Bayesian and Frequentist Analytical Approaches Using Log-Normal and Gamma Frailty Parametric Models for Breast Cancer Mortality

Abstract

One of the major causes of death among females in Saudi Arabia is breast cancer. Newly diagnosed cases of breast cancer among the female population in Saudi Arabia is 19.5%. With this high incidence, it is crucial that we explore the determinants associated with breast cancer among the Saudi Arabia populace—the focus of this current study. The total sample size for this study is 8312 (8172 females and about 140 representing 1.68% males) patients that were diagnosed with advanced breast cancer. These are facility-based cross-sectional data collected over a 9-year period (2004 to 2013) from a routine health information system database. The data were obtained from the Saudi Cancer Registry (SCR). Both descriptive and inferential (Cox with log-normal and gamma frailties) statistics were conducted. The deviance information criterion (DIC), Watanabe–Akaike information criterion (WAIC), Bayesian information criterion (BIC), and Akaike information criterion were used to evaluate or discriminate between models. For all the six models fitted, the models which combined the fixed and random effects performed better than those with only the fixed effects. This is so because those models had smaller AIC and BIC values. The analyses were done using R and the INLA statistical software. There are evident disparities by regions with Riyadh, Makkah, and Eastern Province having the highest number of cancer patients at 28%, 26%, and 20% respectively. Grade II (46%) and Grade III (45%) are the most common cancer grades. Left paired site laterality (51%) and regional extent (52%) were also most common characteristics. Overall marital status, grade, and cancer extent increased the risk of a cancer patient dying. Those that were married had a hazard ratio of 1.36 (95% CI: 1.03–1.80) while widowed had a hazard ratio of 1.57 (95% CI: 1.14–2.18). Both the married and widowed were at higher risk of dying with cancer relative to respondents who had divorced. For grade, the risk was higher for all the levels, that is, Grade I (Well diff) (HR = 7.11, 95% CI: 3.32–15.23), Grade II (Mod diff) (HR = 7.89, 95% CI: 3.88–16.06), Grade III (Poor diff) (HR = 5.90, 95% CI (2.91–11.96), and Grade IV (Undiff) (HR = 5.44, 95% (2.48–11.9), relative to B-cell. These findings provide empirical evidence that information about individual patients and their region of residence is an important contributor in understanding the inequalities in cancer mortalities and that the application of robust statistical methodologies is also needed to better understand these issues well.