Formal and Informal Model Selection with Incomplete Data

Model selection and assessment with incomplete data pose challenges in addition to the ones encountered with complete data. There are two main reasons for this. First, many models describe characteristics of the complete data, in spite of the fact that only an incomplete subset is observed. Direct comparison between model and data is then less than straightforward. Second, many commonly used models are more sensitive to assumptions than in the complete-data situation and some of their properties vanish when they are fitted to incomplete, unbalanced data. These and other issues are brought forward using two key examples, one of a continuous and one of a categorical nature. We argue that model assessment ought to consist of two parts: (i) assessment of a model's fit to the observed data and (ii) assessment of the sensitivity of inferences to unverifiable assumptions, that is, to how a model described the unobserved data given the observed ones.Comment: Published in at http://dx.doi.org/10.1214/07-STS253 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Basis Expansions for Functional Snippets

Estimation of mean and covariance functions is fundamental for functional data analysis. While this topic has been studied extensively in the literature, a key assumption is that there are enough data in the domain of interest to estimate both the mean and covariance functions. In this paper, we investigate mean and covariance estimation for functional snippets in which observations from a subject are available only in an interval of length strictly (and often much) shorter than the length of the whole interval of interest. For such a sampling plan, no data is available for direct estimation of the off-diagonal region of the covariance function. We tackle this challenge via a basis representation of the covariance function. The proposed approach allows one to consistently estimate an infinite-rank covariance function from functional snippets. We establish the convergence rates for the proposed estimators and illustrate their finite-sample performance via simulation studies and two data applications.Comment: 51 pages, 10 figure

A new class of smart gadolinium contrast agent for tissue pH probing using magnetic resonance imaging

Detecting tissue pH in vivo is extremely vital for medical diagnosis and formulation of treatment decisions. To this end, many investigations have been carried out to develop an accurate and efficient method of in vivo pH measurement. Most of the techniques developed so far suffer from inadequate accuracy, due to poor sensitivity at low concentration of the target or nonspecific interactions within the tissue matrix. To overcome these issues, we describe herein the development of a simple, yet reliable, way to estimate pH with high precision using a Gd(III)-DOTA-silyl-based acid-labile group as a pH-sensitive contrast agent with Magnetic Resonance Imaging (MRI). With this method, a change in T1 weighted image intensity of the newly developed pH-sensitive contrast is directly linked to the proton concentration in the media. As a result, we were able estimate the pH of the target with 95% reliability