Time-Series Panel Analysis (TSPA): Multivariate Modeling of Temporal Associations in Psychotherapy Process.

Objective: Processes occurring in the course of psychotherapy are characterized by the simple fact that they unfold in time and that the multiple factors engaged in change processes vary highly between individuals (idiographic phenomena). Previous research, however, has neglected the temporal perspective by its traditional focus on static phenomena, which were mainly assessed at the group level (nomothetic phenomena). To support a temporal approach, the authors introduce time-series panel analysis (TSPA), a statistical methodology explicitly focusing on the quantification of temporal, session-to-session aspects of change in psychotherapy. TSPA-models are initially built at the level of individuals and are subsequently aggregated at the group level, thus allowing the exploration of prototypical models. Method: TSPA is based on vector auto-regression (VAR), an extension of univariate auto-regression models to multivariate time-series data. The application of TSPA is demonstrated in a sample of 87 outpatient psychotherapy patients who were monitored by postsession questionnaires. Prototypical mechanisms of change were derived from the aggregation of individual multivariate models of psychotherapy process. In a 2nd step, the associations between mechanisms of change (TSPA) and pre- to postsymptom change were explored. Results: TSPA allowed a prototypical process pattern to be identified, where patient's alliance and self-efficacy were linked by a temporal feedback-loop. Furthermore, therapist's stability over time in both mastery and clarification interventions was positively associated with better outcomes. Conclusions: TSPA is a statistical tool that sheds new light on temporal mechanisms of change. Through this approach, clinicians may gain insight into prototypical patterns of change in psychotherapy.

M-Functionals of Multivariate Scatter

This survey provides a self-contained account of M-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying M-functionals and discuss their weak continuity and differentiability. This is done in a rather general framework with matrix-valued random variables. By doing so we reveal a connection between Tyler's (1987) M-functional of scatter and the estimation of proportional covariance matrices. Moreover, this general framework allows us to treat a new class of scatter estimators, based on symmetrizations of arbitrary order. Finally these results are applied to M-estimation of multivariate location and scatter via multivariate t-distributions.

Influencing factors on the length of stay in lumbar spine surgery: analysis of the German spine registry

INTRODUCTION Spinal disc herniation, lumbar spinal stenosis and spondylolisthesis are known to be leading causes of lumbar back pain. The cost of low back pain management and related operations are continuously increasing in the healthcare sector. There are many studies regarding complications after spine surgery but little is known about the factors predicting the length of stay in hospital. The purpose of this study was to identify these factors in lumbar spine surgery in order to adapt the postoperative treatment. MATERIAL AND METHODS The current study was carried out as a post hoc analysis on the basis of the German spine registry. Patients who underwent lumbar spine surgery by posterior surgical access and with posterior fusion and/or rigid stabilization, whereby procedures with dynamic stabilization were excluded. Patient characteristics were tested for association with length of stay (LOS) using bivariate and multivariate analyses. RESULTS A total of 356 patients met the inclusion criteria. The average age of all patients was 64.6 years and the mean LOS was 11.9 ± 6.0 days with a range of 2-44 days. Independent factors that were influencing LOS were increased age at the time of surgery, higher body mass index, male gender, blood transfusion of 1-2 erythrocyte concentrates and the presence of surgical complications. CONCLUSION Identification of predictive factors for prolonged LOS may allow for estimation of patient hospitalization time and for optimization of postoperative care. In individual cases this may result of a reduction in the LOS.

On The Breakdown Properties of some Multivariate M-Functionals

For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution-free’ M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

New Algorithms for M-Estimation of Multivariate Scatter and Location

We present new algorithms for M-estimators of multivariate scatter and location and for symmetrized M-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized M-estimators we work with incomplete U-statistics to accelerate our procedures initially.

Influence of prosthesis type and retention mechanism on complications with fixed implant-supported prostheses: a systematic review applying multivariate analyses

PURPOSE To identify the influence of fixed prosthesis type on biologic and technical complication rates in the context of screw versus cement retention. Furthermore, a multivariate analysis was conducted to determine which factors, when considered together, influence the complication and failure rates of fixed implant-supported prostheses. MATERIALS AND METHODS Electronic searches of MEDLINE (PubMed), EMBASE, and the Cochrane Library were conducted. Selected inclusion and exclusion criteria were used to limit the search. Data were analyzed statistically with simple and multivariate random-effects Poisson regressions. RESULTS Seventy-three articles qualified for inclusion in the study. Screw-retained prostheses showed a tendency toward and significantly more technical complications than cemented prostheses with single crowns and fixed partial prostheses, respectively. Resin chipping and ceramic veneer chipping had high mean event rates, at 10.04 and 8.95 per 100 years, respectively, for full-arch screwed prostheses. For "all fixed prostheses" (prosthesis type not reported or not known), significantly fewer biologic and technical complications were seen with screw retention. Multivariate analysis revealed a significantly greater incidence of technical complications with cemented prostheses. Full-arch prostheses, cantilevered prostheses, and "all fixed prostheses" had significantly higher complication rates than single crowns. A significantly greater incidence of technical and biologic complications was seen with cemented prostheses. CONCLUSION Screw-retained fixed partial prostheses demonstrated a significantly higher rate of technical complications and screw-retained full-arch prostheses demonstrated a notably high rate of veneer chipping. When "all fixed prostheses" were considered, significantly higher rates of technical and biologic complications were seen for cement-retained prostheses. Multivariate Poisson regression analysis failed to show a significant difference between screw- and cement-retained prostheses with respect to the incidence of failure but demonstrated a higher rate of technical and biologic complications for cement-retained prostheses. The incidence of technical complications was more dependent upon prosthesis and retention type than prosthesis or abutment material.