The role of histological subtypes in the survival of patients diagnosed with cutaneous or mucosal melanoma in the United States of America.

BACKGROUND: Literature presents limited information on histological subtypes and their association with other factors influencing the survival of melanoma patients. To explore the risk of death due to melanoma associated with histological subtypes, this retrospective study used the Surveillance, Epidemiology, and End Results program (SEER) data from 1998 to 2019. METHODS: A total of 27,532 patients consisting of 15,527 males and 12,005 females. The Hypertabastic Accelerated Failure Time model was used to analyze the impact of histology on the survival of patients with cutaneous or mucosal melanoma. RESULTS: The median survival time (MST) for cutaneous patients was 149 months, whereas those diagnosed with mucosal melanoma was 34 months. Nodular melanoma had a hazard ratio of 3.40 [95% CI: (2.94, 3.94)] compared to lentigo maligna melanoma. Across all histological subtypes, females had a longer MST, when compared to males. The hazard ratio (HR) of distant to localized melanoma was 9.56 [95% CI: (7.58, 12.07)]. CONCLUSIONS: Knowledge of patients' histological subtypes and their hazard assessment would enable clinicians and healthcare providers to perform personalized treatment, resulting in a lower risk of complication and higher survivability of melanoma patients. Significant factors were stage of the disease, age, histology, sex, and income. Focus should be placed on high-risk populations with severe and aggressive histological subtypes. Programs that emphasize preventive measures such as awareness, education, and early screening could reduce risk.

Racial and Gender Disparities in Incidence of Lung and Bronchus Cancer in the United States: A Longitudinal Analysis.

BACKGROUND: Certain population groups in the United States carry a disproportionate burden of cancer. This work models and analyzes the dynamics of lung and bronchus cancer age-adjusted incidence rates by race (White and Black), gender (male and female), and prevalence of daily smoking in 38 U.S. states, the District of Columbia, and across eight U.S. geographic regions from 1999 to 2012. METHODS: Data, obtained from the U.S. Cancer Statistics Section of the Centers for Disease Control and Prevention, reflect approximately 77% of the U.S. population and constitute a representative sample for making inferences about incidence rates in lung and bronchus cancer (henceforth lung cancer). A longitudinal linear mixed-effects model was used to study lung cancer incidence rates and to estimate incidence rate as a function of time, race, gender, and prevalence of daily smoking. RESULTS: Between 1999 and 2012, age-adjusted incidence rates in lung cancer have decreased in all states and regions. However, racial and gender disparities remain. Whites continue to have lower age-adjusted incidence rates for this cancer than Blacks in all states and in five of the eight U.S. geographic regions. Disparities in incidence rates between Black and White men are significantly larger than those between Black and White women, with Black men having the highest incidence rate of all subgroups. Assuming that lung cancer incidence rates remain within reasonable range, the model predicts that the gender gap in the incidence rate for Whites would disappear by mid-2018, and for Blacks by 2026. However, the racial gap in lung cancer incidence rates among Black and White males will remain. Among all geographic regions, the Mid-South has the highest overall lung cancer incidence rate and the highest incidence rate for Whites, while the Midwest has the highest incidence rate for Blacks. Between 1999 and 2012, there was a downward trend in the prevalence of daily smokers in both genders. However, males have significantly higher rates of cigarette smoking than females at all time points. The highest and lowest prevalence of daily smoking are found in the Mid-South and New England, respectively. There was a significant correlation between lung cancer incidence rates and smoking prevalence in all geographic regions, indicating a strong influence of cigarette smoking on regional lung cancer incidence rates. CONCLUSION: Although age-adjusted incidence rates in lung cancer have decreased throughout the U.S., racial and gender disparities remain. This longitudinal model can help health professionals and policy makers make predictions of age-adjusted incidence rates for lung cancer in the U.S. in the next five to ten years.

Disparities in cervical cancer mortality rates as determined by the longitudinal hyperbolastic mixed-effects type II model.

BACKGROUND: The main purpose of this study was to model and analyze the dynamics of cervical cancer mortality rates for African American (Black) and White women residing in 13 states located in the eastern half of the United States of America from 1975 through 2010. METHODS: The cervical cancer mortality rates of the Surveillance, Epidemiology, and End Results (SEER) were used to model and analyze the dynamics of cervical cancer mortality. A longitudinal hyperbolastic mixed-effects type II model was used to model the cervical cancer mortality data and SAS PROC NLMIXED and Mathematica were utilized to perform the computations. RESULTS: Despite decreasing trends in cervical cancer mortality rates for both races, racial disparities in mortality rates still exist. In all 13 states, Black women had higher mortality rates at all times. The degree of disparities and pace of decline in mortality rates over time differed among these states. Determining the paces of decline over 36 years showed that Tennessee had the most rapid decline in cervical cancer mortality for Black women, and Mississippi had the most rapid decline for White Women. In contrast, slow declines in cervical cancer mortality were noted for Black women in Florida and for White women in Maryland. CONCLUSIONS: In all 13 states, cervical cancer mortality rates for both racial groups have fallen. Disparities in the pace of decline in mortality rates in these states may be due to differences in the rates of screening for cervical cancers. Of note, the gap in cervical cancer mortality rates between Black women and White women is narrowing.

A flexible multivariable model for phytoplankton growth.

