Histological and Demographic Characteristics of the Distribution of Brain and Central Nervous System Tumors' Sizes: Results from SEER Registries Using Statistical Methods

Abstract

The examination of brain tumor growth and its variability among cancer patients is an important aspect of epidemiologic and medical data. Several studies for tumors of brain interpreted descriptive data, in this study we perform inference in the extent possible, suggesting possible explanations for the differentiation in the survival rates apparent in the epidemiologic data. Population based information from nine registries in the USA are classified with respect to age, gender, race and tumor histology to study tumor size variation. The Weibull and Dagum distributions are fitted to the highly skewed tumor sizes distributions, the parametric analysis of the tumor sizes showed significant differentiation between sexes, increased skewness for both the male and female populations, as well as decreased kurtosis for the black female population. The effect of population characteristics on the distribution of tumor sizes is estimated by quantile regression model and then compared with the ordinary least squares results. The higher quantiles of the distribution of tumor sizes for whites are significantly higher than those of other races. Our model predicted that the effect of age in the lower quantiles of the tumor sizes distribution is negative given the variables race and sex. We apply probability and regression models to explore the effects of demographic and histology types and observe significant racial and gender differences in the form of the distributions. Efforts are made to link tumor size data with available survival rates in relation to other prognostic variables.

Keywords: SEER; brain and CNS; parametric analysis; prognostic variables; quantile regression; survival rate; tumor size.

Figure 1

The above classification scheme for brain tumors is based on the classification scheme proposed by RD Barr and colleagues. The variables were updated from the original ICD-O-2 based classification scheme using ICD-O-3 definitions for cancer morphology and topography.

Figure 2

Average tumor size (the largest dimension or diameter of the primary tumor in mm) against age at diagnosis for tumors diagnosed from 1973-2006 included in the SEER 9 registries database. Average tumor sizes reported for males are shown with bold circles and a hollow circle is used for female records.

Figure 3

Plots of fitted probability distribution functions (PDF) of tumor sizes classified for gender and race. The leftmost triad of curves corresponds to PDF’s for females and the rightmost triad of curves corresponds to males. The identified probability distributions along with the estimates for the corresponding parameters that best fit the tumor sizes data are shown below.

Figure 4

A summary of quantile regression estimates for the tumor sizes model involving three covariates and their interaction. For each of the coefficients we plot the 19 distinct quantile regression estimates. The shaded blue area depicts a 95% pointwise confidence band for the quantile regression estimates.