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1.
ArXiv ; 2024 May 16.
Artigo em Inglês | MEDLINE | ID: mdl-38800658

RESUMO

Automated region of interest detection in histopathological image analysis is a challenging and important topic with tremendous potential impact on clinical practice. The deep-learning methods used in computational pathology may help us to reduce costs and increase the speed and accuracy of cancer diagnosis. We started with the UNC Melanocytic Tumor Dataset cohort that contains 160 hematoxylin and eosin whole-slide images of primary melanomas (86) and nevi (74). We randomly assigned 80% (134) as a training set and built an in-house deep-learning method to allow for classification, at the slide level, of nevi and melanomas. The proposed method performed well on the other 20% (26) test dataset; the accuracy of the slide classification task was 92.3% and our model also performed well in terms of predicting the region of interest annotated by the pathologists, showing excellent performance of our model on melanocytic skin tumors. Even though we tested the experiments on the skin tumor dataset, our work could also be extended to other medical image detection problems to benefit the clinical evaluation and diagnosis of different tumors.

2.
Ann Appl Stat ; 17(4): 2924-2943, 2023 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-38046186

RESUMO

In The Cancer Genome Atlas (TCGA) data set, there are many interesting nonlinear dependencies between pairs of genes that reveal important relationships and subtypes of cancer. Such genomic data analysis requires a rapid, powerful and interpretable detection process, especially in a high-dimensional environment. We study the nonlinear patterns among the expression of pairs of genes from TCGA using a powerful tool called Binary Expansion Testing. We find many nonlinear patterns, some of which are driven by known cancer subtypes, some of which are novel.

3.
NPJ Breast Cancer ; 9(1): 92, 2023 Nov 11.
Artigo em Inglês | MEDLINE | ID: mdl-37952058

RESUMO

Approaches for rapidly identifying patients at high risk of early breast cancer recurrence are needed. Image-based methods for prescreening hematoxylin and eosin (H&E) stained tumor slides could offer temporal and financial efficiency. We evaluated a data set of 704 1-mm tumor core H&E images (2-4 cores per case), corresponding to 202 participants (101 who recurred; 101 non-recurrent matched on age and follow-up time) from breast cancers diagnosed between 2008-2012 in the Carolina Breast Cancer Study. We leveraged deep learning to extract image information and trained a model to identify recurrence. Cross-validation accuracy for predicting recurrence was 62.4% [95% CI: 55.7, 69.1], similar to grade (65.8% [95% CI: 59.3, 72.3]) and ER status (66.3% [95% CI: 59.8, 72.8]). Interestingly, 70% (19/27) of early-recurrent low-intermediate grade tumors were identified by our image model. Relative to existing markers, image-based analyses provide complementary information for predicting early recurrence.

4.
J Clin Oncol ; 41(26): 4192-4199, 2023 Sep 10.
Artigo em Inglês | MEDLINE | ID: mdl-37672882

RESUMO

PURPOSE: To improve on current standards for breast cancer prognosis and prediction of chemotherapy benefit by developing a risk model that incorporates the gene expression-based "intrinsic" subtypes luminal A, luminal B, HER2-enriched, and basal-like. METHODS: A 50-gene subtype predictor was developed using microarray and quantitative reverse transcriptase polymerase chain reaction data from 189 prototype samples. Test sets from 761 patients (no systemic therapy) were evaluated for prognosis, and 133 patients were evaluated for prediction of pathologic complete response (pCR) to a taxane and anthracycline regimen. RESULTS: The intrinsic subtypes as discrete entities showed prognostic significance (P = 2.26E-12) and remained significant in multivariable analyses that incorporated standard parameters (estrogen receptor status, histologic grade, tumor size, and node status). A prognostic model for node-negative breast cancer was built using intrinsic subtype and clinical information. The C-index estimate for the combined model (subtype and tumor size) was a significant improvement on either the clinicopathologic model or subtype model alone. The intrinsic subtype model predicted neoadjuvant chemotherapy efficacy with a negative predictive value for pCR of 97%. CONCLUSION: Diagnosis by intrinsic subtype adds significant prognostic and predictive information to standard parameters for patients with breast cancer. The prognostic properties of the continuous risk score will be of value for the management of node-negative breast cancers. The subtypes and risk score can also be used to assess the likelihood of efficacy from neoadjuvant chemotherapy.

