TEST OF SIGNIFICANCE FOR HIGH-DIMENSIONAL LONGITUDINAL DATA.

This paper concerns statistical inference for longitudinal data with ultrahigh dimensional covariates. We first study the problem of constructing confidence intervals and hypothesis tests for a low dimensional parameter of interest. The major challenge is how to construct a powerful test statistic in the presence of high-dimensional nuisance parameters and sophisticated within-subject correlation of longitudinal data. To deal with the challenge, we propose a new quadratic decorrelated inference function approach, which simultaneously removes the impact of nuisance parameters and incorporates the correlation to enhance the efficiency of the estimation procedure. When the parameter of interest is of fixed dimension, we prove that the proposed estimator is asymptotically normal and attains the semiparametric information bound, based on which we can construct an optimal Wald test statistic. We further extend this result and establish the limiting distribution of the estimator under the setting with the dimension of the parameter of interest growing with the sample size at a polynomial rate. Finally, we study how to control the false discovery rate (FDR) when a vector of high-dimensional regression parameters is of interest. We prove that applying the Storey (2002)'s procedure to the proposed test statistics for each regression parameter controls FDR asymptotically in longitudinal data. We conduct simulation studies to assess the finite sample performance of the proposed procedures. Our simulation results imply that the newly proposed procedure can control both Type I error for testing a low dimensional parameter of interest and the FDR in the multiple testing problem. We also apply the proposed procedure to a real data example.

Constructing a confidence interval for the fraction who benefit from treatment, using randomized trial data.

The fraction who benefit from treatment is the proportion of patients whose potential outcome under treatment is better than that under control. Inference on this parameter is challenging since it is only partially identifiable, even in our context of a randomized trial. We propose a new method for constructing a confidence interval for the fraction, when the outcome is ordinal or binary. Our confidence interval procedure is pointwise consistent. It does not require any assumptions about the joint distribution of the potential outcomes, although it has the flexibility to incorporate various user-defined assumptions. Our method is based on a stochastic optimization technique involving a second-order, asymptotic approximation that, to the best of our knowledge, has not been applied to biomedical studies. This approximation leads to statistics that are solutions to quadratic programs, which can be computed efficiently using optimization tools. In simulation, our method attains the nominal coverage probability or higher, and can have narrower average width than competitor methods. We apply it to a trial of a new intervention for stroke.

Inequality in treatment benefits: Can we determine if a new treatment benefits the many or the few?

In many randomized controlled trials, the primary analysis focuses on the average treatment effect and does not address whether treatment benefits are widespread or limited to a select few. This problem affects many disease areas, since it stems from how randomized trials, often the gold standard for evaluating treatments, are designed and analyzed. Our goal is to learn about the fraction who benefit from a new treatment using randomized trial data. We consider the case where the outcome is ordinal, with binary outcomes as a special case. In general, the fraction who benefit is non-identifiable, and the best that can be obtained are sharp lower and upper bounds. Our contributions include (i) proving the plug-in estimator of the bounds can be inconsistent if support restrictions are made on the joint distribution of the potential outcomes; (ii) developing the first consistent estimator for this case; and (iii) applying this estimator to a randomized trial of a medical treatment to determine whether the estimates can be informative. Our estimator is computed using linear programming, allowing fast implementation. R code is provided.

Testing and Confidence Intervals for High Dimensional Proportional Hazards Model.

This paper proposes a decorrelation-based approach to test hypotheses and construct confidence intervals for the low dimensional component of high dimensional proportional hazards models. Motivated by the geometric projection principle, we propose new decorrelated score, Wald and partial likelihood ratio statistics. Without assuming model selection consistency, we prove the asymptotic normality of these test statistics, establish their semiparametric optimality. We also develop new procedures for constructing pointwise confidence intervals for the baseline hazard function and baseline survival function. Thorough numerical results are provided to back up our theory.

Adipocyte OGT governs diet-induced hyperphagia and obesity.

Palatable foods (fat and sweet) induce hyperphagia, and facilitate the development of obesity. Whether and how overnutrition increases appetite through the adipose-to-brain axis is unclear. O-linked beta-D-N-acetylglucosamine (O-GlcNAc) transferase (OGT) couples nutrient cues to O-GlcNAcylation of intracellular proteins at serine/threonine residues. Chronic dysregulation of O-GlcNAc signaling contributes to metabolic diseases. Here we show that adipocyte OGT is essential for high fat diet-induced hyperphagia, but is dispensable for baseline food intake. Adipocyte OGT stimulates hyperphagia by transcriptional activation of de novo lipid desaturation and accumulation of N-arachidonyl ethanolamine (AEA), an endogenous appetite-inducing cannabinoid (CB). Pharmacological manipulation of peripheral CB1 signaling regulates hyperphagia in an adipocyte OGT-dependent manner. These findings define adipocyte OGT as a fat sensor that regulates peripheral lipid signals, and uncover an unexpected adipose-to-brain axis to induce hyperphagia and obesity.

Generalized Alternating Direction Method of Multipliers: New Theoretical Insights and Applications.

Recently, the alternating direction method of multipliers (ADMM) has received intensive attention from a broad spectrum of areas. The generalized ADMM (GADMM) proposed by Eckstein and Bertsekas is an efficient and simple acceleration scheme of ADMM. In this paper, we take a deeper look at the linearized version of GADMM where one of its subproblems is approximated by a linearization strategy. This linearized version is particularly efficient for a number of applications arising from different areas. Theoretically, we show the worst-case 𝒪(1/k) convergence rate measured by the iteration complexity (k represents the iteration counter) in both the ergodic and a nonergodic senses for the linearized version of GADMM. Numerically, we demonstrate the efficiency of this linearized version of GADMM by some rather new and core applications in statistical learning. Code packages in Matlab for these applications are also developed.