Narrow Results

Cox's proportional hazard model is potentially the most used method in life data and survival analysis. Although the method is relatively simple to understand, its major difficulties in estimation are observed when time-dependent covariates with repeated events are used as input variables. An alternative approach to simplify hazard ratio prediction for repeated events is evaluated for a practical application using small appliances reliability data from an accelerated experimental design based on consumer usage.

Pancreatic cancer is the fourth leading cause of cancer deaths in the United States with five-year survival rates less than 5% due to rare detection in early stages. Identification of genes that are directly correlated to pancreatic cancer survival is crucial for pancreatic cancer diagnostics and treatment. However, no existing GWAS or transcriptome studies are available for addressing this problem. We apply lasso penalized Cox regression to a transcriptome study to identify genes that are directly related to pancreatic cancer survival. This method is capable of handling the right censoring effect of survival times and the ultrahigh dimensionality of genetic data. A cyclic coordinate descent algorithm is employed to rapidly select the most relevant genes and eliminate the irrelevant ones. Twelve genes have been identified and verified to be directly correlated to pancreatic cancer survival time and can be used for the prediction of future patient's survival.

The Cox proportional hazards model has been widely used in cancer genomic research that aims to identify genes from high-dimensional gene expression space associated with the survival time of patients. With the increase in expertly curated biological pathways, it is challenging to incorporate such complex networks in fitting a high-dimensional Cox model. This paper considers a Bayesian framework that employs the Ising prior to capturing relations among genes represented by graphs. A spike-and-slab prior is also assigned to each of the coefficients for the purpose of variable selection. The iterated conditional modes/medians (ICM/M) algorithm is proposed for the implementation for Cox models. The ICM/M estimates hyperparameters using conditional modes and obtains coefficients through conditional medians. This procedure produces some coefficients that are exactly zero, making the model more interpretable. Comparisons of the ICM/M and other regularized Cox models were carried out with both simulated and real data. Compared to lasso, adaptive lasso, elastic net, and DegreeCox, the ICM/M yielded more parsimonious models with consistent variable selection. The ICM/M model also provided a smaller number of false positives than the other methods and showed promising results in terms of predictive accuracy. In terms of computing times among the network-aware methods, the ICM/M algorithm is substantially faster than DegreeCox even when incorporating a large complex network. The implementation of the ICM/M algorithm for Cox regression model is provided in R package icmm, available on the Comprehensive R Archive Network (CRAN).

The following sections are included:

• Introduction

• Resource

• Generalized Sedyakin's model

• Additive accumulation of damages model

• Proportional hazards model

• Generalized proportional hazards models

• The main classes of GPH models.

• Parametrization of the function r in AAD and GPH models

• Changing shape and scale models

• Generalizations

• The heredity hypothesis

• References

Recent interest in the application of microarray technology focuses on relating gene expression profiles to censored survival outcome such as patients' overall survival time or time to cancer relapse. Due to the high-dimensional nature of the gene expression data, regularization becomes an effective approach for such analyses. In this chapter, we review several aspects of the recent development of penalized regression models for censored survival data with high-dimensional covariates, e.g. gene expressions. We first discuss the Cox proportional hazards model (Cox 1972) as the primary example and then the accelerated failure time model (Kalbfleisch and Prentice 2002) for further consideration.

The counting process and martingale have been the research topic in probability for a long time and there exists a great deal of literature for both their studies and their applications. This article discusses their applications in survival analysis, a field that plays an essential and fundamental role in biostatistics and deals with experiments concerning times to events. In addition to being a key component in most of medical and public health studies, survival analysis is applied to many other fields including demographical studies, economics, reliability studies and social studies. Although survival analysis has existed for a long time, the modern survival analysis really started about 30 years ago when the counting process and martingale tools were applied for the advance of the field (Aalen, 1975, 1980; Andersen et al., 1993).