5.
BMC Bioinformatics ; 24(1): 256, 2023 Jun 17.
Artigo em Inglês | MEDLINE | ID: mdl-37330471

RESUMO

BACKGROUND: Modeling of single cell RNA-sequencing (scRNA-seq) data remains challenging due to a high percentage of zeros and data heterogeneity, so improved modeling has strong potential to benefit many downstream data analyses. The existing zero-inflated or over-dispersed models are based on aggregations at either the gene or the cell level. However, they typically lose accuracy due to a too crude aggregation at those two levels. RESULTS: We avoid the crude approximations entailed by such aggregation through proposing an independent Poisson distribution (IPD) particularly at each individual entry in the scRNA-seq data matrix. This approach naturally and intuitively models the large number of zeros as matrix entries with a very small Poisson parameter. The critical challenge of cell clustering is approached via a novel data representation as Departures from a simple homogeneous IPD (DIPD) to capture the per-gene-per-cell intrinsic heterogeneity generated by cell clusters. Our experiments using real data and crafted experiments show that using DIPD as a data representation for scRNA-seq data can uncover novel cell subtypes that are missed or can only be found by careful parameter tuning using conventional methods. CONCLUSIONS: This new method has multiple advantages, including (1) no need for prior feature selection or manual optimization of hyperparameters; (2) flexibility to combine with and improve upon other methods, such as Seurat. Another novel contribution is the use of crafted experiments as part of the validation of our newly developed DIPD-based clustering pipeline. This new clustering pipeline is implemented in the R (CRAN) package scpoisson.


Assuntos
RNA , Análise de Célula Única , Análise de Sequência de RNA/métodos , Distribuição de Poisson , Análise de Célula Única/métodos , Análise por Conglomerados , RNA/genética , Perfilação da Expressão Gênica/métodos
6.
Front Genet ; 14: 1093326, 2023.
Artigo em Inglês | MEDLINE | ID: mdl-37007972

RESUMO

Advanced genomic and molecular profiling technologies accelerated the enlightenment of the regulatory mechanisms behind cancer development and progression, and the targeted therapies in patients. Along this line, intense studies with immense amounts of biological information have boosted the discovery of molecular biomarkers. Cancer is one of the leading causes of death around the world in recent years. Elucidation of genomic and epigenetic factors in Breast Cancer (BRCA) can provide a roadmap to uncover the disease mechanisms. Accordingly, unraveling the possible systematic connections between-omics data types and their contribution to BRCA tumor progression is crucial. In this study, we have developed a novel machine learning (ML) based integrative approach for multi-omics data analysis. This integrative approach combines information from gene expression (mRNA), microRNA (miRNA) and methylation data. Due to the complexity of cancer, this integrated data is expected to improve the prediction, diagnosis and treatment of disease through patterns only available from the 3-way interactions between these 3-omics datasets. In addition, the proposed method bridges the interpretation gap between the disease mechanisms that drive onset and progression. Our fundamental contribution is the 3 Multi-omics integrative tool (3Mint). This tool aims to perform grouping and scoring of groups using biological knowledge. Another major goal is improved gene selection via detection of novel groups of cross-omics biomarkers. Performance of 3Mint is assessed using different metrics. Our computational performance evaluations showed that the 3Mint classifies the BRCA molecular subtypes with lower number of genes when compared to the miRcorrNet tool which uses miRNA and mRNA gene expression profiles in terms of similar performance metrics (95% Accuracy). The incorporation of methylation data in 3Mint yields a much more focused analysis. The 3Mint tool and all other supplementary files are available at https://github.com/malikyousef/3Mint/.

