Low-rank regression models for multiple binary responses and their applications to cancer cell-line encyclopedia data.

In this paper, we study high-dimensional multivariate logistic regression models in which a common set of covariates is used to predict multiple binary outcomes simultaneously. Our work is primarily motivated from many biomedical studies with correlated multiple responses such as the cancer cell-line encyclopedia project. We assume that the underlying regression coefficient matrix is simultaneously low-rank and row-wise sparse. We propose an intuitively appealing selection and estimation framework based on marginal model likelihood, and we develop an efficient computational algorithm for inference. We establish a novel high-dimensional theory for this nonlinear multivariate regression. Our theory is general, allowing for potential correlations between the binary responses. We propose a new type of nuclear norm penalty using the smooth clipped absolute deviation, filling the gap in the related non-convex penalization literature. We theoretically demonstrate that the proposed approach improves estimation accuracy by considering multiple responses jointly through the proposed estimator when the underlying coefficient matrix is low-rank and row-wise sparse. In particular, we establish the non-asymptotic error bounds, and both rank and row support consistency of the proposed method. Moreover, we develop a consistent rule to simultaneously select the rank and row dimension of the coefficient matrix. Furthermore, we extend the proposed methods and theory to a joint Ising model, which accounts for the dependence relationships. In our analysis of both simulated data and the cancer cell line encyclopedia data, the proposed methods outperform the existing methods in better predicting responses.

Debiased inference for heterogeneous subpopulations in a high-dimensional logistic regression model.

Due to the prevalence of complex data, data heterogeneity is often observed in contemporary scientific studies and various applications. Motivated by studies on cancer cell lines, we consider the analysis of heterogeneous subpopulations with binary responses and high-dimensional covariates. In many practical scenarios, it is common to use a single regression model for the entire data set. To do this effectively, it is critical to quantify the heterogeneity of the effect of covariates across subpopulations through appropriate statistical inference. However, the high dimensionality and discrete nature of the data can lead to challenges in inference. Therefore, we propose a novel statistical inference method for a high-dimensional logistic regression model that accounts for heterogeneous subpopulations. Our primary goal is to investigate heterogeneity across subpopulations by testing the equivalence of the effect of a covariate and the significance of the overall effects of a covariate. To achieve overall sparsity of the coefficients and their fusions across subpopulations, we employ a fused group Lasso penalization method. In addition, we develop a statistical inference method that incorporates bias correction of the proposed penalized method. To address computational issues due to the nonlinear log-likelihood and the fused Lasso penalty, we propose a computationally efficient and fast algorithm by adapting the ideas of the proximal gradient method and the alternating direction method of multipliers (ADMM) to our settings. Furthermore, we develop non-asymptotic analyses for the proposed fused group Lasso and prove that the debiased test statistics admit chi-squared approximations even in the presence of high-dimensional variables. In simulations, the proposed test outperforms existing methods. The practical effectiveness of the proposed method is demonstrated by analyzing data from the Cancer Cell Line Encyclopedia (CCLE).

Quantile forward regression for high-dimensional survival data.

Despite the urgent need for an effective prediction model tailored to individual interests, existing models have mainly been developed for the mean outcome, targeting average people. Additionally, the direction and magnitude of covariates' effects on the mean outcome may not hold across different quantiles of the outcome distribution. To accommodate the heterogeneous characteristics of covariates and provide a flexible risk model, we propose a quantile forward regression model for high-dimensional survival data. Our method selects variables by maximizing the likelihood of the asymmetric Laplace distribution (ALD) and derives the final model based on the extended Bayesian Information Criterion (EBIC). We demonstrate that the proposed method enjoys a sure screening property and selection consistency. We apply it to the national health survey dataset to show the advantages of a quantile-specific prediction model. Finally, we discuss potential extensions of our approach, including the nonlinear model and the globally concerned quantile regression coefficients model.

Varying-coefficients for regional quantile via KNN-based LASSO with applications to health outcome study.

Health outcomes, such as body mass index and cholesterol levels, are known to be dependent on age and exhibit varying effects with their associated risk factors. In this paper, we propose a novel framework for dynamic modeling of the associations between health outcomes and risk factors using varying-coefficients (VC) regional quantile regression via K-nearest neighbors (KNN) fused Lasso, which captures the time-varying effects of age. The proposed method has strong theoretical properties, including a tight estimation error bound and the ability to detect exact clustered patterns under certain regularity conditions. To efficiently solve the resulting optimization problem, we develop an alternating direction method of multipliers (ADMM) algorithm. Our empirical results demonstrate the efficacy of the proposed method in capturing the complex age-dependent associations between health outcomes and their risk factors.

Depletion of L-ascorbic acid alternating with its supplementation in the treatment of patients with acute myeloid leukemia or myelodysplastic syndromes.

PURPOSE: L-ascorbic acid (LAA) modifies the in vitro growth of leukemic cells from approximately 50% of patients with acute myeloid leukemia (AML) or myelodysplastic syndromes (MDS). To test the hypothesis that depletion of LAA, alternating with supplementation to prevent scurvy, would provide therapeutic benefit, a single-arm pilot trial was conducted (ClinicalTrials.gov identifier: NCT00329498). Experimental results: During depletion phase, patients with refractory AML or MDS were placed on a diet deficient in LAA; during supplementation phase, patients received daily intravenous administration of LAA. An in vitro assay was performed pretherapy for LAA sensitivity of leukemic cells from individual patients. RESULTS: Of 18 patients enrolled, eight of 16 evaluable patients demonstrated a clinical response. Responses were obtained during depletion (four patients) as well as during supplementation (five patients) but at a pharmacologic plasma level achievable only with intravenous administration. Of nine patients for whom the in vitro assay indicated their leukemic cells were sensitive to LAA, seven exhibited a clinical response; compared with none of six patients who were insensitive to LAA. CONCLUSIONS: The clinical benefit, along with a conspicuous absence of significant adverse events, suggests that further testing of LAA depletion alternating with pharmacologic dose intravenous supplementation in patients with these and other malignancies is warranted.