Cancer is a highly heterogeneous disease underpinned by complex molecular alterations. Accurate subtyping is critical for guiding personalized treatment and improving clinical outcomes. However, multi-omics data are high-dimensional, noisy, and heterogeneous across platforms, posing major challenges for reliable subtyping. To address this, dimensionality reduction is necessary to capture underlying molecular patterns in a low-dimensional space, facilitating both computational efficiency and biological interpretation. We present Consensus subtyping method with Ensemble Dimensionality Reduction for multi-omics data integration (CEDR), a consensus subtyping framework that integrates complementary linear and nonlinear dimensionality reduction methods with robust clustering and probabilistic ensemble modeling. Different from existing dimensionality reduction techniques, our framework adopts an ensemble learning framework that integrates multiple dimensionality reduction techniques with robust clustering to achieve reliable consensus cancer subtyping. We apply Optimally Tuned Robust Improper Maximum Likelihood Estimator to the concatenated low-dimensional matrix for robust subtyping, and ensemble the result with the Mixture Model for Clustering Ensembles to identify stable subtypes. Across extensive simulations, CEDR consistently outperformed conventional dimensionality reduction-based clustering, the Cluster Of Clusters Analysis (COCA) ensemble strategy, and state-of-the-art multi-omics integration algorithms (SNF and CIMLR) in both accuracy and robustness. Application to clear cell renal cell carcinoma and lower-grade glioma revealed biologically interpretable subtypes characterized by distinctive survival outcomes, pathway activities, and immune infiltration patterns. These findings demonstrate that CEDR provides a powerful and reliable strategy for multi-omics data integration and cancer subtyping, with strong potential for broader applications in high-dimensional multimodal data analysis.

Cancer is a highly heterogeneous disease characterized by complex molecular changes. Subtypes identified through multi-omics data hold significant promise for improving prognosis and facilitating personalized precision treatment. Recent multi-omics integration methods have mostly focused on capturing complementary information from different data types, often overlooking potential interactions between omics data. Here we develop a novel method named interactive multi-kernel learning (iMKL), which incorporates omics-omics interactions alongside heterogeneous data types under the unsupervised multi-kernel learning framework, to improve subtype identification. Using the sample-similarity kernel for each dataset, we propose a joint Hadamard product strategy to capture higher-order interactive effects from different omics data types. We applied iMKL to two renal cell carcinoma (RCC) datasets-clear renal cell carcinoma (ccRCC) and type II papillary renal cell carcinoma (type II pRCC)-both including miRNA expression, mRNA expression, and DNA methylation data. Stability analysis through random sampling of patients or features demonstrated that iMKL exhibits strong robustness and accuracy in identifying patient subtypes. The identified subtypes revealed dramatic differences in patient survival, with both ccRCC and type II pRCC classified into three distinct subtypes. The findings in the real application highlight potential biomarkers associated with adverse patient outcomes and demonstrate substantial advancement in cancer subtype identification. The iMKL method effectively identifies tumor molecular subtypes that are strongly associated with clinical features and survival rates, providing valuable insights for accurate cancer subtyping, clinical decision-making, and the realization of personalized treatment strategies.

Transfer learning aims to integrate useful information from multi-source datasets to improve the learning performance of target data. This can be effectively applied in genomics when we learn the gene associations in a target tissue, and data from other tissues can be integrated. However, heavy-tail distribution and outliers are common in genomics data, which poses challenges to the effectiveness of current transfer learning approaches. In this paper, we study the transfer learning problem under high-dimensional linear models with t-distributed error (Trans-PtLR), which aims to improve the estimation and prediction of target data by borrowing information from useful source data and offering robustness to accommodate complex data with heavy tails and outliers. In the oracle case with known transferable source datasets, a transfer learning algorithm based on penalized maximum likelihood and expectation-maximization algorithm is established. To avoid including non-informative sources, we propose to select the transferable sources based on cross-validation. Extensive simulation experiments as well as an application demonstrate that Trans-PtLR demonstrates robustness and better performance of estimation and prediction when heavy-tail and outliers exist compared to transfer learning for linear regression model with normal error distribution. Data integration, Variable selection, T distribution, Expectation maximization algorithm, Genotype-Tissue Expression, Cross validation.

