Chang-Xing Ma

Beyond Food Deserts Measuring and Mapping Racial Disparities in Neighborhood Food Environments

Given the emerging focus on improving food environments and food systems through planning, this article investigates racial disparities in neighborhood food environments. An empirical case of Erie County, New York tests the hypothesis that people belonging to different racial groups have access to different neighborhood food destinations. Using multiple methods—Gini coefficients and Poisson regression—we show that contrary to studies elsewhere in the country there are no food deserts in Erie County. However, like other studies, we find an absence of supermarkets in neighborhoods of color when compared to white neighborhoods. Nonetheless, our study reveals an extensive network of small grocery stores in neighborhoods of color. Rather than soliciting supermarkets, supporting small, high-quality grocery stores may be a more efficient strategy for ensuring access to healthful foods in minority neighborhoods.

An Empirical Comparison of Statistical Models for Value-Added Assessment of School Performance

Hierarchical Linear Models (HLM) have been used extensively for value-added analysis, adjusting for important student and school-level covariates such as socioeconomic status. A recently proposed alternative, the Layered Mixed Effects Model (LMEM) also analyzes learning gains, but ignores sociodemographic factors. Other features of LMEM, such as its ability to apportion credit for learning gains among multiple schools and its utilization of incomplete observations, make it appealing. A third model that is appealing due to its simplicity is the Simple Fixed Effects Models (SFEM). Statistical and computing specifications are given for each of these models. The models were fitted to obtain value-added measures of school performance by grade and subject area, using a common data set with two years of test scores. We investigate the practical impact of differences among these models by comparing their value-added measures. The value-added measures obtained from the SFEM were highly correlated with those from the LMEM. Thus, due to its simplicity, the SFEM is recommended over LMEM. Results of comparisons of SFEM with HLM were equivocal. Inclusion of student level variables such as minority status and poverty leads to results that differ from those of the SFEM. The question of whether to adjust for such variables is, perhaps, the most important issue faced when developing a school accountability system. Either inclusion or exclusion of them is likely to lead to a biased system. Which bias is most tolerable may depend on whether the system is to be a high-stakes one.

Centered L 2 -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.

A General Framework for Analyzing the Genetic Architecture of Developmental Characteristics

The genetic architecture of growth traits plays a central role in shaping the growth, development, and evolution of organisms. While a limited number of models have been devised to estimate genetic effects on complex phenotypes, no model has been available to examine how gene actions and interactions alter the ontogenetic development of an organism and transform the altered ontogeny into descendants. In this article, we present a novel statistical model for mapping quantitative trait loci (QTL) determining the developmental process of complex traits. Our model is constructed within the traditional maximum-likelihood framework implemented with the EM algorithm. We employ biologically meaningful growth curve equations to model time-specific expected genetic values and the AR(1) model to structure the residual variance-covariance matrix among different time points. Because of a reduced number of parameters being estimated and the incorporation of biological principles, the new model displays increased statistical power to detect QTL exerting an effect on the shape of ontogenetic growth and development. The model allows for the tests of a number of biological hypotheses regarding the role of epistasis in determining biological growth, form, and shape and for the resolution of developmental problems at the interface with evolution. Using our newly developed model, we have successfully detected significant additive × additive epistatic effects on stem height growth trajectories in a forest tree.

On the construction of multi-level supersaturated designs

New criteria of comparing multi-level supersaturated designs are proposed and their properties are studied. A new class of multi-level supersaturated designs are obtained by collapsing a U-type uniform design to an orthogonal array. A global optimization algorithm, the threshold accepting algorithm, is then applied to search for the best supersaturated designs under any prespecified criterion. Examples show that these newly constructed supersaturated designs have good modeling properties.

A logistic mixture model for characterizing genetic determinants causing differentiation in growth trajectories

The logistic or S-shaped curve of growth is one of the few universal laws in biology. It is certain that there exist specific genes affecting growth curves, but, due to a lack of statistical models, it is unclear how these genes cause phenotypic differentiation in growth and developmental trajectories. In this paper we present a statistical model for detecting major genes responsible for growth trajectories. This model is incorporated with pervasive logistic growth curves under the maximum likelihood framework and, thus, is expected to improve over previous models in both parameter estimation and inference. The power of this model is demonstrated by an example using forest tree data, in which evidence of major genes affecting stem growth processes is successfully detected. The implications for this model and its extensions are discussed.

