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The statistical distance of conditional distributions is an essential element of generating target data given some data as in video prediction. We establish how the statistical distances between two joint distributions are related to those between two conditional distributions for three popular statistical distances: f-divergence, Wasserstein distance, and integral probability metrics. Such characterization plays a crucial role in deriving a tractable form of the objective function to learn a conditional generator. For Wasserstein distance, we show that the distance between joint distributions is an upper bound of the expected distance between conditional distributions, and derive a tractable representation of the upper bound. Based on this theoretical result, we propose a new conditional generator, the conditional Wasserstein generator. Our proposed algorithm can be viewed as an extension of Wasserstein autoencoders [1] to conditional generation or as a Wasserstein counterpart of stochastic video generation (SVG) model by Denton and Fergus [2]. We apply our algorithm to video prediction and video interpolation. Our experiments demonstrate that the proposed algorithm performs well on benchmark video datasets and produces sharper videos than state-of-the-art methods.

In multilevel regression models for observational clustered data, regressors can be correlated with cluster-level error components, namely endogenous, due to omitted cluster-level covariates, measurement error, and simultaneity. When endogeneity is ignored, regression coefficient estimators can be severely biased. To deal with endogeneity, instrument variable methods have been widely used. However, the instrument variable method often requires external instrument variables with certain conditions that cannot be verified empirically. Methods that use the within-cluster variations of the endogenous variable work under the restriction that either the outcome or the endogenous variable has a linear relationship with the cluster-level random effect. We propose a new method for binary outcome when it follows a logistic mixed-effects model and the endogenous variable is normally distributed but not linear in the random effect. The proposed estimator capitalizes on the nested data structure without requiring external instrument variables. We show that the proposed estimator is consistent and asymptotically normal. Furthermore, our method can be applied when the endogenous variable is missing in a cluster-specific nonignorable mechanism, without requiring that the missing mechanism be correctly specified. We evaluate the finite sample performance of the proposed approach via simulation and apply the method to a health care study using a San Diego inpatient dataset. Our study demonstrates that the clustered structure can be exploited to draw valid analysis of multilevel data with correlated effects.

In cohort studies the outcome is often time to a particular event, and subjects are followed at regular intervals. Periodic visits may also monitor a secondary irreversible event influencing the event of primary interest, and a significant proportion of subjects develop the secondary event over the period of follow-up. The status of the secondary event serves as a time-varying covariate, but is recorded only at the times of the scheduled visits, generating incomplete time-varying covariates. While information on a typical time-varying covariate is missing for entire follow-up period except the visiting times, the status of the secondary event are unavailable only between visits where the status has changed, thus interval-censored. One may view interval-censored covariate of the secondary event status as missing time-varying covariates, yet missingness is partial since partial information is provided throughout the follow-up period. Current practice of using the latest observed status produces biased estimators, and the existing missing covariate techniques cannot accommodate the special feature of missingness due to interval censoring. To handle interval-censored covariates in the Cox proportional hazards model, we propose an available-data estimator, a doubly robust-type estimator as well as the maximum likelihood estimator via EM algorithm and present their asymptotic properties. We also present practical approaches that are valid. We demonstrate the proposed methods using our motivating example from the Northern Manhattan Study.

When analyzing time-to-event cohort data, two different ways of choosing a time scale have been discussed in the literature: time-on-study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time-varying coefficient for left-truncated and right-censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well-established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.

We consider the problem of learning a binary classifier from only positive and unlabeled observations (called PU learning). Recent studies in PU learning have shown superior performance theoretically and empirically. However, most existing algorithms may not be suitable for large-scale datasets because they face repeated computations of a large Gram matrix or require massive hyperparameter optimization. In this paper, we propose a computationally efficient and theoretically grounded PU learning algorithm. The proposed PU learning algorithm produces a closed-form classifier when the hypothesis space is a closed ball in reproducing kernel Hilbert space. In addition, we establish upper bounds of the estimation error and the excess risk. The obtained estimation error bound is sharper than existing results and the derived excess risk bound has an explicit form, which vanishes as sample sizes increase. Finally, we conduct extensive numerical experiments using both synthetic and real datasets, demonstrating improved accuracy, scalability, and robustness of the proposed algorithm., 32 pages; Accepted for ACML 2019

Supplemental material, SMM876959 Supplemental Material for Cluster-specific nonignorably missing, endogenous, and continuous regressors in multilevel model for binary outcome by Gi-Soo Kim, Youngjo Lee, Hongsoo Kim and Myunghee Cho Paik in Statistical Methods in Medical Research

Weighting adjustment is commonly used in survey sampling to correct for unit nonresponse. In cluster sampling, the missingness indicators are often correlated within clusters and the response mechanism is subject to cluster-specific nonignorable missingness. Based on a parametric working model for the response mechanism that incorporates cluster-specific nonignorable missingness, we propose a method of weighting adjustment. We provide a consistent estimator of the mean or totals in cases where the study variable follows a generalized linear mixed-effects model. The proposed method is robust in the sense that the consistency of the estimator does not require correct specification of the functional forms of the response and outcome models. A consistent variance estimator based on Taylor linearization is also proposed. Numerical results, including a simulation and a real-data application, are presented.

