CostEffective Prediction in Medicine and Marketing: Only the Difference Between Bayesian Model Averaging and the Single BestFit Model There is a need for costeffective tools to identify a small fraction of the population with a high probability of having a disease (in medicine) or buying the product (in marketing). Instead of the most probable model, Bayesian model averaging attempts to find the most probable prediction, given the data. None of these methods give satisfactory results in predicting from smalldata, lowsignal data sets. Using an example problem of predicting who has a rare lung cancer, this paper demonstrates that improved results can be found from considering only the difference between the predictions of the single bestfit model and Bayesian model averaging, and shows the correlation between precision for cancer and the size of that difference in predictions.

Bayesian and Frequentist Analytical Approaches Using LogNormal and Gamma Frailty Parametric Models for Breast Cancer Mortality 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 populacexe2x80x94the 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 facilitybased crosssectional data collected over a 9year 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 lognormal and gamma frailties) statistics were conducted. The deviance information criterion (DIC), Watanabexe2x80x93Akaike 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: 1.03xe2x80x931.80) while widowed had a hazard ratio of 1.57 (95% CI: 1.14xe2x80x932.18). 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) (HRxe2x80x89xe2x80x897.11, 95% CI: 3.32xe2x80x9315.23), Grade II (Mod diff) (HRxe2x80x89xe2x80x897.89, 95% CI: 3.88xe2x80x9316.06), Grade III (Poor diff) (HRxe2x80x89xe2x80x895.90, 95% CI (2.91xe2x80x9311.96), and Grade IV (Undiff) (HRxe2x80x89xe2x80x895.44, 95% (2.48xe2x80x9311.9), relative to Bcell. 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.