The RODEO Approach for Nonparametric Density Estimation

Der von Lafferty und Wasserman (2008) entwickelte RODEO-Ansatz (Regularization of Derivative Expectation Operator) ist eine Regularisierungstechnik, die auf eine Vielzahl nichtparametrischer Kernel-Smoother angewendet werden kann. Die Idee des Ansatzes ist, die Reduktion der Verzerrung des Kernel-Smoothers, die mit einer Verringerung der Bandweiten einhergeht, entlang eines glatten Weges von abnehmenden Bandweite-Parameterwerten zu bestrafen. Der Einfluss von Dimensionen mit geringer lokaler Variation wird so effektiv ``herausgeglättet'', wodurch eine Art implizite Variablenauswahl stattfindet. Unter bestimmten Annahmen können so schnellere Konvergenzraten für den mittleren integrierten quadratischen Fehler des Kernel-Smoothers erreicht werden. Dies macht den RODEO-Ansatz vor allem für höhere Dimensionen attraktiv. In der vorliegenden Arbeit wird eine Implementierung präsentiert, die den RODEO-Ansatz mit lokal polynomialer Dichteschätzung kombiniert. Die Implementierung wurde durch das R-Paket lpderodeo realisiert. Ziel der vorliegenden Arbeit ist es, die Performance der Implementierung anhand einiger Beispiele zu evaluieren und mit einer Auswahl von acht weiteren nichtparametrischen Dichteschätzverfahren zu vergleichen. Die Ergebnisse legen nahe, dass RODEO-Ansatz im Vergleich zu den anderen Ansätzen schlechter ist. Darüber hinaus leidet die Implementierung aufgrund einer naiven Auswertungsabfolge unter relativ langen Rechenzeiten. Das wohl wichtigste Ergebnis dieser Arbeit ist jedoch die Tatsache, dass die von Liu, Lafferty und Wasserman (2007) entwickelte Theorie fehlerhaft ist. So führt bereits eine simple Rotation der Daten dazu, dass der Algorithmus nicht mehr richtig funktioniert.The regularization of derivative expectation operator (RODEO) approach developed by Lafferty and Wasserman (2008) is a regularization technique designed for a wide range of nonparametric kernel smoothers. The approach applies regularization by penalizing the bias reduction associated with a bandwidth reduction along a smooth path of decreasing bandwidth parameter values in order to avoid overfitting. Dimensions with small local variation are effectively smoothed out, thus implicitly carrying out variable selection. Under certain conditions, faster rates of converges of convergence for the mean integrated square error can be achieved, which makes the approach attractive for applications in high dimensions. In this paper we apply the RODEO approach to local polynomial density estimation. We implemented the approach in the R package lpderodeo. We apply our implementation to a few examples, and evaluate its performance in a comparative study using a sample of eight other approaches for nonparametric density estimation. Our findings suggest that the approach does not work well in comparison to the other considered approaches with regard to the applied performance metrics. Furthermore, our implementation suffers from long computation time due to a naive query. Our main finding, however, concerns the fact that the theoretical framework proposed by Liu, Lafferty, and Wasserman (2007) has severe shortcomings. In fact, we demonstrate that a simple rotation of the data makes the algorithm fail in practice

Follow-Up of Men Who Have Undergone Focal Therapy for Prostate Cancer with HIFU—A Real-World Experience

Purpose: To determine oncological and functional outcomes and side effects after focal therapy of prostate cancer (PCa) with high-intensity focused ultrasound (HIFU). Methods: This retrospective single-center study included 57 consecutive patients with localised PCa. Aged 18–80 with ≤2 suspicious lesions on mpMRI (PIRADS ≥ 3), PSA of ≤15 ng/mL, and an ISUP GG of ≤2. HIFU was performed between November 2014 and September 2018. All men had an MRI/US fusion-guided targeted biopsy (TB) combined with a TRUS-guided 10-core systematic biopsy (SB) prior to focal therapy. HIFU treatment was performed as focal, partial, or hemiablative, depending on the prior histopathology. Follow-up included Questionnaires (IIEF-5, ICIQ, and IPSS), prostate-specific antigen (PSA) measurement, follow-up mpMRI, and follow-up biopsies. Results: The median age of the cohort was 72 years (IQR 64–76), and the median PSA value before HIFU was 7.3 ng/mL (IQR 5.75–10.39 ng/mL). The median follow-up was 27.5 (IQR 23–41) months. At the time of the follow-up, the median PSA value was 2.5 ng/mL (IQR 0.94–4.96 ng/mL), which shows a significant decrease (p p < 0.001). The rate of post-HIFU complications was low, at 19.3% (11 patients). The limitation of this study is the lack of long-term follow-up. Conclusions: HIFU as a therapy option for nonmetastatic, significant prostate cancer is effective in the short term for carefully selected patients and shows a low risk of adverse events and side effects

Long-term symptom severity and clinical biomarkers in post-COVID-19/chronic fatigue syndrome: results from a prospective observational cohortResearch in context

Summary: Background: Post-COVID-19 syndrome (PCS) is characterised by a wide range of symptoms, primarily fatigue and exertion intolerance. While disease courses in the early months post-infection have been well-described, the long-term health consequences for patients with PCS with disabling fatigue remain unclear. Methods: In this prospective observational cohort study, we evaluated symptom severity and various biomarkers, including hand grip strength (HGS), cardiovascular function, and laboratory parameters, in 106 patients with PCS with moderate to severe fatigue and exertion intolerance at three time points after infection (3–8, 9–16, and 17–20 months). The study was conducted at the Charité’s Fatigue Centre and the Charité’s outpatient clinic for neuroimmunology at Berlin, Germany from July 16, 2020, to February 18, 2022. A subset of patients (PCS-ME/CFS) met the diagnostic criteria for myalgic encephalomyelitis/chronic fatigue syndrome according to the Canadian Consensus Criteria (CCC). The aim was to determine differences in the disease course between the two patient groups (i.e., PCS vs PCS-ME/CFS) and identify correlating biomarkers. Findings: Patients with PCS-ME/CFS reported persistently high severity of most symptoms up to 20 months after infection, while patients with PCS showed overall health improvement. Although fatigue and post-exertional malaise (PEM), hallmarks of post-infectious fatigue syndromes, were still evident in both groups, they remained more pronounced in PCS-ME/CFS. Inflammatory biomarkers decreased in both groups, but not antinuclear antibodies. Lower HGS at onset correlated with symptom persistence, particularly in patients with PCS-ME/CFS. Interpretation: Our findings suggest that PCS can persist beyond 20 months post-infection and encompass the full scope of post-infectious ME/CFS as defined by the CCC. Sub-classifying patients with PCS based on the CCC can assist in the management and monitoring of patients with PCS-ME/CFS due to their persistently higher symptom severity. Funding: C. S. was supported by a grant from the Weidenhammer-Zoebele Foundation. F. K. was supported by the Volkswagen Foundation