Background and Purpose— Interleukin-6 (IL-6) is a proinflammatory cytokine with known autoregulatory feedback mechanisms. We hypothesized that elevated high-sensitivity C-reactive protein (hsCRP) relative to IL-6 confers an increased risk of ischemic stroke (IS), and low hsCRP relative to IL-6 a decreased risk, for individuals in the prospective, multiethnic, population-based Northern Manhattan Study (NOMAS). Methods— Serum hsCRP and IL-6 were measured in NOMAS participants at baseline. We created a trichotomized predictor based on the dominant biomarker in terms of quartiles: hsCRP-dominant, IL-6–dominant, and codominant groups. Cox proportional hazards models were used to calculate hazard ratios and 95% confidence intervals for the association between inflammatory biomarker group status and risk of incident IS. Results— Of 3298 participants, both hsCRP and IL-6 were available in 1656 participants (mean follow-up, 7.8 years; 113 incident IS). The hsCRP-dominant group had increased risk of IS (adjusted hazard ratio, 2.62; 95% confidence interval, 1.56–4.41) and the IL-6–dominant group had decreased risk (adjusted hazard ratio, 0.38; 95% confidence interval, 0.18–0.82) when compared with the referent group, after adjusting for potential confounders. Model fit was improved using the inflammation-dominant construct, over either biomarker alone. Conclusions— In this multiethnic cohort, when hsCRP-quartile was higher than IL-6 quartile, IS risk was increased, and conversely when IL-6 quartiles were elevated relative to hsCRP, IS risk was decreased. Construct validity requires confirmation in other cohorts.

Multilevel functional data is collected in many biomedical studies. For example, in a study of the effect of Nimodipine on patients with subarachnoid hemorrhage (SAH), patients underwent multiple 4-hour treatment cycles. Within each treatment cycle, subjects' vital signs were reported every 10 minutes. This data has a natural multilevel structure with treatment cycles nested within subjects and measurements nested within cycles. Most literature on nonparametric analysis of such multilevel functional data focus on conditional approaches using functional mixed effects models. However, parameters obtained from the conditional models do not have direct interpretations as population average effects. When population effects are of interest, we may employ marginal regression models. In this work, we propose marginal approaches to fit multilevel functional data through penalized spline generalized estimating equation (penalized spline GEE). The procedure is effective for modeling multilevel correlated generalized outcomes as well as continuous outcomes without suffering from numerical difficulties. We provide a variance estimator robust to misspecification of correlation structure. We investigate the large sample properties of the penalized spline GEE estimator with multilevel continuous data and show that the asymptotics falls into two categories. In the small knots scenario, the estimated mean function is asymptotically efficient when the true correlation function is used and the asymptotic bias does not depend on the working correlation matrix. In the large knots scenario, both the asymptotic bias and variance depend on the working correlation. We propose a new method to select the smoothing parameter for penalized spline GEE based on an estimate of the asymptotic mean squared error (MSE). We conduct extensive simulation studies to examine property of the proposed estimator under different correlation structures and sensitivity of the variance estimation to the choice of smoothing parameter. Finally, we apply the methods to the SAH study to evaluate a recent debate on discontinuing the use of Nimodipine in the clinical community.

In survival studies, classical inferences for left-truncated data require quasi-independence, a property that the joint density of truncation time and failure time is factorizable into their marginal densities in the observable region. The quasi-independence hypothesis is testable; many authors have developed tests for left-truncated data with or without right-censoring. In this paper, we propose a class of test statistics for testing the quasi-independence which unifies the existing methods and generates new useful statistics such as conditional Spearman's rank correlation coefficient. Asymptotic normality of the proposed class of statistics is given. We show that a new set of tests can be powerful under certain alternatives by theoretical and empirical power comparison., Comment: Accepted in Statistica Sinica

