The behavior of the NPMLE of a decreasing density near the boundaries of the support

We investigate the behavior of the nonparametric maximum likelihood estimator $\hat{f}_n$ for a decreasing density $f$ near the boundaries of the support of $f$. We establish the limiting distribution of $\hat{f}_n(n^{-\alpha})$, where we need to distinguish between different values of $0<\alpha<1$. Similar results are obtained for the upper endpoint of the support, in the case it is finite. This yields consistent estimators for the values of $f$ at the boundaries of the support. The limit distribution of these estimators is established and their performance is compared with the penalized maximum likelihood estimator.Comment: Published at http://dx.doi.org/10.1214/009053606000000100 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Asymptotic normality of the LkL_k-error of the Grenander estimator

We investigate the limit behavior of the $L_k$-distance between a decreasing density $f$ and its nonparametric maximum likelihood estimator $\hat{f}_n$ for $k\geq1$. Due to the inconsistency of $\hat{f}_n$ at zero, the case $k=2.5$ turns out to be a kind of transition point. We extend asymptotic normality of the $L_1$-distance to the $L_k$-distance for $1\leq k<2.5$, and obtain the analogous limiting result for a modification of the $L_k$-distance for $k\geq2.5$. Since the $L_1$-distance is the area between $f$ and $\hat{f}_n$, which is also the area between the inverse $g$ of $f$ and the more tractable inverse $U_n$ of $\hat{f}_n$, the problem can be reduced immediately to deriving asymptotic normality of the $L_1$-distance between $U_n$ and $g$. Although we lose this easy correspondence for $k>1$, we show that the $L_k$-distance between $f$ and $\hat{f}_n$ is asymptotically equivalent to the $L_k$-distance between $U_n$ and $g$.Comment: Published at http://dx.doi.org/10.1214/009053605000000462 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The limit distribution of the L∞L_{\infty}-error of Grenander-type estimators

Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of $[0,1]$. The rate of convergence is found to be of order $(n/\log n)^{-1/3}$ and the limiting distribution to be Gumbel.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1015 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Preferences and beliefs of Dutch orthopaedic surgeons and patients reduce the implementation of "Choosing Wisely" recommendations in degenerative knee disease

Purpose: The purpose of this study was to assess which factors were associated with the implementation of “Choosing Wisely” recommendations to refrain from routine MRI and arthroscopy use in degenerative knee disease. Methods: Cross-sectional surveys were sent to 123 patients (response rate 95%) and 413 orthopaedic surgeons (response rate 62%) fulfilling the inclusion criteria. Univariate and multivariate logistic regression analyses were used to identify factors associated with implementation of “Choosing Wisely” recommendations. Results: Factors reducing implementation of the MRI recommendation among patients included explanation of added value by an orthopaedic surgeon [OR 0.18 (95% CI 0.07–0.47)] and patient preference for MRI [OR 0.27 (95% CI 0.08–0.92)]. Factors reducing implementation among orthopaedic surgeons were higher valuation of own MRI experience than existing evidence [OR 0.41 (95% CI 0.19–0.88)] and higher estimated patients’ knowledge to participate in shared decision-making [OR 0.38 (95% CI 0.17–0.88)]. Factors reducing implementation of the arthroscopy recommendation among patients were orthopaedic surgeons’ preferences for an arthroscopy [OR 0.03 (95% CI 0.00–0.22)] and positive experiences with arthroscopy of friends/family [OR 0.03 (95% CI 0.00–0.39)]. Factors reducing implementation among orthopaedic surgeons were higher valuation of own arthroscopy experience than existing evidence [OR 0.17 (95% CI 0.07–0.46)] and belief in the added value [OR 0.28 (95% CI 0.10–0.81)]. Conclusions: Implementation of “Choosing Wisely” recommendations in degenerative knee disease can be improved by strategies to change clinician beliefs about the added value of MRIs and arthroscopies, and by patient-directed strategies addressing patient preferences and underlying beliefs for added value of MRI and arthroscopies resulting from experiences of people in their environment. Level of evidence: IV

The limit process of the difference between the empirical distribution function and its concave majorant

We consider the process -Fn, being the difference between the empirical distribution function Fn and its least concave majorant , corresponding to a sample from a decreasing density. We extend Wang's result on pointwise convergence of -Fn and prove that this difference converges as a process in distribution to the corresponding process for two-sided Brownian motion with parabolic drift.Least concave majorant Empirical distribution function Brownian motion with parabolic drift Isotonic estimation Monotone density

