Spatial Statistics with S-Plus

An overview is given over the S-Plus libraries and modules for statistical analysis of spatial data that are currently available at the Department of Statistics, University of Dortmund. It is believed that this includes all libraries currently available on the internet. Listings of functions show what statistical techniques are implemented, and where to find them. This facilitates the search for any particular function, and saves from re-programming of techniques that are already available. This overview may therefore also be viewed as a starting point for developing further analysis tools for spatial and spatio-temporal statistics in S-Plus

On the estimation of smooth autoregressive parameter fields with applications in ophthalmology

The focus of this doctoral thesis is on the analysis of data obtained from the multifocal ERG. An exploratory analysis of the data available is presented in Chapter 2. It is demonstrated that the data carry both spatial as well as temporal information. Therefore, a combination of techniques both from spatial statistics and time series analysis should be used to more adequately describe multifocal ERG data within a statistical framework.Ordinary least squares estimates for parameters from autoregressive time series models are the starting point. They are introduced in Chapter 3. It is seen there that a purely temporal analysis only partly describes the dynamics in the multifocal ERG data sets at hand, and that the spatial layout of the data should be accounted for explicitly.Chapter 4 therefore provides a spatial analysis of the data. Spatial smoothing is performed to remove noise inherent in the resulting estimators. The techniques of Kriging and SplineSmoothing are two candidates under study. They are introduced in Chapters 4 and 5, respectively. Applications to multifocal ERG data are added at the end of each of thesechapters, and arguments are given why modifications are desirable.A modified smoothing approach referred to as smoothing of AR-parameter fields is described in Chapter 6. It makes use of a fitting criterion that accounts both for spatial smoothness of the autoregressive parameter estimates as well as a satisfactory temporal fit to the observed data. It will be seen that the smoothed parameter estimates are well interpretable, while giving rise to only a small increase in the overall sum of squares for fit. Chapter 7 summarizes these results and gives some suggestions for future research. Empirical results obtained for the available data sets are combined in the appendix and complement the examples already described in the foregoing text.Die vorgelegte Arbeit befasst sich mit der statistischen Analyse zeitlich-räumlicher Daten aus dem Bereich der Augenheilkunde. Zur näheren Untersuchung der sog. altersabhängigen Makula-Degeneration (AMD), einer Gruppe von Erkrankungen der Netzhaut, wurden mit Hilfe des sogenannten multifokalen Elektroretinogramms an der Augenklinik der Universität Essen Daten gesammelt, die die elektrophysiologische Reaktion der auf der Retina befindlichen Rezeptoren auf optische Reize widerspiegeln. Die dabei gewonnen Daten können als zeitlich-räumliche Datensätze betrachtet werden, die auf einem auf die Retina projezierten Gitter von 103 Teilflächen erhoben werden. Jeder Teilfläche ist dabei eine Zeitreihe der Länge 122 msec zuordnenbar. Vier derartiger Datensätze standen für eine Analyse zur Verfügung. Eigentliches Ziel der Essener Studie ist die nähere Charakterisierung der elektrophysiologischen Response bei verschiedenen Ausprägungen der AMD. Dies soll zu einer verbesserten Diagnose führen. Die vorliegenden Datensätze bieten einen ersten Einstieg zu dem Versuch, die zu beobachtenden Dynamiken statistisch näher zu beschreiben. Eine erste explorative Analyse bestätigte die Erfahrung aus der Medizin, dass sich sowohl räumliche als auch zeitliche Strukturen in den Daten erkennen lassen. Diese werden in der aktuellen medizinischen Literatur jedoch vorwiegend deskriptiv analysiert. Dabei