Renal cell carcinoma (RCC) ranks among the most prevalent cancers worldwide, with both incidence and mortality rates increasing annually. The heterogeneity among RCC patients presents considerable challenges for developing universally effective treatment strategies, emphasizing the necessity of in-depth research into RCC's molecular mechanisms, understanding the variations among RCC patients and further identifying distinct molecular subtypes for precise treatment. We proposed a metagene-based similarity network fusion (Meta-SNF) method for RCC subtype identification with multi-omics data, using a non-negative matrix factorization technique to capture alternative structures inherent in the dataset as metagenes. These latent metagenes were then integrated to construct a fused network under the Similarity Network Fusion (SNF) framework for more precise subtyping. We conducted simulation studies and analyzed real-world data from two RCC datasets, namely kidney renal clear cell carcinoma (KIRC) and kidney renal papillary cell carcinoma (KIRP) to demonstrate the utility of Meta-SNF. The simulation studies indicated that Meta-SNF achieved higher accuracy in subtype identification compared with the original SNF and other state-of-the-art methods. In analyses of real data, Meta-SNF produced more distinct and well-separated clusters, classifying both KIRC and KIRP into four subtypes with significant differences in survival outcomes. Subsequently, we performed comprehensive bioinformatics analyses focused on subtypes with poor prognoses in KIRC and KIRP and identified several potential biomarkers. Meta-SNF offers a novel strategy for subtype identification using multi-omics data, and its application to RCC datasets has yielded diverse biological insights which are highly valuable for informing clinical decision-making processes in the treatment of RCC.

Recently, there has been a growing interest in variable selection for causal inference within the context of high-dimensional data. However, when the outcome exhibits a skewed distribution, ensuring the accuracy of variable selection and causal effect estimation might be challenging. Here, we introduce the generalized median adaptive lasso (GMAL) for covariate selection to achieve an accurate estimation of causal effect even when the outcome follows skewed distributions. A distinctive feature of our proposed method is that we utilize a linear median regression model for constructing penalty weights, thereby maintaining the accuracy of variable selection and causal effect estimation even when the outcome presents extremely skewed distributions. Simulation results showed that our proposed method performs comparably to existing methods in variable selection when the outcome follows a symmetric distribution. Besides, the proposed method exhibited obvious superiority over the existing methods when the outcome follows a skewed distribution. Meanwhile, our proposed method consistently outperformed the existing methods in causal estimation, as indicated by smaller root-mean-square error. We also utilized the GMAL method on a deoxyribonucleic acid methylation dataset from the Alzheimer's disease (AD) neuroimaging initiative database to investigate the association between cerebrospinal fluid tau protein levels and the severity of AD.

In recent work, researchers have paid considerable attention to the estimation of causal effects in observational studies with a large number of covariates, which makes the unconfoundedness assumption plausible. In this paper, we review propensity score (PS) methods developed in high-dimensional settings and broadly group them into model-based methods that extend models for prediction to causal inference and balance-based methods that combine covariate balancing constraints. We conducted systematic simulation experiments to evaluate these two types of methods, and studied whether the use of balancing constraints further improved estimation performance. Our comparison methods were post-double-selection (PDS), double-index PS (DiPS), outcome-adaptive LASSO (OAL), group LASSO and doubly robust estimation (GLiDeR), high-dimensional covariate balancing PS (hdCBPS), regularized calibrated estimators (RCAL) and approximate residual balancing method (balanceHD). For the four model-based methods, simulation studies showed that GLiDeR was the most stable approach, with high estimation accuracy and precision, followed by PDS, OAL and DiPS. For balance-based methods, hdCBPS performed similarly to GLiDeR in terms of accuracy, and outperformed balanceHD and RCAL. These findings imply that PS methods do not benefit appreciably from covariate balancing constraints in high-dimensional settings. In conclusion, we recommend the preferential use of GLiDeR and hdCBPS approaches for estimating causal effects in high-dimensional settings; however, further studies on the construction of valid confidence intervals are required.

