Quefeng Li

Estimation of high dimensional mean regression in the absence of symmetry and light tail assumptions

Data subject to heavy-tailed errors are commonly encountered in various scientific fields. To address this problem, procedures based on quantile regression and Least Absolute Deviation (LAD) regression have been developed in recent years. These methods essentially estimate the conditional median (or quantile) function. They can be very different from the conditional mean functions, especially when distributions are asymmetric and heteroscedastic. How can we efficiently estimate the mean regression functions in ultra-high dimensional setting with existence of only the second moment? To solve this problem, we propose a penalized Huber loss with diverging parameter to reduce biases created by the traditional Huber loss. Such a penalized robust approximate quadratic (RA-quadratic) loss will be called RA-Lasso. In the ultra-high dimensional setting, where the dimensionality can grow exponentially with the sample size, our results reveal that the RA-lasso estimator produces a consistent estimator at the same rate as the optimal rate under the light-tail situation. We further study the computational convergence of RA-Lasso and show that the composite gradient descent algorithm indeed produces a solution that admits the same optimal rate after sufficient iterations. As a byproduct, we also establish the concentration inequality for estimating population mean when there exists only the second moment. We compare RA-Lasso with other regularized robust estimators based on quantile regression and LAD regression. Extensive simulation studies demonstrate the satisfactory finite-sample performance of RA-Lasso.

Regularized outcome weighted subgroup identification for differential treatment effects

To facilitate comparative treatment selection when there is substantial heterogeneity of treatment effectiveness, it is important to identify subgroups that exhibit differential treatment effects. Existing approaches model outcomes directly and then define subgroups according to interactions between treatment and covariates. Because outcomes are affected by both the covariate-treatment interactions and covariate main effects, direct modeling outcomes can be hard due to model misspecification, especially in presence of many covariates. Alternatively one can directly work with differential treatment effect estimation. We propose such a method that approximates a target function whose value directly reflects correct treatment assignment for patients. The function uses patient outcomes as weights rather than modeling targets. Consequently, our method can deal with binary, continuous, time-to-event, and possibly contaminated outcomes in the same fashion. We first focus on identifying only directional estimates from linear rules that characterize important subgroups. We further consider estimation of comparative treatment effects for identified subgroups. We demonstrate the advantages of our method in simulation studies and in analyses of two real data sets.

The association of health literacy and blood pressure reduction in a cohort of patients with hypertension: The heart healthy lenoir trial

OBJECTIVE Lower health literacy is associated with poorer health outcomes. Few interventions poised to mitigate the impact of health literacy in hypertensive patients have been published. We tested if a multi-level quality improvement intervention could differentially improve Systolic Blood Pressure (SBP) more so in patients with low vs. higher health literacy. METHODS We conducted a non-randomized prospective cohort trial of 525 patients referred with uncontrolled hypertension. Stakeholder informed and health literacy sensitive strategies were implemented at the practice and patient level. Outcomes were assessed at 0, 6, 12, 18 and 24 months. RESULTS At 12 months, the low and higher health literacy groups had statistically significant decreases in mean SBP (6.6 and 5.3mmHg, respectively), but the between group difference was not significant (Δ 1.3mmHg, P=0.067). At 24 months, the low and higher health literacy groups reductions were 8.1 and 4.6mmHg, respectively, again the between group difference was not significant (Δ 3.5mmHg, p=0.25). CONCLUSIONS/PRACTICE IMPLICATIONS A health literacy sensitive multi-level intervention may equally lower SBP in patients with low and higher health literacy. Practical health literacy appropriate tools and methods can be implemented in primary care settings using a quality improvement approach.

Site-specific, adult bone benefits attributed to loading during youth: A preliminary longitudinal analysis.