We introduce a new multivariable model to be used to study the growth dynamics of phytoplankton as a function of both time and the concentration of nutrients. This model is applied to a set of experimental data which describes the rate of growth as a function of these two variables. The form of the model allows easy extension to additional variables. Thus, the model can be used to analyze experimental data regarding the effects of various factors on phytoplankton growth rate. Such a model will also be useful in analysis of the role of concentration of various nutrients or trace elements, temperature, and light intensity, or other important explanatory variables, or combinations of such variables, in analyzing phytoplankton growth dynamics.

T model of growth and its application in systems of tumor-immune dynamics.

In this paper we introduce a new growth model called T growth model. This model is capable of representing sigmoidal growth as well as biphasic growth. This dual capability is achieved without introducing additional parameters. The T model is useful in modeling cellular proliferation or regression of cancer cells, stem cells, bacterial growth and drug dose-response relationships. We recommend usage of the T growth model for the growth of tumors as part of any system of differential equations. Use of this model within a system will allow more flexibility in representing the natural rate of tumor growth. For illustration, we examine some systems of tumor-immune interaction in which the T growth rate is applied. We also apply the model to a set of tumor growth data.

Clinical and multiple gene expression variables in survival analysis of breast cancer: analysis with the hypertabastic survival model.

BACKGROUND: We explore the benefits of applying a new proportional hazard model to analyze survival of breast cancer patients. As a parametric model, the hypertabastic survival model offers a closer fit to experimental data than Cox regression, and furthermore provides explicit survival and hazard functions which can be used as additional tools in the survival analysis. In addition, one of our main concerns is utilization of multiple gene expression variables. Our analysis treats the important issue of interaction of different gene signatures in the survival analysis. METHODS: The hypertabastic proportional hazards model was applied in survival analysis of breast cancer patients. This model was compared, using statistical measures of goodness of fit, with models based on the semi-parametric Cox proportional hazards model and the parametric log-logistic and Weibull models. The explicit functions for hazard and survival were then used to analyze the dynamic behavior of hazard and survival functions. RESULTS: The hypertabastic model provided the best fit among all the models considered. Use of multiple gene expression variables also provided a considerable improvement in the goodness of fit of the model, as compared to use of only one. By utilizing the explicit survival and hazard functions provided by the model, we were able to determine the magnitude of the maximum rate of increase in hazard, and the maximum rate of decrease in survival, as well as the times when these occurred. We explore the influence of each gene expression variable on these extrema. Furthermore, in the cases of continuous gene expression variables, represented by a measure of correlation, we were able to investigate the dynamics with respect to changes in gene expression. CONCLUSIONS: We observed that use of three different gene signatures in the model provided a greater combined effect and allowed us to assess the relative importance of each in determination of outcome in this data set. These results point to the potential to combine gene signatures to a greater effect in cases where each gene signature represents some distinct aspect of the cancer biology. Furthermore we conclude that the hypertabastic survival models can be an effective survival analysis tool for breast cancer patients.

Mathematical modeling of stem cell proliferation.

The mathematical models prevalently used to represent stem cell proliferation do not have the level of accuracy that might be desired. The hyperbolastic growth models promise a greater degree of precision in representing data of stem cell proliferation. The hyperbolastic growth model H3 is applied to experimental data in both embryonic stem cells and adult mesenchymal stem cells. In the embryonic stem cells the results are compared with other popular models, including the Deasy model, which is used prevalently for stem cell growth. In the case of modelling adult mesenchymal stem cells, H3 is also successfully applied to describe the proliferative index. We demonstrated that H3 can accurately represent the dynamics of stem cell proliferation for both embryonic and adult mesenchymal stem cells. We also recognize the importance of additional factors, such as cytokines, in determining the rate of growth. We propose the question of how to extend H3 to a multivariable model that can include the influence of growth factors.

Hyperbolastic modeling of tumor growth with a combined treatment of iodoacetate and dimethylsulphoxide.

BACKGROUND: An understanding of growth dynamics of tumors is important in understanding progression of cancer and designing appropriate treatment strategies. We perform a comparative study of the hyperbolastic growth models with the Weibull and Gompertz models, which are prevalently used in the field of tumor growth. METHODS: The hyperbolastic growth models H1, H2, and H3 are applied to growth of solid Ehrlich carcinoma under several different treatments. These are compared with results from Gompertz and Weibull models for the combined treatment. RESULTS: The growth dynamics of the solid Ehrlich carcinoma with the combined treatment are studied using models H1, H2, and H3, and the models are highly accurate in representing the growth. The growth dynamics are also compared with the untreated tumor, the tumor treated with only iodoacetate, and the tumor treated with only dimethylsulfoxide, and the combined treatment. CONCLUSIONS: The hyperbolastic models prove to be effective in representing and analyzing the growth dynamics of the solid Ehrlich carcinoma. These models are more precise than Gompertz and Weibull and show less error for this data set. The precision of H3 allows for its use in a comparative analysis of tumor growth rates between the various treatments.

Hypertabastic survival model.

A new two-parameter probability distribution called hypertabastic is introduced to model the survival or time-to-event data. A simulation study was carried out to evaluate the performance of the hypertabastic distribution in comparison with popular distributions. We then demonstrate the application of the hypertabastic survival model by applying it to data from two motivating studies. The first one demonstrates the proportional hazards version of the model by applying it to a data set from multiple myeloma study. The second one demonstrates an accelerated failure time version of the model by applying it to data from a randomized study of glioma patients who underwent radiotherapy treatment with and without radiosensitizer misonidazole. Based on the results from the simulation study and two applications, the proposed model shows to be a flexible and promising alternative to practitioners in this field.