Efficiency of the Sieved-NPMLE in CAR-Missing Data Models

We consider nonparametric missing data models for which the censoring mechanism satisfies coarsening at random and which allow complete observations on the variable X of interest. W show that beyond some empirical process conditions the only essential condition for efficiency of an NPMLE of the distribution of X is that the regions associated with incomplete observations on X contain enough complete observations. This is heuristically explained by describing the EM-algorithm. We provide identifiably of the self-consistency equation and efficiency of the NPMLE in order to make this statement rigorous. The usual kind of differentiability conditions in the proof are avoided by using an identity which holds for the NPMLE of linear parameters in convex models. We provide a bivariate censoring application in which the condition and hence the NPMLE fails, but where other estimators, not based on the NPMLE principle, are highly inefficient. It is shown how to slightly reduce the data so that the conditions hold for the reduced data. The conditions are verified for the univariate censoring, double censored, and Ibragimov-Has'minski models.

The Two-Interval Line-Segment Problem

In this paper, the NPMLE in the one-dimensional line segment problem is defined and studied, where line segments on the real line through two non-overlapping intervals are observed. The self-consistency equations for the NPMLE are defined and a quick algorithm for solving them is provided. Supnorm weak convergence to a Gaussian process and efficiency of the NPMLE is proved. The problem has a strong geological application in the study of the lifespan of species.

Self-Reported Memory Symptoms with Coronary Artery Disease: A Prospective of CABG Patients and Nonsurgical Controls

Background. Subjective memory complaints are common after coronary artery bypass grafting (CABG), but previous studies have concluded that such symptoms are more closely associated with depressed mood than objective cognitive dysfunction. We compared the incidence of self-reported memory symptoms at 3 and 12 months after CABG with that of a control group of patients with comparable risk factors for coronary artery disease but without surgery. Methods. Patients undergoing CABG (n = 140) and a demographically similar nonsurgical control group with coronary artery disease (n = 92) were followed prospectively at 3 and 12 months. At each follow-up time, participants were asked about changes since the previous evaluation in areas of memory, calculations, reading, and personality. A Functional Status Questionnaire (FSQ) and self-report measure of symptoms of depression (CES-D) were also completed. Results. The frequency of self-reported changes in memory, personality, and reading at 3 months was significantly higher among CABG patients than among nonsurgical controls. By contrast, there were no differences in the frequency of self-reported symptoms relating to calculations or overall rating of functional status. After adjusting for a measure of depression (CES-D rating score), the risk for self-reported memory changes remained nearly 5 times higher among the CABG patients than control subjects. The relative risk of developing new self-reported memory symptoms between 3 and 12 months was 2.5 times higher among CABG patients than among nonsurgical controls (CI 1.24 – 5.02), and the overall prevalence of memory symptoms at 12 months was also higher among CABG patients (39%) than controls (14%). Conclusions. The frequency of self-reported memory symptoms 3 and 12 months after baseline is significantly higher among CABG patients than control patients with comparable risk factors for coronary and cerebrovascular disease. These differences could not be accounted for by symptoms of depression. The self-reported cognitive symptoms appear to be relatively specific for memory, and may reflect aspects of memory functioning that are not captured by traditional measures of new verbal learning and memory. The etiology of these self-reported memory symptoms remains unclear, but our findings as well as those of others, may implicate factors other than cardiopulmonary bypass itself.