We examined site-specific bone development in relation to childhood and adolescent artistic gymnastics exposure, comparing up to 10years of prospectively acquired longitudinal data in 44 subjects, including 31 non-gymnasts (NON) and 13 gymnasts (GYM) who participated in gymnastics from pre-menarche to ≥1.9years post-menarche. Subjects underwent annual regional and whole-body DXA scans; indices of bone geometry and strength were calculated. Anthropometrics, physical activity, and maturity were assessed annually, coincident with DXA scans. Non-linear mixed effect models centered growth in bone outcomes at menarche and adjusted for menarcheal age, height, and non-bone fat-free mass to evaluate GYM-NON differences. A POST-QUIT variable assessed the withdrawal effect of quitting gymnastics. Curves for bone area, mass (BMC), and strength indices were higher in GYM than NON at both distal radius metaphysis and diaphysis (p<0.0001). At the femoral neck, greater GYM BMC (p<0.01), narrower GYM endosteal diameter (p<0.02), and similar periosteal width (p=0.09) yielded GYM advantages in narrow neck cortical thickness and buckling ratio (both p<0.001; lower BR indicates lower fracture risk). Lumbar spine and sub-head BMC were greater in GYM than NON (p<0.036). Following gymnastics cessation, GYM slopes increased for distal radius diaphysis parameters (p≤0.01) and for narrow neck BR (p=0.02). At the distal radius metaphysis, GYM BMC and compressive strength slopes decreased, as did slopes for lumbar spine BMC, femoral neck BMC, and narrow neck cortical thickness (p<0.02). In conclusion, advantages in bone mass, geometry, and strength at multiple skeletal sites were noted across growth and into young adulthood in girls who participated in gymnastics loading to at least 1.9years post-menarche. Following gymnastics cessation, advantages at cortical bone sites improved or stabilized, while advantages at corticocancellous sites stabilized or diminished. Additional longitudinal observation is necessary to determine whether residual loading benefits enhance lifelong skeletal strength.

Embracing the Blessing of Dimensionality in Factor Models

ABSTRACT Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the blessing of dimensionality has not yet been fully embraced in the literature: much of the available data are often ignored in constructing covariance matrix estimates. If our goal is to accurately estimate a covariance matrix of a set of targeted variables, shall we employ additional data, which are beyond the variables of interest, in the estimation? In this article, we provide sufficient conditions for an affirmative answer, and further quantify its gain in terms of Fisher information and convergence rate. In fact, even an oracle-like result (as if all the factors were known) can be achieved when a sufficiently large number of variables is used. The idea of using data as much as possible brings computational challenges. A divide-and-conquer algorithm is thus proposed to alleviate the computational burden, and also shown not to sacrifice any statistical accuracy in comparison with a pooled analysis. Simulation studies further confirm our advocacy for the use of full data, and demonstrate the effectiveness of the above algorithm. Our proposal is applied to a microarray data example that shows empirical benefits of using more data. Supplementary materials for this article are available online.

The influence of organized physical activity (including gymnastics) on young adult skeletal traits: Is maturity phase important?

We prospectively evaluated adolescent organized physical activity (PA) as a factor in adult female bone traits. Annual DXA scans accompanied semiannual records of anthropometry, maturity, and PA for 42 participants in this preliminary analysis (criteria: appropriately timed DXA scans at ~1 year premenarche [predictor] and ~5 years postmenarche [dependent variable]). Regression analysis evaluated total adolescent interscan PA and PA over 3 maturity subphases as predictors of young adult bone outcomes: 1) bone mineral content (BMC), geometry, and strength indices at nondominant distal radius and femoral neck; 2) subhead BMC; 3) lumbar spine BMC. Analyses accounted for baseline gynecological age (years pre- or postmenarche), baseline bone status, adult body size and interscan body size change. Gymnastics training was evaluated as a potentially independent predictor, but did not improve models for any outcomes (p > .07). Premenarcheal bone traits were strong predictors of most adult outcomes (semipartial r2 = .21-0.59, p ≤ .001). Adult 1/3 radius and subhead BMC were predicted by both total PA and PA 1-3 years postmenarche (p < .03). PA 3-5 years postmenarche predicted femoral narrow neck width, endosteal diameter, and buckling ratio (p < .05). Thus, participation in organized physical activity programs throughout middle and high school may reduce lifetime fracture risk in females.

Robust estimation of high-dimensional covariance and precision matrices

High-dimensional data are often most plausibly generated from distributions with complex structure and leptokurtosis in some or all components. Covariance and precision matrices provide a useful summary of such structure, yet the performance of popular matrix estimators typically hinges upon a sub-Gaussianity assumption. This paper presents robust matrix estimators whose performance is guaranteed for a much richer class of distributions. The proposed estimators, under a bounded fourth moment assumption, achieve the same minimax convergence rates as do existing methods under a sub-Gaussianity assumption. Consistency of the proposed estimators is also established under the weak assumption of bounded 2 + ε moments for ε ∈ (0, 2). The associated convergence rates depend on ε.