werden in aller Regel nicht die gesamten zur Verfügung stehenden Daten verwendet, sondern lediglich abgeleitete Statistiken, wie etwa Amplituden, betrachtet. Dies führt zu einem Verlust an Informationen, der vermieden werden sollte.In dem Bestreben, die in der Praxis verwendeten Analysetechniken aus statistischer Sicht zu verbessern, wurden zunächst bekannte Verfahren der Zeitreihenanalyse und der räumlichen Statistik betrachtet. Speziell wurden autoregressive (AR) Modelle sowie Kriging-Verfahren verwendet. Während erstere eine kompakte Parametrisierung der zeitlichen Dynamiken durch wenige Parameter erlauben, führen Kriging-Verfahren zu optimalen räumlichen Prognosen. Jedoch sind dabei die Modellierung der räumlichen Kovarianzstruktur sowie Kenntnisse über die Grundstruktur des zugrundeliegenden räumlichen Trends erforderlich. Da letztere in der Regel nicht im vorhinein vorhanden sind, wurden Thin Plate Spline-Verfahren als Alternative betrachtet. Diese Verfahren entsprechen unter gewissen Modellannahmen dem Kriging, eignen sich aber besser zur Schätzung glatter lokaler Trendstrukturen. Die Spline-Schätzer lassen sich dabei über einen Kleinste-Quadrate-Ansatz mit integriertem Strafterm ableiten, in welchem die Glätte der geschätzten Trendfläche über Bedingungen an deren Ableitungen beeinflusst wird.Der in dieser Arbeit vorgestellte neue Ansatz besteht nun in einer direkten Verknüpfung von Techniken der Zeitreihenanalyse mit denen der Schätzung räumlicher Trends durch Splines. Um eine kompakte und zugleich gut interpretierbare Charakterisierung der in einem Datensatz zu beobachtenden Dynamiken zu erreichen, erfolgt eine Glättung nicht im Beobachtungsraum selbst. Stattdessen werden die abgeleiteten AR-Parameter, welche räumlich zu Parameterfeldern anordnenbar sind, selbst geglättet. Um dabei die eigentlichen Beobachtungen nicht außer acht zu lassen, wird als Kriterium zur optimalen Schätzung eine zeitlich-räumliche Quadratsumme mit entsprechendem Strafterm für die Glattheit der AR-Parameter eingeführt. Ausgangspunkt sind dabei die lokal (d.h. für jede einzelne Zeitreihe) geschätzten Kleinste-Quadrate-Schätzer der AR-Parameter, da diese per constructionem die optimale Anpassung an die Daten liefern. Im Ergebnis erhält man Schätzer mit optimaler Anpassung an die Daten, bei gleichzeitig vorgegebener Glattheit der geschätzten Parameterfelder. Eine geschlossen Darstellung der so geglätteten Schätzer kann angegeben werden. Ausdrücke für die Differenz des neuen Schätzers zum ursprünglichen Kleinste-Quadrate-Schätzer, sowie zu dem aus einer einfachen Glättung der AR-Parameter (ohne Berücksichtigung der zeitlichen Anpassung) abgeleiteten Schätzer werden angegeben. Ebenso lässt sich die Veränderung in der Summe der quadrierten Residuen geschlossen darstellen.Bei der Glättung mit Splines ist die Auswahl von besonderen Glättungsparametern notwendig. Neben der expliziten Auswahl durch den Datenanalysten lässt sich dieser Parameter auch automatisch mit Hilfe der Verallgemeinerten Kreuzvalidierung bestimmen. Dieser Ansatz wurde auf den neu eingeführten Schätzer übertragen und auf die vier Datensätze angewandt. Es zeigte sich dabei, dass die resultierende kreuzvalidierte Schätzung der AR-Parameter numerisch sehr aufwendig zu berechnen und zugleich bisweilen unbefriedigend ist, da u.U. sehr stark geglättet wird. Dies ist insbesondere dann der Fall, wenn die AR-Parameter aus der zugrundeliegenden Kleinste-Quadrate-Schätzung kaum räumlich variieren und stattdessen eine starke Variabilität im Verhältnis zu eventuellen Trendstrukturen zeigen. Eine direkte Auswahl der Glättungs-parameter erscheint in solchen Fällen möglicherweise eher angezeigt. Gute Ergebnisse ließen sich jedoch dann erzielen, wenn grobe Strukturen bereits in den räumlich angeordneten Kleinste-Quadrate-Schätzeren zu erkennen waren. Diese traten nach der Glättung durch Kreuzvalidierung umso deutlicher hervor

Spectral estimation for psycho-physiological data Estimating lower-dimensional representations in frequency space