Heritability, the proportion of phenotypic variance explained by genome-wide single nucleotide polymorphisms (SNPs) in unrelated individuals, is an important measure of the genetic contribution to human diseases and plays a critical role in studying the genetic architecture of human diseases. Linear mixed model (LMM) has been widely used for SNP heritability estimation, where variance component parameters are commonly estimated by using a restricted maximum likelihood (REML) method. REML is an iterative optimization algorithm, which is computationally intensive when applied to large-scale datasets (e.g. UK Biobank). To facilitate the heritability analysis of large-scale genetic datasets, we develop a fast approach, minimum norm quadratic unbiased estimator (MINQUE) with batch training, to estimate variance components from LMM (LMM.MNQ.BCH). In LMM.MNQ.BCH, the parameters are estimated by MINQUE, which has a closed-form solution for fast computation and has no convergence issue. Batch training has also been adopted in LMM.MNQ.BCH to accelerate the computation for large-scale genetic datasets. Through simulations and real data analysis, we demonstrate that LMM.MNQ.BCH is much faster than two existing approaches, GCTA and BOLT-REML.

Over the past decade, statistical methods have been developed to estimate single nucleotide polymorphism (SNP) heritability, which measures the proportion of phenotypic variance explained by all measured SNPs in the data. Estimates of SNP heritability measure the degree to which the available genetic variants influence phenotypes and improve our understanding of the genetic architecture of complex phenotypes. In this article, we review the recently developed and commonly used SNP heritability estimation methods for continuous and binary phenotypes from the perspective of model assumptions and parameter optimization. We primarily focus on their capacity to handle multiple phenotypes and longitudinal measurements, their ability for SNP heritability partition and their use of individual-level data versus summary statistics. State-of-the-art statistical methods that are scalable to the UK Biobank dataset are also elucidated in detail.

Building an accurate disease risk prediction model is an essential step in the modern quest for precision medicine. While high-dimensional genomic data provides valuable data resources for the investigations of disease risk, their huge amount of noise and complex relationships between predictors and outcomes have brought tremendous analytical challenges. Deep learning model is the state-of-the-art methods for many prediction tasks, and it is a promising framework for the analysis of genomic data. However, deep learning models generally suffer from the curse of dimensionality and the lack of biological interpretability, both of which have greatly limited their applications. In this work, we have developed a deep neural network (DNN) based prediction modeling framework. We first proposed a group-wise feature importance score for feature selection, where genes harboring genetic variants with both linear and non-linear effects are efficiently detected. We then designed an explainable transfer-learning based DNN method, which can directly incorporate information from feature selection and accurately capture complex predictive effects. The proposed DNN-framework is biologically interpretable, as it is built based on the selected predictive genes. It is also computationally efficient and can be applied to genome-wide data. Through extensive simulations and real data analyses, we have demonstrated that our proposed method can not only efficiently detect predictive features, but also accurately predict disease risk, as compared to many existing methods.

Propensity score (PS) methods are popular when estimating causal effects in non-randomized studies. Drawing causal conclusion relies on the unconfoundedness assumption. This assumption is untestable and is considered more plausible if a large number of pre-treatment covariates are included in the analysis. However, previous studies have shown that including unnecessary covariates into PS models can lead to bias and efficiency loss. With the ever-increasing amounts of available data, such as the omics data, there is often little prior knowledge of the exact set of important covariates. Therefore, variable selection for causal inference in high-dimensional settings has received considerable attention in recent years. However, recent studies have focused mainly on binary treatments. In this study, we considered continuous treatments and proposed the generalized outcome-adaptive LASSO (GOAL) to select covariates that can provide an unbiased and statistically efficient estimation. Simulation studies showed that when the outcome model was linear, the GOAL selected almost all true confounders and predictors of outcome and excluded other covariates. The accuracy and precision of the estimates were close to ideal. Furthermore, the GOAL is robust to model misspecification. We applied the GOAL to seven DNA methylation datasets from the Gene Expression Omnibus database, which covered four brain regions, to estimate the causal effects of epigenetic aging acceleration on the incidence of Alzheimer's disease.