Objectives: To examine the association between successful aging without subsequent cognitive decline (SA-ND) and the Northern Manhattan Study (NOMAS) global vascular risk score (GVRS), which is predictive of stroke, myocardial infarction, and vascular death. Design: Prospective cohort study. Setting: A stroke-free sample of Hispanic, black, and white participants living in the same community enrolled in a magnetic resonance imaging (MRI) substudy of NOMAS, a population-based prospective cohort study. Participants: One thousand two hundred ninety individuals in whom a cognitive screen was administered at baseline and at enrollment in the MRI substudy. Measurements: SA-ND was based on disease, disability, and cognitive function. The GVRS includes age, sex, race and ethnicity, waist circumference, alcohol intake, smoking, physical activity, blood pressure, antihypertensive medication use, fasting blood sugar, lipid levels, and peripheral vascular disease. Results: Data at baseline and follow-up were available for 1,162 participants (mean age 70 ± 9; 61% women; 13% white, 16% black, 69% Hispanic; mean GVRS 8.6 ± 0.9). Logistic regression, adjusted for education, socioeconomic status, and follow-up time, showed that the odds of SA-ND were 38% greater for each additional 1-point decrease on the GVRS (odds ratio = 1.38, 95% confidence interval = 1.17�1.61; P < .001). An inverse dose-response was observed between quartiles of GVRS and SA-ND. Greater diastolic blood pressure in participants taking antihypertensive medication and a history of claudication (P = .003) or peripheral arterial disease (P < .001) were inversely associated with SA-ND in the fully adjusted model. Conclusion: Potentially modifiable vascular risk factors were independently associated with SA-ND in a multiethnic community-based sample. Improvements in GVRSs could help promote healthy longevity in the aging population.

We hypothesized that infectious burden (IB), a composite serologic measure of exposure to common pathogens (i.e., Chlamydia pneumoniae, Helicobacter pylori, cytomegalovirus, and herpes simplex virus 1 and 2) associated with vascular risk in the prospective Northern Manhattan Study (NOMAS), would also be associated with cognition.Cognition was assessed using the Mini-Mental State Examination (MMSE) at enrollment and the modified Telephone Interview for Cognitive Status (TICS-m) at annual follow-up visits. Adjusted linear and logistic regressions were used to measure the association between IB index and MMSE. Generalized estimating equation models were used to evaluate associations with TICS-m and its change over time.Serologies and cognitive assessments were available in 1,625 participants of the NOMAS cohort. In unadjusted analyses, higher IB index was associated with worse cognition (change per standard deviation [SD] of IB for MMSE was -0.77, p0.0001, and for first measurements of TICS-m was -1.89, p0.0001). These effects were attenuated after adjusting for risk factors (for MMSE adjusted change per SD of IB = -0.17, p = 0.06, for TICS-m adjusted change per SD IB = -0.68, p0.0001). IB was associated with MMSE ≤24 (compared to MMSE24, adjusted odds ratio 1.26 per SD of IB, 95% confidence interval 1.06-1.51). IB was not associated with cognitive decline over time. The results were similar when IB was limited to viral serologies only.A measure of IB associated with stroke risk and atherosclerosis was independently associated with cognitive performance in this multiethnic cohort. Past infections may contribute to cognitive impairment.

Objective: to study the association between soluble tumour necrosis factor receptor 1 (sTNFR1) levels and mortality in the population-based Northern Manhattan Study (NOMAS). Methods: NOMAS is a multi-ethnic, community-based cohort study with mean 8.4 years of follow-up. sTNFR1 was measured using ELISA. Cox proportional hazards models were used to calculate hazard ratios and 95% confidence intervals (HR, 95% CI) for the association of sTNFR1 with risk of all-cause mortality after adjusting for relevant confounders. Results: sTNFR1 measurements were available in 1,862 participants (mean age 69.2 ± 10.2 years) with 512 all-cause deaths. Median sTNFR1 was 2.28 ng/ml. Those with sTNFR1 levels in the highest quartile (Q4), compared with those with sTNFR1 in the lowest quartile (Q1), were at an increased risk of all-cause mortality (adjusted HR: 1.8, 95% CI: 1.4– 2.4) and non-vascular mortality (adjusted HR: 2.5, 95% CI: 1.5–3.6), but not vascular mortality (adjusted HR: 1.3, 95% CI: 0.9–1.9). There were interactions between sTNFR1 quartiles and medical insurance-status [likelihood ratio test (LRT) with 3 degrees of freedom, Pinteraction= 0.02] and alcohol consumption (LRT with 3 degrees of freedom, Pinteraction< 0.01) for all-cause mortality. In participants with no insurance or Medicaid, those with sTNFR1 in the top quartile had nearly a threefold increased risk of total mortality than the lowest quartile (adjusted HR: 2.9, 95% CI: 1.9–4.4). Conclusion: in this multi-ethnic cohort, sTNFR1 was associated with all-cause and non-vascular mortality, particularly among those of a lower socioeconomic status.