Classification and selection of biomarkers in genomic data using LASSO

High-throughput gene expression technologies such as microarrays have been utilized in a variety of scientific applications. Most of the work has been on assessing univariate associations between gene expression with clinical outcome (variable selection) or on developing classification procedures with gene expression data (supervised learning). We consider a hybrid variable selection/classification approach that is based on linear combinations of the gene expression profiles that maximize an accuracy measure summarized using the receiver operating characteristic curve. Under a specific probability model, this leads to consideration of linear discriminant functions. We incorporate an automated variable selection approach using LASSO. An equivalence between LASSO estimation with support vector machines allows for model fitting using standard software. We apply the proposed method to simulated data as well as data from a recently published prostate cancer study.

Effects of Silvicultural Practices on Soil Carbon and Nitrogen in a Nitrogen Saturated Central Appalachian (USA) Hardwood Forest Ecosystem

Silvicultural treatments represent disturbances to forest ecosystems often resulting in transient increases in net nitrification and leaching of nitrate and base cations from the soil. Response of soil carbon (C) is more complex, decreasing from enhanced soil respiration and increasing from enhanced postharvest inputs of detritus. Because nitrogen (N) saturation can have similar effects on cation mobility, timber harvesting in N-saturated forests may contribute to a decline in both soil C and base cation fertility, decreasing tree growth. Although studies have addressed effects of either forest harvesting or N saturation separately, few data exist on their combined effects. Our study examined the responses of soil C and N to several commercially used silvicultural treatments within the Fernow Experimental Forest, West Virginia, USA, a site with N-saturated soils. Soil analyses included soil organic matter (SOM), C, N, C/N ratios, pH, and net nitrification. We hypothesized the following gradient of disturbance intensity among silvicultural practices (from most to least intense): even-age with intensive harvesting (EA-I), even-age with extensive harvesting, even-age with commercial harvesting, diameter limit, and single-tree harvesting (ST). We anticipated that effects on soil C and N would be greatest for EA-I and least with ST. Tree species exhibited a response to the gradient of disturbance intensity, with early successional species more predominant in high-intensity treatments and late successional species more predominant in low-intensity treatments. Results for soil variables, however, generally did not support our predictions, with few significant differences among treatments and between treatments and their paired controls for any of the measured soil variables. Multiple regression indicated that the best predictors for net nitrification among samples were SOM (positive relationship) and pH (negative relationship). This finding confirms the challenge of sustainable management of N-saturated forests.

Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.