7.
Osteoarthr Cartil Open ; 5(1): 100334, 2023 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-36817090

RESUMO

Objective: To employ novel methodologies to identify phenotypes in knee OA based on variation among three baseline data blocks: 1) femoral cartilage thickness, 2) tibial cartilage thickness, and 3) participant characteristics and clinical features. Methods: Baseline data were from 3321 Osteoarthritis Initiative (OAI) participants with available cartilage thickness maps (6265 knees) and 77 clinical features. Cartilage maps were obtained from 3D DESS MR images using a deep-learning based segmentation approach and an atlas-based analysis developed by our group. Angle-based Joint and Individual Variation Explained (AJIVE) was used to capture and quantify variation, both shared among multiple data blocks and individual to each block, and to determine statistical significance. Results: Three major modes of variation were shared across the three data blocks. Mode 1 reflected overall thicker cartilage among men, those with higher education, and greater knee forces; Mode 2 showed associations between worsening Kellgren-Lawrence Grade, medial cartilage thinning, and worsening symptoms; and Mode 3 contrasted lateral and medial-predominant cartilage loss associated with BMI and malalignment. Each data block also demonstrated individual, independent modes of variation consistent with the known discordance between symptoms and structure in knee OA and reflecting the importance of features such as physical function, symptoms, and comorbid conditions independent of structural damage. Conclusions: This exploratory analysis, combining the rich OAI dataset with novel methods for determining and visualizing cartilage thickness, reinforces known associations in knee OA while providing insights into the potential for data integration in knee OA phenotyping.

8.
Commun Biol ; 6(1): 179, 2023 02 16.
Artigo em Inglês | MEDLINE | ID: mdl-36797360

RESUMO

Model systems are an essential resource in cancer research. They simulate effects that we can infer into humans, but come at a risk of inaccurately representing human biology. This inaccuracy can lead to inconclusive experiments or misleading results, urging the need for an improved process for translating model system findings into human-relevant data. We present a process for applying joint dimension reduction (jDR) to horizontally integrate gene expression data across model systems and human tumor cohorts. We then use this approach to combine human TCGA gene expression data with data from human cancer cell lines and mouse model tumors. By identifying the aspects of genomic variation joint-acting across cohorts, we demonstrate how predictive modeling and clinical biomarkers from model systems can be improved.


Assuntos
Neoplasias , Transcriptoma , Animais , Camundongos , Humanos , Neoplasias/genética , Neoplasias/patologia , Perfilação da Expressão Gênica , Biomarcadores
9.
Res Sq ; 2023 Feb 06.
Artigo em Inglês | MEDLINE | ID: mdl-36798423

RESUMO

Background: Modeling of single cell RNA-sequencing (scRNA-seq) data remains challenging due to a high percentage of zeros and data heterogeneity, so improved modeling has strong potential to benefit many downstream data analyses. The existing zero-inflated or over-dispersed models are based on aggregations at either the gene or the cell level. However, they typically lose accuracy due to a too crude aggregation at those two levels. Results: We avoid the crude approximations entailed by such aggregation through proposing an Independent Poisson Distribution (IPD) particularly at each individual entry in the scRNA-seq data matrix. This approach naturally and intuitively models the large number of zeros as matrix entries with a very small Poisson parameter. The critical challenge of cell clustering is approached via a novel data representation as Departures from a simple homogeneous IPD (DIPD) to capture the per-gene-per-cell intrinsic heterogeneity generated by cell clusters. Our experiments using real data and crafted experiments show that using DIPD as a data representation for scRNA-seq data can uncover novel cell subtypes that are missed or can only be found by careful parameter tuning using conventional methods. Conclusions: This new method has multiple advantages, including (1) no needfor prior feature selection or manual optimization of hyperparameters; (2) flexibility to combine with and improve upon other methods, such as Seurat. Another novel contribution is the use of crafted experiments as part of the validation of our newly developed DIPD-based clustering pipeline. This new clustering pipeline is implemented in the R (CRAN) package scpoisson .

