ESTIMATING TEMPORAL ASSOCIATIONS IN ELECTROCORTICOGRAPHIC (ECoG) TIME SERIES WITH FIRST ORDER PRUNING

Granger causality (GC) is a statistical technique used to estimate temporal associations in multivariate time series. Many applications and extensions of GC have been proposed since its formulation by Granger in 1969. Here we control for potentially mediating or confounding associations between time series in the context of event-related electrocorticographic (ECoG) time series. A pruning approach to remove spurious connections and simultaneously reduce the required number of estimations to fit the effective connectivity graph is proposed. Additionally, we consider the potential of adjusted GC applied to independent components as a method to explore temporal relationships between underlying source signals. Both approaches overcome limitations encountered when estimating many parameters in multivariate time-series data, an increasingly common predicament in today's brain mapping studies.

Causal Inference in Observational Studies with Outcome-Dependent Sampling

In this paper, we consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals are drawn from a population. On these individuals, information is obtained on treatment, outcome, and a few low-dimensional confounders. These individuals are then stratified according to these factors. In the second phase, a random sub-sample of individuals are drawn from each stratum, with known, stratum-specific selection probabilities. On these individuals, a rich set of confounding factors are collected. In this setting, we introduce four estimators: (1) simple inverse weighted, (2) locally efficient, (3) doubly robust and (4)enriched inverse weighted. We evaluate the finite-sample performance of these estimators in a simulation study. We also use our methodology to estimate the causal effect of trauma care on in-hospital mortality using data from the National Study of Cost and Outcomes of Trauma.

Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part aggress with the more general information bound calculations of Robins, Hsieh, and Newey (1995). By verifying the conditions of Murphy and Van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.

Designed Extension of Survival Studies: Application to Clinical Trials with Unrecognized Heterogeneity

It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of the weighted log rank test under the assumption of a proportional hazards frailty model. The proposed method is illustrated through application to a brain tumor trial.

A BAYESIAN HIERARCHICAL FRAMEWORK FOR SPATIAL MODELING OF fMRI DATA

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric,neurological, and substance abuse disorders, as well as into the neural responses to their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. First, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance for regional mean parameters allows for the study of inter-regional functional connectivity, provided enough subjects are available to allow for accurate estimation. Finally, an exchangeable correlation structure within regions allows for the consideration of intra-regional functional connectivity. We perform estimation for our model using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling which, despite the high throughput nature of the data, can be executed quickly (less than 30 minutes). We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer’s disease. The unifying hierarchical model presented in this manuscript is shown to enhance the interpretation content of these data sets.

Analyzing Bivariate Survival Data with Interval Sampling and Application to Cancer Epidemiology

In medical follow-up studies, ordered bivariate survival data are frequently encountered when bivariate failure events are used as the outcomes to identify the progression of a disease. In cancer studies interest could be focused on bivariate failure times, for example, time from birth to cancer onset and time from cancer onset to death. This paper considers a sampling scheme where the first failure event (cancer onset) is identified within a calendar time interval, the time of the initiating event (birth) can be retrospectively confirmed, and the occurrence of the second event (death) is observed sub ject to right censoring. To analyze this type of bivariate failure time data, it is important to recognize the presence of bias arising due to interval sampling. In this paper, nonparametric and semiparametric methods are developed to analyze the bivariate survival data with interval sampling under stationary and semi-stationary conditions. Numerical studies demonstrate the proposed estimating approaches perform well with practical sample sizes in different simulated models. We apply the proposed methods to SEER ovarian cancer registry data for illustration of the methods and theory.