ± 0.02. In white women, analogous hazards in Connecticut vs. San Francisco-Oakland and Detroit vs. San Francisco-Oakland are 1.22 ± 0.02 and 1.32 ± 0.02, correspondingly. The proposed computing procedure can be used for assessing hazard functions for other categorical risk factors, such as gender, race, lifestyle, diet, obesity, etc

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

A simple, computationally efficient procedure for analyses of the time period and birth cohort effects on the distribution of the age-specific incidence rates of cancers is proposed. Assuming that cohort effects for neighboring cohorts are almost equal and using the Log-Linear Age-Period-Cohort Model, this procedure allows one to evaluate temporal trends and birth cohort variations of any type of cancer without prior knowledge of the hazard function. This procedure was used to estimate the influence of time period and birth cohort effects on the distribution of the age-specific incidence rates of first primary, microscopically confirmed lung cancer (LC) cases from the SEER9 database. It was shown that since 1975, the time period effect coefficients for men increase up to 1980 and then decrease until 2004. For women, these coefficients increase from 1975 up to 1990 and then remain nearly constant. The LC birth cohort effect coefficients for men and women increase from the cohort of 1890–94 until the cohort of 1925–29, then decrease until the cohort of 1950–54 and then remain almost unchanged. Overall, LC incidence rates, adjusted by period and cohort effects, increase up to the age of about 72–75, turn over, and then fall after the age of 75–78. The peak of the adjusted rates in men is around the age of 77–78, while in women, it is around the age of 72–73. Therefore, these results suggest that the age distribution of the incidence rates in men and women fall at old ages

Breast cancer incidence in black and white women stratified by estrogen and progesterone receptor statuses.

BACKGROUND: There is increasing evidence that breast cancer is a heterogeneous disease presented by different phenotypes and that white women have a higher breast cancer incidence rate, whereas black women have a higher mortality rate. It is also well known that white women have lower incidence rates than black women until approximately age 40, when rate curves cross over and white women have higher rates. The goal of this study was to validate the risk of white and black women to breast cancer phenotypes, stratified by statuses of the estrogen (ER) and progesterone (PR) receptors. METHODOLOGY/PRINCIPAL FINDINGS: SEER17 data were fractioned by receptor status into [ER+, PR+], [ER-, PR-], [ER+, PR-], and [ER-, PR+] phenotypes. It was shown that in black women compared to white women, cumulative age-specific incidence rates are: (i) smaller for the [ER+, PR+] phenotype; (ii) larger for the [ER-, PR-] and [ER-, PR+] phenotypes; and (iii) almost equal for the [ER+, PR-] phenotype. Clemmesen\u27s Hook, an undulation unique to women\u27s breast cancer age-specific incidence rate curves, is shown here to exist in both races only for the [ER+, PR+] phenotype. It was also shown that for all phenotypes, rate curves have additional undulations and that age-specific incidence rates are nearly proportional in all age intervals. CONCLUSIONS/SIGNIFICANCE: For black and white women, risk for the [ER+, PR+], [ER-, PR-] and [ER-, PR+] phenotypes are race dependent, while risk for the [ER+, PR-] phenotype is almost independent of race. The processes of carcinogenesis in aging, leading to the development of each of the considered breast cancer phenotypes, are similar in these racial groups. Undulations exhibited on the curves of age-specific incidence rates of the considered breast cancer phenotypes point to the presence of several subtypes (to be determined) of each of these phenotypes

A Generalized Beta model for the age distribution of cancers: application to pancreatic and kidney cancer.

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

Extension of Cox Proportional Hazard Model for Estimation of Interrelated Age-Period-Cohort Effects on Cancer Survival

In the frame of the Cox proportional hazard (PH) model, a novel two-step procedure for estimating age-period-cohort (APC) effects on the hazard function of death from cancer was developed. In the first step, the procedure estimates the influence of joint APC effects on the hazard function, using Cox PH regression procedures from a standard software package. In the second step, the coefficients for age at diagnosis, time period and birth cohort effects are estimated. To solve the identifiability problem that arises in estimating these coefficients, an assumption that neighboring birth cohorts almost equally affect the hazard function was utilized. Using an anchoring technique, simple procedures for obtaining estimates of interrelated age at diagnosis, time period and birth cohort effect coefficients were developed

Role of disulphide bond formation in folding, secretion, and assembly of human chorionic gonadotropin subunits.

Ability of a glycoprotein hormone to fold and assemble correctly is an essential requirement for the attainment of its biological activity . Cells have a quality control system to assure that when proteins of the endoplasmic reticulum mi sfold or fail to assemble correctly they do not exit the cell. But human chorionic gonadotropin (hCG) is an exception to this rule as is illustrated by the following observations. First, both hCG subunits are secreted efficiently as unassembled monomers. Second, some mis(un)folded forms of hCG-β can be efficiently secreted from cells that do not facilitate the secretion of other misfolded proteins. Third, the efficient secretion of an assembly incompetent α-subunit occurs in spite of lacking both of its non-cystine knot disulphide bonds. And fourth, hCG heterodimers that contain misfolded α-subunits as a result of lack ing cystine knot disulphides are also secreted. In this report, we review direct ex perimental evidence demonstrating that the structural requirements necessary for the secretion of hCG subunits differ from the structural requirements necessary for hCG assembly by using disulphide bond formation as an index with which to monitor the folding, assembly, and secretion of hCG and its α - and β-subunits