A note on the choice of the number of slices in sliced inverse regression

Sliced inverse regression (SIR) is a clever technique for reducing the dimension of the predictor in regression problems, thus avoiding the curse of dimensionality. There exist many contributions on various aspects of the performance of SIR. Up to now, few attention has been paid to the problem of choosing the number of slices within the SIR procedure appropriately. The aim of this paper is to show that especially the estimation of the reduced dimension can be strongly in?uenced by the chosen number of slices. --dimension reduction,estimation of dimension

Is there a Superior Distance Function for Matching in Small Samples?

The study contributes to the development of ’standards’ for the application of matching algorithms in empirical evaluation studies. The focus is on the first step of the matching procedure, the choice of an appropriate distance function. Supplementary o most former studies, the simulation is strongly based on empirical evaluation ituations. This reality orientation induces the focus on small samples. Furthermore, ariables with different scale levels must be considered explicitly in the matching rocess. The choice of the analysed distance functions is determined by the results of former theoretical studies and recommendations in the empirical literature. Thus, in the simulation, two balancing scores (the propensity score and the index score) and the Mahalanobis distance are considered. Additionally, aggregated statistical distance functions not yet used for empirical evaluation are included. The matching outcomes are compared using non-parametrical scale-specific tests for identical distributions of the characteristics in the treatment and the control groups. The simulation results show that, in small samples, aggregated statistical distance functions are the better choice for summarising similarities in differently scaled variables compared to the commonly used measures.distance functions, matching, microeconometric evaluation, propensity score, simulation

Population-based studies on the epidemiology of migraine and Parkinson's disease

With epidemiologic analyses the effect of certain exposures on diseases can be studied in large population samples. Pharmacoepidemiology is a speciality which focuses on beneficial or harmful drug effects on the development of diseases. In my thesis I carried out different epidemiological studies in order to increase the knowledge on the natural history of migraine and Parkinson's disease. Another focus was to evaluate the effect of certain drug therapies on teh risk of developing migraine or Parkinson's disease (PD) or complications of the diseases. I used data from the General Practice Research Database (GPRD), which contains electronic records from primary-care of several million people in the United Kingdom (UK). Additionally, information on patient demographics (e.g. age, gender, body mass index, smoking status) is available for a large portion of the patiens as well as data on hospital and specialist diagnoses. The GPRD has been the source for many important studies in epidemiology as well as in drug safety. In my first project I identified 51'688 individuals of the FPRD with a firyst-time migraine diagnosis between 1994 and 2001 and an equal amount of control subjects without such a diagnosis. The incidence rates (IR) of first-time diagnoses of migraine by the general practitioners (GPs) were 2.5 times higher in women than in men and highest in puberty. The comorbid disorders of the migraineurs were also quantified in migraineurs and controls. By means of a case-control study design which included matching on several important confounders such as gender, age, general practice and index date, the odds ratios (ORs) for the comorbidities in migraineurs compared to non-migraineurs were investigated. This resulted in an increased OR for the migraineurs for most chronic diseases. Determination of the health resource utilisation (HRU) revealed that migraineurs with triptan prescriptions needed more health care, defined as visits to their GP or neurological specialists as well as prescriptions for headeche related drugs. In a second part of the migraine project I followed a cohort of migraineurs and their matched controls until they developed a stroke, a transient ischaemic attack (TIA), they died of until they were diagnosed with asthma for the first time. Again IRs were calculated and a nested case-control analysis performed. A previous history of migraine was associated with an approximately twofold increased risk for stroke or TIA, however, residual confounding by migraine recency or severity could not totally be ruled out. Furthermore it is challenging to determine the stroke risk in association with prior triptan use because in the GPRD the actual timing of the drug intake is not recorded. The mortality of migraineurs was slightly decreased and no increased asthma risk was seen in migraineurs with or without triptan use. In my second project I investigated the impact of prior drug use on the risk of being diagnosed with PD. During the study period from 1994 to 2005 3'637 individuals with idiopathic PD were identified from the GPRD. The majority of the cases with a first-time PD diagnosis were men older than 60 years of age. In two separate case-control studies, in which I used the same matching criteria as in the migraine project, I found a decreased risk of PD in patients with current use of calcium channel blockers. This finding is in accordance with a recent hypothesis regarding the involvement of calcium channels in the PD pathophysiology. After the assumption of an increased risk for PD associated with the use of statins, the results of the other case control study gave reassurance that in a large population sample from the GPRD the risk for a PD diagnosis was not increased for current or past use of statins. To conclude, the GPRD data is very useful for the description of the natural history of diseases as well as for the investigation of particular drug safety questions. The potentials of the database could be further increased if genetic information was also available in future. Certainly, special diligence has to be exercised regarding the issue of data protection

Outlier detection in experimental data using a modified Hampel identifier

The present method allows to detect outlying observations in data which may be described by a deterministic function plus a stochastic component. This type of functional relationship often occurs in experimental data, in toxicological research, for instance. The Hampel identifier, an outlier identification method designed for location-scale models, is modified to account for the special structure of the data. Simulated standardisation values for the procedure are given for sample sizes from 16 to 21. The procedure is applied to a toxicological study with one of the basic petrochemical compounds ethylene (ethene). This study was designed to determine the individual and population parameters, i. e. the parameters which describe the general behaviour of the investigated process in the whole population, as well as the intra- and interindividual variability of the processes of inhalation, exhalation, and metabolic elimination of the chemical ethylene in male Sprague- Dawley rats. The results are discussed for various methods determining the functional relationship and for two possible approaches of applying the outlier identification method, one based on the simulated (exact) standardisation values for all sample sizes, the other based on taking a tabled value corresponding to the sample size 'nearest' to the real sample

