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In cancer studies, patients often experience two different types of events: a non-terminal event such as recurrence or metastasis, and a terminal event such as cancer-specific death. Identifying pathways and networks of genes associated with one or both of these events is an important step in understanding disease development and targeting new biological processes for potential intervention. These correlated outcomes are commonly dealt with by modeling progression-free survival, where the event time is the minimum between the times of recurrence and death. However, identifying pathways only associated with progression-free survival may miss out on pathways that affect time to recurrence but not death, or vice versa. We propose a combined testing procedure for a pathway's association with both the cause-specific hazard of recurrence and the marginal hazard of death. The dependency between the two outcomes is accounted for through perturbation resampling to approximate the test's null distribution, without any further assumption on the nature of the dependency. Even complex non-linear relationships between pathways and disease progression or death can be uncovered thanks to a flexible kernel machine framework. The superior statistical power of our approach is demonstrated in numerical studies and in a gene expression study of breast cancer.

Integrating genomic information with traditional clinical risk factors to improve the prediction of disease outcomes could profoundly change the practice of medicine. However, the large number of potential markers and possible complexity of the relationship between markers and disease make it difficult to construct accurate risk prediction models. Standard approaches for identifying important markers often rely on marginal associations or linearity assumptions and may not capture non-linear or interactive effects. In recent years, much work has been done to group genes into pathways and networks. Integrating such biological knowledge into statistical learning could potentially improve model interpretability and reliability. One effective approach is to employ a kernel machine (KM) framework, which can capture nonlinear effects if nonlinear kernels are used (Scholkopf and Smola, 2002; Liu et al., 2007, 2008). For survival outcomes, KM regression modeling and testing procedures have been derived under a proportional hazards (PH) assumption (Li and Luan, 2003; Cai, Tonini, and Lin, 2011). In this article, we derive testing and prediction methods for KM regression under the accelerated failure time (AFT) model, a useful alternative to the PH model. We approximate the null distribution of our test statistic using resampling procedures. When multiple kernels are of potential interest, it may be unclear in advance which kernel to use for testing and estimation. We propose a robust Omnibus Test that combines information across kernels, and an approach for selecting the best kernel for estimation. The methods are illustrated with an application in breast cancer., (© 2013, The International Biometric Society.)

Simple Summary: Colorectal cancer risk and survival have previously been associated with telomere length in peripheral blood leukocytes and tumor tissues. We quantitatively assessed these associations through a systematic review and meta-analysis. Following PRISMA guidelines, we identified relevant studies through database searches, and performed meta-analyses using random effects models. We found no association between telomere length in circulating leukocytes and the risk of developing colorectal cancer, however, shorter leukocyte telomeres were associated with a worse survival in patients with colorectal cancer. Therefore, telomere length may serve as a potential biomarker especially for colorectal cancer prognosis. Larger prospective cohort studies are needed to further confirm this potential association. (1) Background: Colorectal cancer risk and survival have previously been associated with telomere length in peripheral blood leukocytes and tumor tissue. A systematic review and meta-analysis of the literature was conducted. The PubMed, Embase, and Web of Science databases were searched through March 2022. (2) Methods: Relevant studies were identified through database searching following PRISMA guidelines. Risk estimates were extracted from identified studies; meta-analyses were conducted using random effects models. (3) Results: Fourteen studies were identified (eight on risk; six on survival) through systematic review. While no association was observed between circulating leukocyte telomere length and the risk of colorectal cancer [overall OR (95% CI) = 1.01 (0.82–1.24)], a worse survival for those with shorter telomeres in leukocytes and longer telomeres in tumor tissues was observed [Quartile1/Quartile2–4 overall HR (95% CI) = 1.41 (0.26–7.59) and 0.82 (0.69–0.98), respectively]. (4) Conclusions: Although there was no association with colorectal cancer risk, a poorer survival was observed among those with shorter leukocyte telomere length. Future larger studies evaluating a potentially non-linear relationship between telomeres and colorectal cancer are needed. [ABSTRACT FROM AUTHOR]