Genes do not function independently; rather, they interact with each other to fulfill their joint tasks. Identification of gene-gene interactions has been critically important in elucidating the molecular mechanisms responsible for the variation of a phenotype. Regression models are commonly used to model the interaction between two genes with a linear product term. The interaction effect of two genes can be linear or nonlinear, depending on the true nature of the data. When nonlinear interactions exist, the linear interaction model may not be able to detect such interactions; hence, it suffers from substantial power loss. While the true interaction mechanism (linear or nonlinear) is generally unknown in practice, it is critical to develop statistical methods that can be flexible to capture the underlying interaction mechanism without assuming a specific model assumption. In this study, we develop a mixed kernel function which combines both linear and Gaussian kernels with different weights to capture the linear or nonlinear interaction of two genes. Instead of optimizing the weight function, we propose a grid search strategy and use a Cauchy transformation of the P-values obtained under different weights to aggregate the P-values. We further extend the two-gene interaction model to a high-dimensional setup using a de-biased LASSO algorithm. Extensive simulation studies are conducted to verify the performance of the proposed method. Application to two case studies further demonstrates the utility of the model. Our method provides a flexible and computationally efficient tool for disentangling complex gene-gene interactions associated with complex traits.

High-throughput omics data are generated almost with no limit nowadays. It becomes increasingly important to integrate different omics data types to disentangle the molecular machinery of complex diseases with the hope for better disease prevention and treatment. Since the relationship among different omics data features are typically unknown, a supervised learning model assuming a particular distribution with a specific structure will not serve the purpose to capture the underlying complex relationship between multiple features and a disease phenotype. In this work, we briefly reviewed methods for kernel fusion (KF) based on support vector machine and kernel partial least squares (KPLS) algorithms. We then proposed a fused KPLS (fKPLS) model for disease classification and prediction with multilevel omics data. The fused kernel can deal with effect heterogeneity in which different omic data types may have different effect contribution to the trait of interest, with the purpose to improve the prediction performance. We proposed to optimize the kernel parameters and kernel weights with the genetic algorithm (GA). The proposed GA-fKPLS model can substantially improve disease classification performance by integrating multiple omics data types, demonstrated via extensive simulations and real data analysis. With properly defined fitness functions during GA optimization, the proposed KF method can be extended to other kernel-based analyses such as in kernel association analysis with common or rare variants.

BACKGROUND: Previous studies have reported that labeling errors are not uncommon in omics data. Potential outliers may severely undermine the correct classification of patients and the identification of reliable biomarkers for a particular disease. Three methods have been proposed to address the problem: sparse label-noise-robust logistic regression (Rlogreg), robust elastic net based on the least trimmed square (enetLTS), and Ensemble. Ensemble is an ensembled classification based on distinct feature selection and modeling strategies. The accuracy of biomarker selection and outlier detection of these methods needs to be evaluated and compared so that the appropriate method can be chosen. RESULTS: The accuracy of variable selection, outlier identification, and prediction of three methods (Ensemble, enetLTS, Rlogreg) were compared for simulated and an RNA-seq dataset. On simulated datasets, Ensemble had the highest variable selection accuracy, as measured by a comprehensive index, and lowest false discovery rate among the three methods. When the sample size was large and the proportion of outliers was ≤5%, the positive selection rate of Ensemble was similar to that of enetLTS. However, when the proportion of outliers was 10% or 15%, Ensemble missed some variables that affected the response variables. Overall, enetLTS had the best outlier detection accuracy with false positive rates < 0.05 and high sensitivity, and enetLTS still performed well when the proportion of outliers was relatively large. With 1% or 2% outliers, Ensemble showed high outlier detection accuracy, but with higher proportions of outliers Ensemble missed many mislabeled samples. Rlogreg and Ensemble were less accurate in identifying outliers than enetLTS. The prediction accuracy of enetLTS was better than that of Rlogreg. Running Ensemble on a subset of data after removing the outliers identified by enetLTS improved the variable selection accuracy of Ensemble. CONCLUSIONS: When the proportion of outliers is ≤5%, Ensemble can be used for variable selection. When the proportion of outliers is > 5%, Ensemble can be used for variable selection on a subset after removing outliers identified by enetLTS. For outlier identification, enetLTS is the recommended method. In practice, the proportion of outliers can be estimated according to the inaccuracy of the diagnostic methods used.