Asymptotic expansion of the minimum covariance determinant estimators

In arXiv:0907.0079 by Cator and Lopuhaa, an asymptotic expansion for the MCD estimators is established in a very general framework. This expansion requires the existence and non-singularity of the derivative in a first-order Taylor expansion. In this paper, we prove the existence of this derivative for multivariate distributions that have a density and provide an explicit expression. Moreover, under suitable symmetry conditions on the density, we show that this derivative is non-singular. These symmetry conditions include the elliptically contoured multivariate location-scatter model, in which case we show that the minimum covariance determinant (MCD) estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent identically distributed vector and matrix valued random elements, respectively. This provides a proof of asymptotic normality and a precise description of the limiting covariance structure for the MCD estimators.Comment: 21 page

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

A robust measure of correlation between two genes on a microarray

<p>Abstract</p> <p>Background</p> <p>The underlying goal of microarray experiments is to identify gene expression patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions could be co-expressed and show similar patterns of expression on a microarray. Using any of a variety of clustering methods or gene network analyses we can partition genes of interest into groups, clusters, or modules based on measures of similarity. Typically, Pearson correlation is used to measure distance (or similarity) before implementing a clustering algorithm. Pearson correlation is quite susceptible to outliers, however, an unfortunate characteristic when dealing with microarray data (well known to be typically quite noisy.)</p> <p>Results</p> <p>We propose a resistant similarity metric based on Tukey's biweight estimate of multivariate scale and location. The resistant metric is simply the correlation obtained from a resistant covariance matrix of scale. We give results which demonstrate that our correlation metric is much more resistant than the Pearson correlation while being more efficient than other nonparametric measures of correlation (e.g., Spearman correlation.) Additionally, our method gives a systematic gene flagging procedure which is useful when dealing with large amounts of noisy data.</p> <p>Conclusion</p> <p>When dealing with microarray data, which are known to be quite noisy, robust methods should be used. Specifically, robust distances, including the biweight correlation, should be used in clustering and gene network analysis.</p

Consistency and asymptotic normality of least squares estimators in generalized STAR models

Abstract Space-time autoregressive (STAR) models, introduced b

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

Atopy, lung function, and obstructive airways disease after prenatal exposure to famine

BACKGROUND: Associations have been found between a large head size at birth and atopy, and between low birth weight and obstructive airways disease. A study was undertaken of people born around the time of the Dutch famine in 1944-5 to determine the effects of maternal malnutrition during specific periods of gestation on the prevalence of obstructive airways disease and atopy. METHODS: Nine hundred and twelve people aged about 50, born at term between November 1943 and February 1947 in Amsterdam, were asked about their medical history. Lung function was measured in 733 and serum concentrations of total IgE and specific IgE against mite, pollen and cat were measured in 726. Those exposed in late, mid, and early gestation (exposed participants) were compared with those born before or conceived after the famine (non-exposed participants). RESULTS: Exposure to famine during gestation affected neither the concentrations of total or specific IgE nor lung function values. The prevalence of obstructive airways disease was increased in people exposed to famine in mid gestation (odds ratio adjusted for sex 1.7, 95% confidence interval (CI) 1.1 to 2.6) and tended to be higher in those exposed in early gestation (odds ratio 1.5, 95% CI 0. 9 to 2.6). CONCLUSIONS: The observed increase in the prevalence of obstructive airways disease in people exposed to famine in mid and early gestation was not parallelled by effects on IgE concentrations or lung function. The link between exposure to famine in mid and early gestation and obstructive airways disease in adulthood suggests that fetal lungs can be permanently affected by nutritional challenges during periods of rapid growt

Bounded influence regression using high breakdown scatter matrices

Fisher-consistency, influence function, robust regression, S-estimators, scatter matrices,