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Hepatocellular carcinoma (HCC) is one of the most fatal cancers in the world. There is an urgent need to understand the molecular background of HCC to facilitate the identification of biomarkers and discover effective therapeutic targets. Published transcriptomic studies have reported a large number of genes that are individually significant for HCC. However, reliable biomarkers remain to be determined. In this study, built on max-linear competing risk factor models, we developed a machine learning analytical framework to analyze transcriptomic data to identify the most miniature set of differentially expressed genes (DEGs). By analyzing 9 public whole-transcriptome datasets (containing 1184 HCC samples and 672 nontumor controls), we identified 5 critical differentially expressed genes (DEGs) (ie, CCDC107, CXCL12, GIGYF1, GMNN, and IFFO1) between HCC and control samples. The classifiers built on these 5 DEGs reached nearly perfect performance in identification of HCC. The performance of the 5 DEGs was further validated in a US Caucasian cohort that we collected (containing 17 HCC with paired nontumor tissue). The conceptual advance of our work lies in modeling gene-gene interactions and correcting batch effect in the analytic framework. The classifiers built on the 5 DEGs demonstrated clear signature patterns for HCC. The results are interpretable, robust, and reproducible across diverse cohorts/populations with various disease etiologies, indicating the 5 DEGs are intrinsic variables that can describe the overall features of HCC at the genomic level. The analytical framework applied in this study may pave a new way for improving transcriptome profiling analysis of human cancers. 

Hoping to find genomic clues linked to COVID-19 and end the pandemic has driven scientists’ tremendous efforts to try all kinds of research. Signs of progress have been achieved but are still limited. This paper intends to prove the existence of at least three genomic signature patterns and at least seven subtypes of COVID-19 driven by five critical genes (the smallest subset of genes) using three blood-sampled datasets. These signatures and subtypes provide crucial genomic information in COVID-19 diagnosis (including ICU patients), research focuses, and treatment methods. Unlike existing approaches focused on gene fold-changes and pathways, gene-gene nonlinear and competing interactions are the driving forces in finding the signature patterns and subtypes. Furthermore, the method leads to high accuracy with hospitalized patients, showing biological and mathematical equivalences between COVID-19 status and the signature patterns and a methodological advantage over other methods that cannot lead to high accuracy. As a result, as new biomarkers, the new findings and genomic clues can be much more informative than other findings for interpreting biological mechanisms, developing the second (third) generation of vaccines, antiviral drugs, and treatment methods, and eventually bringing new hopes of an end to the pandemic. 

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. 

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. 

Logistic regression is widely used in the analysis of medical data with binary outcomes to study treatment effects through (absolute) treatment effect parameters in the models. However, the indicative parameters of relative treatment effects are not introduced in logistic regression models, which can be a severe problem in efficiently modeling treatment effects and lead to the wrong conclusions with regard to treatment effects. This paper introduces a new enhanced logistic regression model that offers a new way of studying treatment effects by measuring the relative changes in the treatment effects and also incorporates the way in which logistic regression models the treatment effects. The new model, called the Absolute and Relative Treatment Effects (AbRelaTEs) model, is viewed as a generalization of logistic regression and an enhanced model with increased flexibility, interpretability, and applicability in real data applications than the logistic regression. The AbRelaTEs model is capable of modeling significant treatment effects via an absolute or relative or both ways. The new model can be easily implemented using statistical software, with the logistic regression model being treated as a special case. As a result, the classical logistic regression models can be replaced by the AbRelaTEs model to gain greater applicability and have a new benchmark model for more efficiently studying treatment effects in clinical trials, economic developments, and many applied areas. Moreover, the estimators of the coefficients are consistent and asymptotically normal under regularity conditions. In both simulation and real data applications, the model provides both significant and more meaningful results. 

Tail risk is an important financial issue today, but directly hedging tail risks with an ad hoc option is still an unresolved problem since it is not easy to specify a suitable and asymmetric pricing kernel. By defining two ad hoc underlying “assets”, this paper designs two novel tail risk options (TROs) for hedging and evaluating short-term tail risks. Under the Fréchet distribution assumption for maximum losses, the closed-form TRO pricing formulas are obtained. Simulation examples demonstrate the accuracy of the pricing formulas. Furthermore, they show that, no matter whether at scale level (symmetric “normal” risk, with greater volatility) or shape level (asymmetric tail risk, with a smaller value in tail index), the greater the risk, the more expensive the TRO calls, and the cheaper the TRO puts. Using calibration, one can obtain the TRO-implied volatility and the TRO-implied tail index. The former is analogous to the Black-Scholes implied volatility, which can measure the overall symmetric market volatility. The latter measures the asymmetry in underlying losses, mirrors market sentiment, and provides financial crisis warnings. Regarding the newly proposed TRO and its implied tail index, economic implications can be offered to investors, portfolio managers, and policy-makers.