Physical Activity, Sedentary Behavior, and Retirement: The Multi-Ethnic Study of Atherosclerosis

INTRODUCTION Physical activity and sedentary behavior are major risk factors for chronic disease. These behaviors may change at retirement, with implications for health in later life. The study objective was to describe longitudinal patterns of moderate to vigorous and domain-specific physical activity and TV watching by retirement status. METHODS Participants in the Multi-Ethnic Study of Atherosclerosis (n=6,814) were recruited from six U.S. communities and were aged 45-84 years at baseline. Retirement status and frequency and duration of domain-specific physical activity (recreational walking, transport walking, non-walking leisure activity, caregiving, household, occupational/volunteer) and TV watching were self-reported at four study exams (2000 to 2012). Fixed effect linear regression models were used to describe longitudinal patterns in physical activity and TV watching by retirement status overall and stratified by socioeconomic position. Analyses were conducted in 2017. RESULTS Of 4,091 Multi-Ethnic Study of Atherosclerosis participants not retired at baseline, 1,012 (25%) retired during a median of 9 years follow-up. Retirement was associated with a 10% decrease (95% CI= -15%, -5%) in moderate to vigorous physical activity and increases of 13% to 29% in recreational walking, household activity, and TV watching. Among people of low socioeconomic position, the magnitude of association was larger for moderate to vigorous physical activity. Among people of high socioeconomic position, the magnitude of association was larger for non-walking leisure and household activity. CONCLUSIONS The retirement transition was associated with changes in physical activity and TV watching. To inform intervention development, future research is needed on the determinants of behavior change after retirement, particularly among individuals of low socioeconomic position.

Correlates of changes in walking during the retirement transition: The Multi-Ethnic Study of Atherosclerosis

Retirement from employment involves disruption in daily routines and has been associated with positive and negative changes in physical activity. Walking is the most common physical activity among older Americans. The factors that influence changes in walking after retirement are unknown. The study objective was to identify correlates of within-person change in recreational walking (for leisure) and transport walking (to get places) during the retirement transition among a multi-ethnic cohort of adults (N = 928) from six US communities. Correlates were measured at the individual (e.g., gender), interpersonal (e.g., social support), and community (e.g., density of walking destinations) levels at study exams between 2000 and 2012. Comparing pre- and post-retirement measures (average 4.5 years apart), 50% of participants increased recreational walking by 60 min or more per week, 31% decreased by 60 min or more per week, and 19% maintained their recreational walking. Forty-one percent of participants increased transport walking by 60 min or more per week, 40% decreased by 60 min or more per week, and 19% maintained their transport walking after retirement. Correlates differed for recreational and transport walking and for increases compared to decreases in walking. Self-rated health, chronic conditions, and perceptions of the neighborhood walking environment were associated with changes in both types of walking after retirement. Further, some correlates differed by gender and retirement age. Findings can inform the targeting of interventions to promote walking during the retirement transition.

The effect of a practice-based multicomponent intervention that includes health coaching on medication adherence and blood pressure control in rural primary care

Low adherence to anti‐hypertensive medications contributes to worse outcomes. The authors conducted a secondary data analysis to examine the effects of a health‐coaching intervention on medication adherence and blood pressure (BP), and to explore whether changes in medication adherence over time were associated with changes in BP longitudinally in 477 patients with hypertension. Data regarding medication adherence and BP were collected at baseline, 6, 12, 18, and 24 months. The intervention resulted in increases in medication adherence (5.75→5.94, P = .04) and decreases in diastolic BP (81.6→76.1 mm Hg, P < .001) over time. The changes in medication adherence were associated with reductions in diastolic BP longitudinally (P = .047). Patients with low medication adherence at baseline had significantly greater improvement in medication adherence and BP over time than those with high medication adherence. The intervention demonstrated improvements in medication adherence and diastolic BP and offers promise as a clinically applicable intervention in rural primary care.