Two different estimation techniques for the spectrum of a nonstationary time series are compared empirically. Both of them are assuming a time-dependent autoregressive (AR-) model for the data. The fifirst estimation technique used is the Frequency State Dependent Model (FSDM-) technique (Schmitz and Urfer, 1997), a modification of the well known Kalman-filter approach. The FSD-Model is based on Priestleys SD-Models for the analysis of nonstationary time series (e.g.,Priestley, 1988). An alternative approach for estimating AR-parameters of nonstationary time series was proposed by Tsatsannis and Giannkis (1993). The basic idea is to directly decompose the time-dependent autoregressive parameters into their wavelet representation and to select suitable wavelet coefficients for reconstruction. In either case, Kitagawa's (1983) "instantaneous spectrum" is calculated to obtain the actual spectral estimates. Applied to empirical data, both approaches lead to similar spectral estimates. However, simulations show how crucial the selection of wavelet coefficients is when applying the latter technique

Responder analysis of a randomized comparison of the 13.3 mg/24 h and 9.5 mg/24 h rivastigmine patch

INTRODUCTION: OPtimizing Transdermal Exelon In Mild-to-moderate Alzheimer’s disease (OPTIMA) was a randomized, double-blind comparison of 13.3 mg/24 h versus 9.5 mg/24 h rivastigmine patch in patients with mild-to-moderate Alzheimer’s disease who declined despite open-label treatment with 9.5 mg/24 h patch. Over 48 weeks of double-blind treatment, high-dose patch produced greater functional and cognitive benefits compared with 9.5 mg/24 h patch. METHODS: Using OPTIMA data, a post-hoc responder analysis was performed to firstly, compare the proportion of patients demonstrating improvement or absence of decline with 13.3 mg/24 h versus 9.5 mg/24 h patch; and secondly, identify predictors of improvement or absence of decline. ‘Improvers’ were patients who improved on the Alzheimer’s Disease Assessment Scale–cognitive subscale (ADAS-cog) by ≥4 points from baseline, and did not decline on the instrumental domain of the Alzheimer’s Disease Cooperative Study–Activities of Daily Living scale (ADCS-IADL). ‘Non-decliners’ were patients who did not decline on either scale. RESULTS: Overall, 265 patients randomized to 13.3 mg/24 h and 271 to 9.5 mg/24 h patch met the criteria for inclusion in the intention-to-treat population and were included in the analyses. Significantly more patients were ‘improvers’ with 13.3 mg/24 h compared with 9.5 mg/24 h patch at Weeks 24 (44 (16.6%) versus 19 (7.0%); P < 0.001) and 48 (21 (7.9%) versus 10 (3.7%); P = 0.023). A significantly greater proportion of patients were ‘non-decliners’ with 13.3 mg/24 h compared with 9.5 mg/24 h patch at Week 24 (71 (26.8%) versus 44 (16.2%); P = 0.002). At Week 48, there was a trend in favor of 13.3 mg/24 h patch. Functional and cognitive assessment scores at double-blind baseline did not consistently predict effects at Weeks 24 or 48. CONCLUSION: More patients with mild-to-moderate Alzheimer’s disease who are titrated to 13.3 mg/24 h rivastigmine patch at time of decline are ‘improvers’ or ‘non-decliners’ i.e. show responses on cognition and activities of daily living compared with patients remaining on 9.5 mg/24 h patch. TRIAL REGISTRATION: Clinicaltrials.gov identifier: NCT00506415; registered July 20, 2007. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13195-014-0088-8) contains supplementary material, which is available to authorized users

Efficacy of Higher Dose 13.3 mg/24 h Rivastigmine Patch on Instrumental Activities of Daily Living in Patients with Mild-to-Moderate Alzheimer's Disease

