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Background Cancer screening has been effective in detecting tumors early before symptoms appear. However, the effectiveness of the regular fecal occult blood test (FOBT) in colorectal cancer in the long term has not been quantified. Methods We applied the statistical method developed by Wu and Rosner [1] using data from the Minnesota Colon Cancer Control Study (MCCCS). All initially asymptomatic participants were classified into four mutually exclusive groups: true-early-detection, no-early-detection, over-diagnosis, and symptom-free life; human lifetime was treated as a random variable and is subject to competing risks. All participants in the screening program will eventually fall into one of the four outcomes above. Predictive inferences on the percentages of the four outcomes for both genders were made using the Minnesota study data. Results Depending on gender, screening frequency and age at the initial screening, for all participants the probability of “symptom-free-life” varies between 95.3% and 96.6%; the probability of “true-early-detection” is 1.9–3.8%; the probability of no-early-detection is 0.3–2.0%; the probability of over-diagnosis is 0.16–0.3%. Among those with colorectal cancer detected by regular FOBT, the probability of over-diagnosis is lower than expected and is between 6% and 9%, with 95% CI (2.5%, 21.3%) for females and (1.9%, 44.7%) for males. The probability of true-early-detection increases as screening interval decreases. The probability of no-early-detection decreases as screening interval decreases. Conclusion The probability of over-diagnosis among the screen-detected cases is not as high as previously thought. We hope this outcome can provide valuable information on the effectiveness of the FOBT in colorectal cancer detection in the long term.

A complex trait like crop yield is determined by its component traits. Multivariable conditional analysis in a general mixed linear model is helpful in dissecting the gene expression for the complex trait due to different effects, such as environment, genotype, and genotype x environment interaction. A recursive approach is presented for constructing a new random vector that can be equivalently used to analyze multivariable conditional variance components and conditional effects. End-of-season plant mapping data, including lint yield and three yield components for nine cultivars of upland cotton (Gossypium hirsutum L.) were used to detect the conditional variance components and conditional effects using this new approach, which can help identify genotypes to be used in selection studies.