Intrinsically weighted means and non-ergodic marked point processes

Malinowski, Alexander; Schlather, Martin; Zhang, Zhengjun

doi:10.1007/s10463-014-0485-6

Cited by 10 publications

(14 citation statements)

References 18 publications

(48 reference statements)

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“…Max-linear models are not only interpretable but also outperform existing methods. In the literature, theoretical statistical and probabilistic foundations related to the competing risk factor models have been established (Cui et al, 2020;Cui and Zhang, 2018;Malinowski et al, 2016;Xu, 2019;Cao and Zhang, 2020;Zhang, 2005Zhang, , 2020. The difference between the max-linear logistic regression and the classical logistic regression is that the original linear combination of predictors is replaced by the maximum of several linear combinations of predictors, called competing factors or competing-risk factors.…”

Section: Statistical Methodologymentioning

confidence: 99%

“…There is one crucial factor, competing (risk) factors, that has not been considered in many existing statistical models, i.e., the existing classifiers do not distinguish the causes and the subtypes of the disease. In scientific studies, competing factors exist in many scenarios (Malinowski et al, 2016). The cause/regulation of each subtype of the disease can be different, i.e., each subtype of the disease can result from one factor or multiple factors.…”

Section: Statistical Methodologymentioning

confidence: 99%

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Five Critical Genes Related to Seven COVID-19 Subtypes: A Data Science Discovery

Zhang¹

2021

Journal of Data Science

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129

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Since the first confirmed case of COVID-19 was identified in December 2019, the total COVID-19 patients are up to 80,675,745, and the number of deaths is 1,764,185 as of December 27, 2020. The problem is that researchers are still learning about it, and new variants of SARS-CoV-2 are not stopping. For medical treatment, essential and informative genes can lead to accurate tests of whether an individual has contracted COVID-19 and help develop highly efficient vaccines, antiviral drugs, and treatments. As a result, identifying critical genes related to COVID-19 has been an urgent task for medical researchers. We conducted a competing risk analysis using the max-linear logistic regression model to analyze 126 blood samples from COVID-19-positive and COVID-19-negative patients. Our research led to a competing COVID-19 risk classifier derived from 19,472 genes and their differential expression values. The final classifier model only involves five critical genes, ABCB6, KIAA1614, MND1, SMG1, RIPK3, which led to 100% sensitivity and 100% specificity of the 126 samples. Given their 100% accuracy in predicting COVID-19 positive or negative status, these five genes can be critical in developing proper, focused, and accurate COVID-19 testing procedures, guiding the second-generation vaccine development, studying antiviral drugs and treatments. It is expected that these five genes can motivate numerous new COVID-19 researches.

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Section: Statistical Methodologymentioning

confidence: 99%

Section: Statistical Methodologymentioning

confidence: 99%

Five Critical Genes Related to Seven COVID-19 Subtypes: A Data Science Discovery

Zhang¹

2021

Journal of Data Science

Self Cite

129

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“…The most recently developed max-linear competing factor models, 18 max-linear regression models, 19 and max-linear logistic models 20 , 21 have proven to be powerful models and analysis approaches to study heteroscedastic populations and competing risks and resources. The theoretical foundations of these models have been established in Cui and Zhang, 18 Cui et al, 19 Malinowski et al, 22 Xu, 20 and Zhang. 21 , 23 The difference between the max-linear competing models and the classical statistical models is that the original linear combination of predictors is replaced by the maximum of a set of linear combinations of predictors, called competing factors or competing-risk factors.…”