Background: Stabilizing/reducing decline in the ability to perform activities of daily living (ADLs) is important in management of Alzheimer's disease (AD). Methods: Post hoc analysis of OPtimizing Transdermal Exelon In Mild-to-moderate Alzheimer's disease (OPTIMA), a double-blind trial comparing 13.3 and 9.5 mg/24 h rivastigmine patch in patients with AD demonstrating functional and cognitive decline with 9.5 mg/24 h patch. Efficacy on Alzheimer's disease Cooperative Study-instrumental ADL (ADCS-IADL) items, higher level function (HLF), and autonomy factors was assessed. Results: The ADCS-IADL, HLF, and autonomy factors favored 13.3 mg/24 h patch at all time points, reaching significance from weeks 16 to 48, 24 to 48, and 32 to 48, respectively. Higher dose patch demonstrated significantly greater efficacy on 10 of 17 ADCS-IADL items at 1 or more time points ( P < .05 vs 9.5 mg/24 h patch). More adverse events were observed with higher dose patch; study discontinuations were similar between the doses. Conclusions: Greater efficacy of 13.3 versus 9.5 mg/24 h patch on ADL, including autonomy and HLF factors, supports this additional dosing option to prolong patients' independence

Alzheimer's Disease Assessment Scale-Cognitive subscale variants in mild cognitive impairment and mild Alzheimer's disease: change over time and the effect of enrichment strategies

Background Development of new treatments for Alzheimer’s disease (AD) has broadened into early interventions in individuals with modest cognitive impairment and a slow decline. The 11-item version of the Alzheimer’s Disease Assessment Scale–Cognitive subscale (ADAS-Cog) was originally developed to measure cognition in patients with mild to moderate AD. Attempts to improve its properties for early AD by removing items prone to ceiling and/or by adding cognitive measures known to be impaired early have yielded a number of ADAS-Cog variants. Using Alzheimer’s Disease Neuroimaging Initiative data, we compared the performance of the 3-, 5-, 11- and 13-item ADAS-Cog variants in subjects with early AD. Given the interest in enrichment strategies, we also examined this aspect with a focus on cerebrospinal fluid (CSF) markers. Methods Subjects with mild cognitive impairment (MCI) and mild AD with available ADAS-Cog 13 and CSF data were analysed. The decline over time was defined by change from baseline. Direct cross-comparison of the ADAS-Cog variants was performed using the signal-to-noise ratio (SNR), with higher values reflecting increased sensitivity to detect change over time. Results The decline over time on any of the ADAS-Cog variants was minimal in subjects with MCI. Approximately half of subjects with MCI fulfilled enrichment criteria for positive AD pathology. The impact of enrichment was detectable but subtle in MCI. The annual decline in mild AD was more pronounced but still modest. More than 90 % of subjects with mild AD had positive AD pathology. SNRs were low in MCI but greater in mild AD. The numerically largest SNRs were seen for the ADAS-Cog 5 in MCI and for both the 5- and 13-item ADAS-Cog variants in mild AD, although associated confidence intervals were large. Conclusions The possible value of ADAS-Cog expansion or reduction is less than compelling, particularly in MCI. In mild AD, adding items known to be impaired at early stages seems to provide more benefit than removing items on which subjects score close to ceiling

der Universität Dortmund

I would like to thank Johannes Hüsing, University of Essen, for first drawing my attention to the analysis of AMD data, and Dr. Bernhard Jurklies and Malte Weismann, Eye Hospital of the University of Essen, for providing the AMD data sets analyzed. Helpful comments on the general structure of the manuscript were given by Dres. Roland Fried and Claudia Becker, University of Dortmund. Dr. Indranil Chakrabarti and Maritza Meléndez, M.Sc., M.Sc. patiently checked my use of the English language and took care of the readability of the result. Thanks also to Professor Dr. E.E. Sutter for kindly giving the permission to include Figure 2.2 into the manuscript. Matthias Schneider took a lot of effort to convert it into a printable format. In also want to thank Professor Dr. Wolfgang Urfer for encouraging me to tackle spatiotemporal statistics in the first place, and Professor Dr. Siegfried Schach for fruitful discussions on the topic while preparing the thesis. My special thanks, however, go to Professor Dr. Ursula Gather, who gave me the opportunity to join her research group, and who guided me through the last stages of my work. This doctorate thesis was written while the author was a member of the collaborative researc

Additional file 3: of Alzheimer’s Disease Assessment Scale–Cognitive subscale variants in mild cognitive impairment and mild Alzheimer’s disease: change over time and the effect of enrichment strategies

MMSE score up to 24 months for subjects with MCI and mild AD. Supplementary table providing details of MMSE score up to 24 months for subjects with MCI and mild AD. (DOCX 14 kb