Survival analysis is concerned with finding models to predict the survival of patients or to assess the efficacy of a clinical treatment. A key part of the model-building process is the selection of the predictor variables. It is standard to use a stepwise procedure guided by a series of significance tests to select a single model, and then to make inference conditionally on the selected model. However, this ignores model uncertainty, which can be substantial. We review the standard Bayesian model averaging solution to this problem and extend it to survival analysis, introducing partial Bayes factors to do so for the Cox proportional hazards model. In two examples, taking account of model uncertainty enhances predictive performance, to an extent that could be clinically useful. 1 Introduction From 1974 to 1984 the Mayo Clinic conducted a double-blinded randomized clinical trial involving 312 patients to compare the drug DPCA with a placebo in the treatment of primary biliary cirrhosis...

We investigate the variable selection problem for Cox’s proportional hazards model, and propose a unified model selection and estimation procedure with desired theoretical properties and computational convenience. The new method is based on a penalized log partial likelihood with the adaptively-weighted L1 penalty on regression coefficients, and is named adaptive-LASSO (ALASSO) estimator. Instead of applying the same penalty to all the coefficients as other shrinkage methods, the ALASSO advocates different penalties for different coefficients: unimportant variables receive larger penalties than important variables. In this way, important variables can be protectively preserved in the model selection process, while unimportant ones are shrunk more towards zero and thus more likely to be dropped from the model. We study the consistency and rate of convergence of the proposed estimator. Further, with proper choice of regularization parameters, we have shown that the ALASSO perform as well as the oracle procedure in variable selection; namely, it works as well as if the correct submodel were known. Another advantage of the ALASSO is its convex optimization form and convenience in implementation. Simulated and real examples show that the ALASSO estimator compares favorably with the LASSO.

Introduction to the prediction problem Many data mining problems depend on the construction of models, equations, or machines that are able to predict future outcomes. Although prediction is an important component of data mining, the abundance of methods such as linear models, neural networks, decision trees, and support vector machines can make a seemingly simple prediction problem rather confusing. Other chapters of this volume focus on particular methods. In this chapter we will briefly assemble these ideas into a common framework within which we can begin to understand how all these methods relate to one another. In many applications we are not only interested in having accurate predictions in the future but also in learning the relationship between the features of an observation and the outcomes. For example, we will consider an example of predicting at age 12 which students are likely to drop out of high school before age 18. Certainly we wish to have an accurate assessment of d

Copyright © 2012 Masaaki Tsujitani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We discuss a flexible method for modeling survival data using penalized smoothing splines when the values of covariates change for the duration of the study. The Cox proportional hazards model has been widely used for the analysis of treatment and prognostic effects with censored survival data. However, a number of theoretical problems with respect to the baseline survival function remain unsolved. We use the generalized additive models (GAMs) with B splines to estimate the survival function and select the optimum smoothing parameters based on a variant multifold cross-validation (CV) method. The methods are compared with the generalized cross-validation (GCV) method using data from a long-term study of patients with primary biliary cirrhosis (PBC). 1.

The concept of endotoxin-mediated rather than direct liver injury in biliary obsruction was investigated using the experimental rat model of bile duct ligation (BDL) and small bowel bacterial overgrowth (SBBO). Small identical doses of intravenous endotoxin (bacterial LPS) caused a significantly more severe liver injury in rats with BDL, compared with sham-operated rats, suggesting the possible contribution of LPS in this type of liver damage. BDL was then combined with surgically created jejunal self-filling blind loops, which resulted in SBBO. Plasma LPS level increased significantly, and once again a more severe liver injury, determined by liver histology and serum gamma-glutamyl transpeptidase levels, was observed compared with the control group of rats with BDL+self-emptying blind loops.The data presented suggest that small amounts of exogenous LPS and/or the ordinarily innocous amounts of LPS constantly absorbed from the intestinal tract may be critical in the hepatic damage caused by obstruction of the biliary tract. KEY WORDS: Endotoxins; bile duct obstruction extrahepatic; liver injury