10.
PLoS One ; 17(5): e0266964, 2022.
Artigo em Inglês | MEDLINE | ID: mdl-35609053

RESUMO

OBJECTIVE: To apply biclustering, a methodology originally developed for analysis of gene expression data, to simultaneously cluster observations and clinical features to explore candidate phenotypes of knee osteoarthritis (KOA) for the first time. METHODS: Data from the baseline Osteoarthritis Initiative (OAI) visit were cleaned, transformed, and standardized as indicated (leaving 6461 knees with 86 features). Biclustering produced submatrices of the overall data matrix, representing similar observations across a subset of variables. Statistical validation was determined using the novel SigClust procedure. After identifying biclusters, relationships with key outcome measures were assessed, including progression of radiographic KOA, total knee arthroplasty, loss of joint space width, and worsening Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) scores, over 96 months of follow-up. RESULTS: The final analytic set included 6461 knees from 3330 individuals (mean age 61 years, mean body mass index 28 kg/m2, 57% women and 86% White). We identified 6 mutually exclusive biclusters characterized by different feature profiles at baseline, particularly related to symptoms and function. Biclusters represented overall better (#1), similar (#2, 3, 6), and poorer (#4, 5) prognosis compared to the overall cohort of knees, respectively. In general, knees in biclusters #4 and 5 had more structural progression (based on Kellgren-Lawrence grade, total knee arthroplasty, and loss of joint space width) but tended to have an improvement in WOMAC pain scores over time. In contrast, knees in bicluster #1 had less incident and progressive KOA, fewer total knee arthroplasties, less loss of joint space width, and stable pain scores compared with the overall cohort. SIGNIFICANCE: We identified six biclusters within the baseline OAI dataset which have varying relationships with key outcomes in KOA. Such biclusters represent potential phenotypes within the larger cohort and may suggest subgroups at greater or lesser risk of progression over time.


Assuntos
Articulação do Joelho , Osteoartrite do Joelho , Progressão da Doença , Feminino , Humanos , Articulação do Joelho/diagnóstico por imagem , Articulação do Joelho/cirurgia , Masculino , Osteoartrite do Joelho/genética , Osteoartrite do Joelho/cirurgia , Dor , Fenótipo
11.
Front Comput Sci ; 42022 Oct.
Artigo em Inglês | MEDLINE | ID: mdl-37692198

RESUMO

Objects and object complexes in 3D, as well as those in 2D, have many possible representations. Among them skeletal representations have special advantages and some limitations. For the special form of skeletal representation called "s-reps," these advantages include strong suitability for representing slabular object populations and statistical applications on these populations. Accomplishing these statistical applications is best if one recognizes that s-reps live on a curved shape space. Here we will lay out the definition of s-reps, their advantages and limitations, their mathematical properties, methods for fitting s-reps to single- and multi-object boundaries, methods for measuring the statistics of these object and multi-object representations, and examples of such applications involving statistics. While the basic theory, ideas, and programs for the methods are described in this paper and while many applications with evaluations have been produced, there remain many interesting open opportunities for research on comparisons to other shape representations, new areas of application and further methodological developments, many of which are explicitly discussed here.

12.
Genome Biol ; 22(1): 232, 2021 08 19.
Artigo em Inglês | MEDLINE | ID: mdl-34412669

RESUMO

Single-cell RNA sequencing (scRNA-seq) provides new opportunities to characterize cell populations, typically accomplished through some type of clustering analysis. Estimation of the optimal cluster number (K) is a crucial step but often ignored. Our approach improves most current scRNA-seq cluster methods by providing an objective estimation of the number of groups using a multi-resolution perspective. MultiK is a tool for objective selection of insightful Ks and achieves high robustness through a consensus clustering approach. We demonstrate that MultiK identifies reproducible groups in scRNA-seq data, thus providing an objective means to estimating the number of possible groups or cell-type populations present.


Assuntos
Análise de Sequência de RNA/métodos , Análise de Célula Única/métodos , Software , Algoritmos , Animais , Linhagem Celular , Análise por Conglomerados , Expressão Gênica , Genômica , Humanos , Glândulas Mamárias Animais , Camundongos , RNA-Seq , Fluxo de Trabalho
13.
Nat Commun ; 12(1): 286, 2021 01 12.
Artigo em Inglês | MEDLINE | ID: mdl-33436599

RESUMO

High-throughput sequencing protocols such as RNA-seq have made it possible to interrogate the sequence, structure and abundance of RNA transcripts at higher resolution than previous microarray and other molecular techniques. While many computational tools have been proposed for identifying mRNA variation through differential splicing/alternative exon usage, challenges in its analysis remain. Here, we propose a framework for unbiased and robust discovery of aberrant RNA transcript structures using short read sequencing data based on shape changes in an RNA-seq coverage profile. Shape changes in selecting sample outliers in RNA-seq, SCISSOR, is a series of procedures for transforming and normalizing base-level RNA sequencing coverage data in a transcript independent manner, followed by a statistical framework for its analysis ( https://github.com/hyochoi/SCISSOR ). The resulting high dimensional object is amenable to unsupervised screening of structural alterations across RNA-seq cohorts with nearly no assumption on the mutational mechanisms underlying abnormalities. This enables SCISSOR to independently recapture known variants such as splice site mutations in tumor suppressor genes as well as novel variants that are previously unrecognized or difficult to identify by any existing methods including recurrent alternate transcription start sites and recurrent complex deletions in 3' UTRs.


