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Colorectal cancer (CRC) is the third most common form of cancer and the third leading cancer killer for both genders in the United States (American Cancer Society, 2011). In 2011, the American Cancer Society estimates 141,210 new cases in the U.S. and 49,380 deaths due to CRC (American Cancer Society, 2011). Similarly, the World Health Organization estimates over 940,000 new cases occurring annually worldwide (World Health Organization, 2003), and nearly 610,000 died from CRC in 2008 (World Health Organization, 2011). Colorectal cancer is often found in people older than fifty, and its mortality rates are higher each year than HIV/AIDS and breast cancer combined (Colon Cancer Prevention Project, 2011). The age-specific colorectal cancer risk rises continuously with advancing age (National Cancer Institute, 2011). CRC is also one of the most preventable among cancers, studies show that regular screening could substantially reduce mortalities (Kronborg et al., 1996, Mandel et al., 1993, 1999). The reason is that colorectal cancer can take 5-15 years to develop, and screening exam, such as digital rectal exam (DRE), colonoscopy, flexible sigmoidoscopy (FSG) and faecal occult blood test (FOBT), can detect polyps before the cancer develops (Screen for Life: National Colorectal Cancer Action Campaign, 2009). The current guidelines in the U.S. for CRC include several options among men and women aged 50 and older at average risk (American Cancer Society, 2011). Many considerations are needed when following the guidelines, including risk factors, type of test, and test interval including flexible sigmoidoscopy, colonoscopy, double-contrast barium enema, computed tomographic colonography, faecal occult blood test and stool DNA test (American Cancer Society, 2011). However, the acceptance of people about CRC screening has been low in the U.S. In most areas of the U.S., less than half of the population is in compliance with recommended CRC guidelines (American Cancer Society, 2011), and only one-third colorectal cancers are being diagnosed at an early and treatable stage, due to lack of screening or lack of disease symptoms (ARUP Laboratories, 2010). The purpose of colorectal cancer screening is to detect early stage of the disease before clinical symptoms take place. CRC has a 90% treatable rate when detected early, therefore

Modelling and Inference in Screening: Exemplification with the Faecal Occult Blood Test