Section: Statistical Methodologymentioning

confidence: 99%

Lift the Veil of Breast Cancers Using 4 or Fewer Critical Genes

Zhang

2022

Cancer Inform

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Known genes in the breast cancer study literature could not be confirmed whether they are vital to breast cancer formations due to lack of convincing accuracy, although they may be biologically directly related to breast cancer based on present biological knowledge. It is hoped vital genes can be identified with the highest possible accuracy, for example, 100% accuracy and convincing causal patterns beyond what has been known in breast cancer. One hope is that finding gene-gene interaction signatures and functional effects may solve the puzzle. This research uses a recently developed competing linear factor analysis method in differentially expressed gene detection to advance the study of breast cancer formation. Surprisingly, 3 genes are detected to be differentially expressed in TNBC and non-TNBC (Her2, Luminal A, Luminal B) samples with 100% sensitivity and 100% specificity in 1 study of triple-negative breast cancers (TNBC, with 54 675 genes and 265 samples). These 3 genes show a clear signature pattern of how TNBC patients can be grouped. For another TNBC study (with 54 673 genes and 66 samples), 4 genes bring the same accuracy of 100% sensitivity and 100% specificity. Four genes are found to have the same accuracy of 100% sensitivity and 100% specificity in 1 breast cancer study (with 54 675 genes and 121 samples), and the same 4 genes bring an accuracy of 100% sensitivity and 96.5% specificity in the fourth breast cancer study (with 60 483 genes and 1217 samples). These results show the 4-gene-based classifiers are robust and accurate. The detected genes naturally classify patients into subtypes, for example, 7 subtypes. These findings demonstrate the clearest gene-gene interaction patterns and functional effects with the smallest numbers of genes and the highest accuracy compared with findings reported in the literature. The 4 genes are considered to be essential for breast cancer studies and practice. They can provide focused, targeted researches and precision medicine for each subtype of breast cancer. New breast cancer disease types may be detected using the classified subtypes, and hence new effective therapies can be developed.

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“…There is one crucial factor, competing (risk) factors, that has not been considered in many existing statistical models, i.e., the existing classifiers do not distinguish the causes and the subtypes of the disease. In scientific studies, competing factors exist in many scenarios 21 . The cause/regulation of each subtype of the disease can be different, i.e., each subtype of the disease can result from one factor or multiple factors.…”

Section: The Algorithmmentioning

confidence: 99%

Functional Effects of Four or Fewer Critical Genes Linked to Lung Cancers and New Subtypes Detected by A New Machine Learning Classifier

Zhang¹

2021

Preprint

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Finding genes biologically directly or indirectly related to lung cancer has been drawing much attention, and many genes directly related to lung cancer have been reported. However, it has not been confirmed whether those published 'key' genes are truly critical to lung cancer formation, i.e., they may be with very limited useful information. As a result, finding essential genes remains a challenging lung cancer research problem. Using a recently developed competing linear factor analysis method in differentially expressed gene detection, we advance the study of lung cancer critical genes detection to a uniformly informative level. A set of common four genes and their functional effects are detected to be differentially expressed in tumor and non-tumor samples with 100% sensitivity and 100% specificity in one study of lung adenocarcinoma (LUAD) and one study of squamous cell lung cancers (LUSC) (two North American cohorts with 20429 genes, 576 and 552 samples respectively). Two additional analyses also gain accuracy of 97.8% sensitivity and 100% specificity in one study of non-small cell lung carcinomas (NSCLC, a European cohort with 20356 genes and 156 samples), and an accuracy of 100% sensitivity and 95% specificity (1 out of 20 non-tumor samples) in one study of ALK-positive and EGFR/KRAS/ALK-negative lung adenocarcinomas (LUAD, a Japanese cohort with 20356 genes and 224 samples). There are some common genes, but different functional effects, within each set of four genes among two North American cohorts and a European cohort and among North American cohorts and the Japanese cohort. These results show the four-gene-based classifiers are robust with different types of lung cancers and different race cohorts and accurate. The functional effects of four genes disclose significantly other mechanisms (mysteries) between LUAD and LUSC. These sets of four genes and their functional effects are considered to be essential for lung cancer studies and practice. These genes' functional effects naturally classify patients into different groups (more than seven subtypes). Subtype information is useful for personalized therapies. The new findings can motivate new lung cancer research in more focused and targeted directions to save lives, protect people, and reduce enormous economic costs in research and lung cancer treatments.

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Intrinsically weighted means and non-ergodic marked point processes

Cited by 10 publications

References 18 publications

Five Critical Genes Related to Seven COVID-19 Subtypes: A Data Science Discovery

Five Critical Genes Related to Seven COVID-19 Subtypes: A Data Science Discovery

Lift the Veil of Breast Cancers Using 4 or Fewer Critical Genes

Functional Effects of Four or Fewer Critical Genes Linked to Lung Cancers and New Subtypes Detected by A New Machine Learning Classifier

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