The Risk of Birth Defects in Multiple Births: A Population-Based Study

Objectives: To determine if multiple births have higher risks of birth defects compared to singletons and to identify types of birth defects that occur more frequently in multiple births, controlling for seven sociodemographic and health-related variables. Methods: A retrospective cohort study was conducted of all resident live births in Florida during 1996–2000 using data from a population-based surveillance system. Birth defects were defined as in the 9th edition of the International Classification of Diseases—Clinical Modification (ICD-9-CM) code for the 42 reportable categories in the Centers for Disease Control and Prevention (CDC) Birth Defects Registry list and eight major birth defects classifications. Relative risks (RR) before and after adjusting for control variables and 95% confidence intervals (95% CI) were calculated. The control variables included mothers race, age, previous adverse pregnancy experience, education, Medicaid participation during pregnancy, infants sex and number of siblings. Results: This study included 972,694 live births (27,727 multiple births and 944,967 singletons). Birth defects prevalence per 10,000 live births was 358.50 for multiple births and 250.54 for singletons. After adjusting for control variables, multiple births had a 46% increased risk of birth defects compared to singletons. Higher risks were found in 23 of 40 birth defects for multiple births. Five highest adjusted relative risks for birth defects among multiple births were: anencephalus, biliary atresia, hydrocephalus without spina bifida, pulmonary valve atresia and stenosis, and bladder exstrophy. Increased risks were also found in 6 out of 8 major birth defects classifications. Conclusions: Multiple births have increased risks of birth defects compared to singletons.

Racial and Gender Differences in the Viability of Extremely Low Birth Weight Infants: A Population-Based Study

OBJECTIVE. The purpose of this study is to provide a race- and gender-specific model for predicting 1-year survival rates for extremely low birth weight (ELBW) infants by using population-based data. METHODS. Birth and death certificates were analyzed for all children (N = 5076) with birth weights between 300 g and 1000 g who were born in Florida between 1996 and 2000. Semiparametric, multivariate, logistic regression analysis was used to model 1-year survival probabilities as a function of birth weight, gestational age, mothers race, and infants gender. Estimated survival rates among different race/gender groups were compared by using odds ratios (ORs). RESULTS. One-year survival rates for 5076 ELBW infants born between 1996 and 2000 did not change during the 5-year period (60–62%). The survival rate at ≤500 g was ≤14% (n = 716). Survival rates at 501 to 600 g and 601 to 700 g were 36% and 62%, respectively. The survival rate reached >85% for infants of >800 g. Modeling indicated a survival advantage for female infants, compared with male infants (OR: 1.7; 95% confidence interval: 1.5–1.9), and for black infants, compared with white infants (OR: 1.3; 95% confidence interval: 1.1–1.5). Black female infants had 2.1 greater odds of survival than did white male infants. CONCLUSIONS. This population-based study highlights the significant race and gender differences in 1-year survival rates for ELBW infants, as well as the interactions of these 2 factors. These findings can assist obstetricians and neonatologists not only in the care of ELBW infants but also in frank discussions with families.

An improved genetic model generates high- resolution mapping of QTL for protein quality in maize endosperm

The genetic mapping of polymorphic markers in a cross between two inbred plant lines has proven to be a powerful method for detecting quantitative trait loci (QTL) underlying complex traits. However, existing methods of QTL mapping were developed for disomic inheritance of both marker and QTL loci in a diploid population. To map QTL influencing traits expressed in the endosperm, a triploid embryo-nourishing tissue resulting from double fertilization, existing QTL mapping models require modification to consider the trisomic inheritance of the endosperm and the generation difference between the mapping population and the endosperm. Such a model requires simultaneous use of two successive generations, which theoretically can lead to an increase in resolution for QTL mapping compared with the use of a single backcross or F2 generation. Using a newly developed model based on these considerations, we demonstrate the improved resolution of QTL, influencing protein quality traits in maize endosperm. The increased resolution made possible with this approach makes identified QTL accessible to positional cloning.

Uniformity in Fractional Factorials

The issue of uniformity is crucial in quasi-Monte Carlo methods and in the design of computer experiments. In this paper we study the role of uniformity in fractional factorial designs. For fractions of two- or three-level factorials, we derive results connecting orthogonality, aberration and uniformity and show that these criteria agree quite well. This provides further justification for the criteria of orthogonality or minimum aberration in terms of uniformity. Our results refer to several natural measures of uniformity and we consider both regular and nonregular fractions. The theory developed here has the potential of significantly reducing the complexity of computation for searching for minimum aberration designs.