Fast, Exact Bootstrap Principal Component Analysis for <i>p</i> > 1 Million

<p>Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject (<i>p</i>) is much larger than the number of subjects (<i>n</i>), calculating and storing the leading principal components (PCs) from each bootstrap sample can be computationally infeasible. To address this, we outline methods for fast, exact calculation of bootstrap PCs, eigenvalues, and scores. Our methods leverage the fact that all bootstrap samples occupy the same <i>n</i>-dimensional subspace as the original sample. As a result, all bootstrap PCs are limited to the same <i>n</i>-dimensional subspace and can be efficiently represented by their low-dimensional coordinates in that subspace. Several uncertainty metrics can be computed solely based on the bootstrap distribution of these low-dimensional coordinates, without calculating or storing the <i>p</i>-dimensional bootstrap components. Fast bootstrap PCA is applied to a dataset of sleep electroencephalogram recordings (<i>p</i> = 900, <i>n</i> = 392), and to a dataset of brain magnetic resonance images (MRIs) (<i>p</i> ≈ 3 million, <i>n</i> = 352). For the MRI dataset, our method allows for standard errors for the first three PCs based on 1000 bootstrap samples to be calculated on a standard laptop in 47 min, as opposed to approximately 4 days with standard methods. Supplementary materials for this article are available online.</p

Variability of therapeutic skills within and between seminars.

Variability of therapeutic skills within and between seminars.</p

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To train novice students adequately, it is crucial to understand where they start and how they develop their skills. This study examined the impact of novice students’ characteristics on their initial clinical micro-skills when treating simulated patients with cognitive behavior therapy. The sample consisted of 44 graduate psychology students treating seven simulated patients. Clinical micro-skills were measured both using video-based ratings in reaction to short video clips of simulated patients (via the Facilitative Interpersonal Skills (FIS) performance task) and by using video-based ratings within a session with a simulated patient (using the Inventory of Therapeutic Interventions and Skills; ITIS). Two separate LASSO regressions were performed using machine learning to select potential predictors for both skills assessments. Subsequently, a bootstrapping algorithm with 10,000 iterations was used to examine the variability of regression coefficients. Using LASSO regression, we identified two predictors for clinical micro-skills in standardized scenarios: extraversion (b = 0.10) and resilience (b = 0.09), both were not significantly associated with clinical micro-skills. Together, they explained 15% of the skill variation. Bootstrapping confirmed the stability of these predictors. For clinical micro-skills in sessions, only competitiveness was excluded by LASSO regression, and all predictors showed significant instability. The results provide initial evidence that trainees’ resilience and extraversion should be promoted in the clinical training of cognitive behavior therapy. More studies on clinical micro-skills and training with larger sample sizes are needed to fully understand clinical development.</div

Distribution of regression coefficients across all 10,000 iterations.

Vertical lines in the violin plots indicate the median and 25% quartiles. Predictors excluded by the LASSO regression are printed in italics. a) Skills in Standardized Situations, b) Skills in Sessions.</p

Flow chart of in- and excluded students.

ITIS = Inventory of Therapeutic Interventions and Skills: used to measure clinical micro-skills in-session; FIS = Facilitative Interpersonal Skills: used to measure clinical micro-skills in standardized situations. Six students’ responses to the video clips were not ratable with the FIS because their comments were based on hypothetical considerations rather than being a direct response in the form of interaction.</p

LASSO regression models for therapeutic competence.

LASSO regression models for therapeutic competence.</p

Descriptive statistics of all potential predictors of clinical micro-skills.

Descriptive statistics of all potential predictors of clinical micro-skills.</p

Fossil Chondrichthyes from the central eastern Pacific Ocean and their paleoceanographic significance

<div><p>Noonan Syndrome with Multiple Lentigines (NSML, formerly LEOPARD syndrome) is an autosomal dominant "RASopathy" disorder manifesting in congenital heart disease. Most cases of NSML are caused by catalytically inactivating mutations in the protein tyrosine phosphatase (PTP), non-receptor type 11 (<i>PTPN11</i>), encoding the SH2 domain-containing PTP-2 (SHP2) protein. We previously generated knock-in mice harboring the <i>PTPN11</i> mutation Y279C, one of the most common NSML alleles; these now-termed SHP2^Y279C/+ mice recapitulate the human disorder and develop hypertrophic cardiomyopathy (HCM) by 12 weeks of age. Functionally, heart and/or cardiomyocyte lysates from SHP2^Y279C/+ mice exhibit increased basal and agonist-induced AKT and mTOR activities. Here, we sought to determine whether we could reverse the hypertrophy in SHP2^Y279C/+ mice using ARQ 092, an oral and selective allosteric AKT inhibitor currently in clinical trials for patients with PI3K/AKT-driven tumors or Proteus syndrome. We obtained echocardiographs of SHP2^Y279C/+ and wildtype (SHP2^+/+) littermates, either in the presence or absence of ARQ 092 at 12, 14, and 16 weeks of age. While SHP2^Y279C/+ mice developed significant left ventricular hypertrophy by 12 weeks, as indicated by decreased chamber dimension and increased posterior wall thickness, treatment of SHP2^Y279C/+ mice with ARQ 092 normalized the hypertrophy in as early as 2 weeks following treatment, with hearts comparable in size to those in wildtype (SHP2^+/+) mice. In addition, we observed an increase in fractional shortening (FS%) in SHP2^Y279C/+ mice, an effect of increased compensatory hypertrophy, which was not apparent in SHP2^Y279C/+ mice treated with ARQ 092, suggesting functional improvement of HCM upon treatment with the AKT inhibitor. Finally, we found that ARQ 092 specifically inhibited AKT activity, as well as its downstream effectors, PRAS and S6RP in NSML mice. Taken together, these data suggest ARQ 092 may be a promising novel therapy for treatment of hypertrophy in NSML patients.</p></div

Anatomic and functional parameters, as assessed by echocardiography, in WT and NSML mice starting at 12 weeks of age and treated for the indicated length of time with vehicle or ARQ 092.

<p>Anatomic and functional parameters, as assessed by echocardiography, in WT and NSML mice starting at 12 weeks of age and treated for the indicated length of time with vehicle or ARQ 092.</p

Additional file 2: of Effective communication of public health guidance to emergency department clinicians in the setting of emerging incidents: a qualitative study and framework

Interview guide for public health decision-makers. Example of data collection instrument. (DOCX 31 kb