Estimation of a decreasing hazard of patients with acute coronary syndrome

The Kaplan-Meier, Nelson-Aalen and Breslow estimators are widely used in the analysis of right-censored time to event data in medical applications. These methods are fully non-parametric and do not put any restriction on the shape of the hazard curve. In some applications, this leads to implausible estimates of the hazard course over time. With non-parametric shape-constrained estimation techniques, one can facilitate an increasing or decreasing hazard and thus generate estimators that better match the biological reasoning, without being as restrictive as parametric methods. We illustrate the advantage of such techniques in the analysis of a large clinical trial in cardiology. Simulation results show that in case the true hazard is monotone, the non-parametric shape-constrained estimators are more accurate than the traditional estimators on the hazard level. On the (cumulative) distribution function level, the shape-constrained estimators show similar performance as the traditional one

Neuroinflammation is increased in the parietal cortex of atypical Alzheimer's disease

BACKGROUND: While most patients with Alzheimer's disease (AD) present with memory complaints, 30% of patients with early disease onset present with non-amnestic symptoms. This atypical presentation is thought to be caused by a different spreading of neurofibrillary tangles (NFT) than originally proposed by Braak and Braak. Recent studies suggest a prominent role for neuroinflammation in the spreading of tau pathology. METHODS: We aimed to explore whether an atypical spreading of pathology in AD is associated with an atypical distribution of neuroinflammation. Typical and atypical AD cases were selected based on both NFT distribution and amnestic or non-amnestic clinical presentation. Immunohistochemistry was performed on the temporal pole and superior parietal lobe of 10 typical and 9 atypical AD cases. The presence of amyloid-beta (N-terminal; IC16), pTau (AT8), reactive astrocytes (GFAP), microglia (Iba1, CD68, and HLA-DP/DQ/DR), and complement factors (C1q, C3d, C4b, and C5b-9) was quantified by image analysis. Differences in lobar distribution patterns of immunoreactivity were statistically assessed using a linear mixed model. RESULTS: We found a temporal dominant distribution for amyloid-beta, GFAP, and Iba1 in both typical and atypical AD. Distribution of pTau, CD68, HLA-DP/DQ/DR, C3d, and C4b differed between AD variants. Typical AD cases showed a temporal dominant distribution of these markers, whereas atypical AD cases showed a parietal dominant distribution. Interestingly, when quantifying for the number of amyloid-beta plaques instead of stained surface area, atypical AD cases differed in distribution pattern from typical AD cases. Remarkably, plaque morphology and localization of neuroinflammation within the plaques was different between the two phenotypes. CONCLUSIONS: Our data show a different localization of neuroinflammatory markers and amyloid-beta plaques between AD phenotypes. In addition, these markers reflect the atypical distribution of tau pathology in atypical AD, suggesting that neuroinflammation might be a crucial link between amyloid-beta deposits, tau pathology, and clinical symptoms

Increase of Mast Cells in COVID-19 Pneumonia may Contribute to Pulmonary Fibrosis and Thrombosis

AIMS: Lung tissue from COVID-19 patients shares similar histomorphological features with chronic lung allograft disease, suggesting activation of autoimmune related pathways in COVID-19 as well. To better understand the underlying spectrum of pathophysiology in COVID-19 pneumonia, we analyzed mRNA expression of autoimmune-related genes in post-mortem lung tissue from COVID-19 patients. METHODS AND RESULTS: Formalin-fixated, paraffin-embedded lung tissue samples of 18 COVID-19 patients and 8 influenza patients were used for targeted gene expression profiling using NanoString technology. Multiplex immunofluorescence for tryptase and chymase was applied for validation. Genes related to mast cells were significantly increased in COVID-19. This finding was strengthened by multiplex immunofluorescence showing a significant increase of tryptase- and chymase positive cells in COVID-19 as well. Furthermore, RAGE (receptor for advanced glycation end-products) and PPBP (pro-platelet basic protein) were upregulated in COVID-19 compared to influenza. Genes associated with type I interferon signaling showed a significant correlation to detected SARS-CoV2 pathway-related genes. The comparison of lung tissue samples from both groups based on the presence of histomorphological features indicative of ARDS did not result in finding any specific gene or pathways. CONCLUSION: Two separate means of measuring show significant increase of mast cells in SARS-CoV-2 infected lung tissue compared to influenza. Additionally, several genes involved in fibrosis and thrombosis, among which are RAGE and PPBP, are upregulated in COVID-19. As mast cells are able to induce thrombosis and fibrosis, they may play an important role in the pathogenesis of COVID-19