Alzheimer disease (AD) is the most common cause of neurodegenerative dementia among elderly patients. It is now well recognized as a public health emergency for the 21st century. By an estimate based on data from the 2000 census, there will be 13.5 million cases by the year 2050 unless treatments are developed to prevent or slow progression of the disease (Hebert et al. 2003
The absence of biomarkers for detecting AD and tracking its progression renders discovery of new treatments more difficult. At this time, the diagnosis cannot be made with confidence in the absence of detailed cognitive testing. These cognitive tests are time consuming and can be difficult to interpret if the participant is not adequately engaged. Some clinical trials in recent years have enrolled patients with mild cognitive impairment (MCI—a condition characterized by memory impairment without dementia) and evaluated rates of conversion from MCI to AD as an outcome measure (Salloway et al. 2004
; Petersen et al. 2005
; Thal et al. 2005
; Feldman et al. 2007
). While it is true that drugs for preventing conversion are highly desirable, conversion has some undesirable properties for an outcome measure. Conversion does not take place suddenly and can be difficult to identify with certainty. Rates of conversion are low and variable, with 6–15% of amnestic MCI patients converting to Alzheimer's disease each year. This means that large numbers of MCI patients must be recruited and followed for a long period of time before it is possible to discern a difference in conversion rates between two randomized groups of participants in a clinical trial. Biomarkers offer the hope of rapid and unambiguous diagnosis, precise tracking of disease severity, and improvements over existing methods for evaluating the efficacy of interventions.
Positron emission tomography (PET) scans for the current study were acquired using 18-fluorodeoxyglucose (FDG), and will be referred to hereafter as FDG-PET or PET scans. FDG is synthesized by replacing one of the hydroxyl groups in glucose with a fluorine atom. Despite this change, the molecule bears sufficient similarity to glucose to be taken up by living cells in proportion to their metabolic demands. The radiation emitted by the tracer after it has been absorbed by the cells can therefore be used to construct a map depicting the glucose demands of the different tissues. FDG-PET scans have a characteristic appearance that can facilitate the diagnosis of AD (Silverman et al. 2001
; Drzezga et al. 2005
). In addition, PET scans have clinical utility for discerning between AD and dementia caused by frontotemporal lobar degeneration (FTLD) (Foster et al. 2007
). Several research studies have evaluated the utility of PET scans for diagnosing AD (Minoshima et al. 1995
; Silverman et al. 2001
) or for predicting the progression of MCI or AD (Chetelat et al. 2003
; Drzezga et al. 2005
; Landau et al. 2010
; Walhovd et al., 2010
). PET scans for studies such as these are often subjected to complex post-processing, such as segmentation into volumes of interest, or surface projection. The current work focuses on automatic detection of AD or elevated MCI conversion risk, making use of elementary information retrieval (IR) techniques.
IR is a broad field that is concerned chiefly with the rapid selection of relevant documents from vast databases. The documents in question are traditionally text, and this has shaped many IR techniques. The simplest approach is to formulate a query as a list of key words and to retrieve only documents that contain all of the key words. This approach does not perform well in practice, however. Another approach that is almost as simple is to arrange word counts from numerous documents in a matrix and then to treat the rows and columns of the matrix as vectors. This permits comparison of documents and queries using simple mathematical measurements on vectors, such as Euclidean distance (a generalization of the Pythagorean theorem) and cosine similarity (a measure of the angle between two vectors that is maximal when the vectors are parallel). More typically, the term-document matrix is subjected to further mathematical processing for extracting the most salient features of the data, such as singular value decomposition or latent semantic analysis (Widdows 2004
). This vector-space model of information has proven to be very useful, and the possibility of extending it to retrieval of images and music is an area of active research (Casey et al. 2008
; Datta et al. 2008
The diagnosis of AD (or identification of patients who meet other clinical criteria) may be approached from an IR perspective. In this case, we wish to search a database of brain images and retrieve those images that belong to patients with AD or elderly controls. Somewhat more compelling (and more difficult) is the retrieval of scans from patients with memory impairment who are destined to develop AD. The immediate problem that arises is the formulation of the query. In text-based IR, the query is simply a list of words (such as a document) that can be converted to a vector and compared to documents in the database. The current research focuses on a relatively simple method for formulating “query” vectors from groups of PET scans and then evaluating the utility of these vectors for retrieving relevant scans (i.e., for making diagnoses or predictions on the subjects who contributed the scans).
summarizes the residual vector analysis method, the first step of which is mathematically identical to computing the ordinary least squares approximation of the solution to a system of linear equations. Geometrically, the ordinary least squares approximation is the projection of one vector (composed of the values of the dependent variable) onto a space defined by other vectors (the matrix of independent variables). This projection is the linear combination of vectors from the matrix column space that is closest to the original vector. Subtraction of this projection vector from the original vector yields a residual vector that is orthogonal to all of the vectors in the matrix column space. Thus, when similarity is quantified in terms of the cosine of the angle between two vectors (i.e., zero for perpendicular vectors, one for parallel vectors), the residual vector will have zero similarity with all of the column vectors in the matrix. Because the residual vector is a component of the original vector, it will maintain some cosine similarity with it (except in the unlikely event that a perfect solution is found, in which case the residual will be the zero vector).
Figure 1 Geometric interpretation of ordinary least squares regression. A vector N (representing the PET scan of an MCI nonconverter) is projected onto a space, C, which is composed of PET scans from MCI patients who converted to AD within 2 years of being scanned. (more ...)
The goal of this project was to determine whether residual vectors computed in this manner have any utility as query vectors when used to search a database of PET scans that were not used in computation of the residual vector itself. The specific questions being posed were: (1) Do cosine similarity scores derived from the residual vectors make a significant contribution to variance in logistic regression models using AD diagnostic status or MCI conversion status as the dependent variable? (2) Can cosine similarity scores predict functional decline? (3) How do these logistic regression models fare when used as classifiers of cases not used in the model computation?