Assuntos
RNA Mensageiro/química , Análise de Sequência de RNA , Software , Ilhas de CpG/genética , Éxons/genética , Loci Gênicos , Genoma Humano , Humanos , Reprodutibilidade dos Testes , Proteína Supressora de Tumor p53/genética
14.
Ann Appl Stat ; 15(4): 1697-1722, 2021 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-35432688

RESUMO

The two main approaches in the study of breast cancer are histopathology (analyzing visual characteristics of tumors) and genomics. While both histopathology and genomics are fundamental to cancer research, the connections between these fields have been relatively superficial. We bridge this gap by investigating the Carolina Breast Cancer Study through the development of an integrative, exploratory analysis framework. Our analysis gives insights - some known, some novel - that are engaging to both pathologists and geneticists. Our analysis framework is based on Angle-based Joint and Individual Variation Explained (AJIVE) for statistical data integration and exploits Convolutional Neural Networks (CNNs) as a powerful, automatic method for image feature extraction. CNNs raise interpretability issues that we address by developing novel methods to explore visual modes of variation captured by statistical algorithms (e.g. PCA or AJIVE) applied to CNN features.

15.
Artigo em Inglês | MEDLINE | ID: mdl-35505894

RESUMO

Microfractures (cracks) are the third most common cause of tooth loss in industrialized countries. If they are not detected early, they continue to progress until the tooth is lost. Cone beam computed tomography (CBCT) has been used to detect microfractures, but has had very limited success. We propose an algorithm to detect cracked teeth that pairs high resolution (hr) CBCT scans with advanced image analysis and machine learning. First, microfractures were simulated in extracted human teeth (n=22). hr-CBCT and microCT scans of the fractured and control teeth (n=14) were obtained. Wavelet pyramid construction was used to generate a phase image of the Fourier transformed scan which were fed to a U-Net deep learning architecture that localizes the orientation and extent of the crack which yields slice-wise probability maps that indicate the presence of microfractures. We then examine the ratio of high-probability voxels to total tooth volume to determine the likelihood of cracks per tooth. In microCT and hr-CBCT scans, fractured teeth have higher numbers of such voxels compared to control teeth. The proposed analytical framework provides a novel way to quantify the structural breakdown of teeth, that was not possible before. Future work will expand our machine learning framework to 3D volumes, improve our feature extraction in hr-CBCT and clinically validate this model. Early detection of microfractures will lead to more appropriate treatment and longer tooth retention.

16.
R J ; 13(2): 266-272, 2021 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-35721233

RESUMO

High-dimensional low sample size (HDLSS) data sets frequently emerge in many biomedical applications. The direction-projection-permutation (DiProPerm) test is a two-sample hypothesis test for comparing two high-dimensional distributions. The DiProPerm test is exact, i.e., the type I error is guaranteed to be controlled at the nominal level for any sample size, and thus is applicable in the HDLSS setting. This paper discusses the key components of the DiProPerm test, introduces the diproperm R package, and demonstrates the package on a real-world data set.

17.
Artigo em Inglês | MEDLINE | ID: mdl-31156288

RESUMO

Temporomandibular Joint (TMJ) Osteoarthritis (OA) is associated with significant pain and disability. It is really hard to diagnose TMJ OA during early stages of the disease. Subchondral bone texture has been observed to change in the TMJ early during TMJ OA progression. We believe that raw probability-distribution matrices describing image texture encode important information that might aid diagnosing TMJ OA. In this paper we present novel statistical methods for High Dimensionality Low Sample Size Data (HDLSSD) to test the discriminatory power of probability-distribution matrices in computed from TMJ OA medical scans. Our results, and comparison with previous results obtained from the summary features obtained from them indicate that probability-distribution matrices are an important piece of information provided by texture analysis methods and should not be down sampled for analysis.