Outlier detection in experimental data using a modified Hampel identifier

The present method allows to detect outlying observations in data which may be described by a deterministic function plus a stochastic component. This type of functional relationship often occurs in experimental data, in toxicological research, for instance. The Hampel identifier, an outlier identification method designed for location-scale models, is modified to account for the special structure of the data. Simulated standardisation values for the procedure are given for sample sizes from 16 to 21. The procedure is applied to a toxicological study with one of the basic petrochemical compounds ethylene (ethene). This study was designed to determine the individual and population parameters, i. e. the parameters which describe the general behaviour of the investigated process in the whole population, as well as the intra- and interindividual variability of the processes of inhalation, exhalation, and metabolic elimination of the chemical ethylene in male Sprague-Dawley rats. The results are discussed for various methods determining the functional relationship and for two possible approaches of applying the outlier identification method, one based on the simulated (exact) standardisation values for all sample sizes, the other based on taking a tabled value corresponding to the sample size 'nearest' to the real sample

A note on the choice of the number of slices in sliced inverse regression

Sliced inverse regression (SIR) is a clever technique for reducing the dimension of the predictor in regression problems, thus avoiding the curse of dimensionality. There exist many contributions on various aspects of the performance of SIR. Up to now, few attention has been paid to the problem of choosing the number of slices within the SIR procedure appropriately. The aim of this paper is to show that especially the estimation of the reduced dimension can be strongly influenced by the chosen number of slices. 2000 Mathematics Subject Classification: 62H1

Sliced Inverse Regression for High-dimensional Time Series

Methods of dimension reduction are very helpful and almost a necessity if we want to analyze high-dimensional time series since otherwise modelling affords many parameters because of interactions at various time-lags. We use a dynamic version of Sliced Inverse Regression (SIR; Li (1991)), which was developed to reduce the dimension of the regressor in regression problems, as an exploratory tool for analyzing multivariate time series. Analyzing each variable individually, we search for those directions, i.e., linear combinations of past and present observations of the other variables which explain most of the variability of the variable considered. This can also provide information on possible nonlinearities. We apply a dynamic version of SIR to multivariate physiological time series observed in intensive care

Is there a Superior Distance Function for Matching in Small Samples?

The study contributes to the development of 'standards' for the application of matching algorithms in empirical evaluation studies. The focus is on the first step of the matching procedure, the choice of an appropriate distance function. Supplementary to most former studies, the simulation is strongly based on empirical evaluation situations. This reality orientation induces the focus on small samples. Furthermore, variables with different scale levels must be considered explicitly in the matching process. The choice of the analysed distance functions is determined by the results of former theoretical studies and recommendations in the empirical literature. Thus, in the simulation, two balancing scores (the propensity score and the index score) and the Mahalanobis distance are considered. Additionally, aggregated statistical distance functions not yet used for empirical evaluation are included. The matching outcomes are compared using non-parametrical scale-specific tests for identical distributions of the characteristics in the treatment and the control groups. The simulation results show that, in small samples, aggregated statistical distance functions are the better choice for summarising similarities in differently scaled variables compared to the commonly used measures.Die Studie leistet einen Beitrag zur Entwicklung von "Standards" für den Einsatz von Matchingverfahren in empirischen Evaluationsstudien. Der Fokus liegt dabei auf der Entscheidung für ein geeignetes Distanzmaß. Die strenge Orientierung der durchgeführten Simulation an realen Entscheidungssituationen stellt eine Ergänzung zu den meisten bisher bekannten Studien dar. Sie erklärt zum einen die Fokussierung auf kleine Stichproben, zum anderen die explizite Berücksichtigung unterschiedlich skalierter Variablen, die im Matchingprozess berücksichtigt werden müssen. Die Analyse umfasst diejenigen Distanzmaße, die in der theoretischen Literatur als vorteilhaft angesehen bzw. häufig in empirischen Studien eingesetzt werden: die Mahalanobisdistanz und Balancing Scores. Darüber hinaus werden zwei aus der Statistik bekannte - in Evaluationsstudien bisher allerdings nicht verwendete - aggregierte Distanzmaße untersucht. Die erzielten Matchingergebnisse werden anhand nichtparametrischer skalenspezifischer Tests auf Übereinstimmung der Merkmalsverteilungen bewertet. Die Ergebnisse zeigen, dass aggregierte Distanzmaße in kleinen Stichproben besser in der Lage sind, Ähnlichkeiten in unterschiedlich skalierten Merkmalen zusammenzufassen als die bisher gebräuchlichen Maße

Robust Sliced Inverse Regression Procedures

Sliced Inverse Regression (SIR) is a promising technique for the purpose of dimension reduction. Several properties of this relatively new method have been examined already, but little attention has been paid to robustness aspects. We show that SIR is very sensitive towards outliers in the data. Therefore a generalized estimation procedure which allows for robustness properties, especially for a high breakdown point, is proposed

A Survey of Psychologists’ Attitudes Towards and Utilization of Exposure Therapy for PTSD

Although research supports the efficacy of exposure therapy for PTSD, some evidence suggests that exposure is under-utilized in general clinical practice. The purpose of this study was to assess licensed psychologists’ use of imaginal exposure for PTSD and to investigate perceived barriers to its implementation. A total of 852 psychologists from 3 states were randomly selected and surveyed. An additional 50 members of a trauma special interest group of a national behavior therapy organization were also surveyed. The main survey results indicate that a large majority of licensed doctoral level psychologists do not report use of exposure therapy to treat patients with PTSD. Although approximately half of the main study sample reported that they were at least somewhat familiar with exposure for PTSD, only a small minority used it to treat PTSD in their clinical practice. Even among psychologists with strong interest and training in behavioral treatment for PTSD, exposure therapy is not completely accepted or widely used. Clinicians also appear to perceive a significant number of barriers to implementing exposure