18.
Osteoarthritis Cartilage ; 27(7): 994-1001, 2019 07.
Artigo em Inglês | MEDLINE | ID: mdl-31002938

RESUMO

OBJECTIVE: Knee osteoarthritis (KOA) is a heterogeneous condition representing a variety of potentially distinct phenotypes. The purpose of this study was to apply innovative machine learning approaches to KOA phenotyping in order to define progression phenotypes that are potentially more responsive to interventions. DESIGN: We used publicly available data from the Foundation for the National Institutes of Health (FNIH) osteoarthritis (OA) Biomarkers Consortium, where radiographic (medial joint space narrowing of ≥0.7 mm), and pain progression (increase of ≥9 Western Ontario and McMaster Universities Osteoarthritis Index [WOMAC] points) were defined at 48 months, as four mutually exclusive outcome groups (none, both, pain only, radiographic only), along with an extensive set of covariates. We applied distance weighted discrimination (DWD), direction-projection-permutation (DiProPerm) testing, and clustering methods to focus on the contrast (z-scores) between those progressing by both criteria ("progressors") and those progressing by neither ("non-progressors"). RESULTS: Using all observations (597 individuals, 59% women, mean age 62 years and BMI 31 kg/m2) and all 73 baseline variables available in the dataset, there was a clear separation among progressors and non-progressors (z = 10.1). Higher z-scores were seen for the magnetic resonance imaging (MRI)-based variables than for demographic/clinical variables or biochemical markers. Baseline variables with the greatest contribution to non-progression at 48 months included WOMAC pain, lateral meniscal extrusion, and serum N-terminal pro-peptide of collagen IIA (PIIANP), while those contributing to progression included bone marrow lesions, osteophytes, medial meniscal extrusion, and urine C-terminal crosslinked telopeptide type II collagen (CTX-II). CONCLUSIONS: Using methods that provide a way to assess numerous variables of different types and scalings simultaneously in relation to an outcome of interest enabled a data-driven approach that identified key variables associated with a progression phenotype.


Assuntos
Variação Biológica da População/genética , Cartilagem Articular/patologia , Aprendizado de Máquina , Osteoartrite do Joelho/genética , Osteoartrite do Joelho/patologia , Idoso , Biomarcadores/sangue , Cartilagem Articular/diagnóstico por imagem , Cartilagem Articular/fisiopatologia , Colágeno Tipo II/sangue , Congressos como Assunto , Bases de Dados Factuais , Progressão da Doença , Feminino , Humanos , Masculino , Meniscos Tibiais/patologia , Pessoa de Meia-Idade , National Institutes of Health (U.S.) , Osteoartrite do Joelho/diagnóstico por imagem , Medição da Dor , Índice de Gravidade de Doença , Estados Unidos
19.
Artigo em Inglês | MEDLINE | ID: mdl-31031512

RESUMO

Computed tomography (CT) images can potentially provide insights into bone structure for diagnosis of disorders and diseases. However, evaluation of trabecular bone structure and whole bone shape is often qualitative or semi-quantitative. This limits inter-study comparisons and the ability to detect subtle bone quality variations during early disease onset or in response to new treatments. In this work, we enable quantitative characterization of bone diseases through bone morphometry, texture analysis, and shape analysis methods. The potential of our analysis methods to identify the impact of hemophilia is validated in a mouse femur wound model. In our results, shape localizes and characterizes the formation of spurious bone, and our texture and bone morphometry analysis results provide extra information about the composition of that bone. Some of our one-dimensional (1D) textural features were able to significantly differentiate our injured femurs from our healthy femurs, even with this small sample size demonstrating the potential of the proposed analysis framework. While trabecular bone morphometrics have been a pillar in 3D microCT bone research for decades, the proposed analysis framework augments how we define and understand phenotypical presentation of bone disease. The contributed open source software is exposed to the medical image analysis community through 3D Slicer extensions to ensure both robustness and reproducibility.

20.
Aust N Z J Stat ; 60(1): 4-19, 2018 Mar.
Artigo em Inglês | MEDLINE | ID: mdl-30197552

RESUMO

Peter Hall's work illuminated many aspects of statistical thought, some of which are very well known including the bootstrap and smoothing. However, he also explored many other lesser known aspects of mathematical statistics. This is a survey of one of those areas, initiated by a seminal paper in 2005, on high dimension low sample size asymptotics. An interesting characteristic of that first paper, and of many of the following papers, is that they contain deep and insightful concepts which are frequently surprising and counter-intuitive, yet have mathematical underpinnings which tend to be direct and not difficult to prove.

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