Three Essays on Extremal Quantiles

Extremal quantile index is a concept that the quantile index will drift to zero (or one)

as the sample size increases. The three chapters of my dissertation consists of three

applications of this concept in three distinct econometric problems. In Chapter 2, I

use the concept of extremal quantile index to derive new asymptotic properties and

inference method for quantile treatment effect estimators when the quantile index

of interest is close to zero. In Chapter 3, I rely on the concept of extremal quantile

index to achieve identification at infinity of the sample selection models and propose

a new inference method. Last, in Chapter 4, I use the concept of extremal quantile

index to define an asymptotic trimming scheme which can be used to control the

convergence rate of the estimator of the intercept of binary response models.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Scaling limits of a model for selection at two scales

The dynamics of a population undergoing selection is a central topic in evolutionary biology. This question is particularly intriguing in the case where selective forces act in opposing directions at two population scales. For example, a fast-replicating virus strain outcompetes slower-replicating strains at the within-host scale. However, if the fast-replicating strain causes host morbidity and is less frequently transmitted, it can be outcompeted by slower-replicating strains at the between-host scale. Here we consider a stochastic ball-and-urn process which models this type of phenomenon. We prove the weak convergence of this process under two natural scalings. The first scaling leads to a deterministic nonlinear integro-partial differential equation on the interval $[0,1]$ with dependence on a single parameter, $\lambda$. We show that the fixed points of this differential equation are Beta distributions and that their stability depends on $\lambda$ and the behavior of the initial data around $1$. The second scaling leads to a measure-valued Fleming-Viot process, an infinite dimensional stochastic process that is frequently associated with a population genetics.

Bayesian Analysis of Latent Threshold Dynamic Models

We discuss a general approach to dynamic sparsity modeling in multivariate time series analysis. Time-varying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing natural mechanisms for dynamic variable inclusion/selection. We discuss Bayesian model specification, analysis and prediction in dynamic regressions, time-varying vector autoregressions, and multivariate volatility models using latent thresholding. Application to a topical macroeconomic time series problem illustrates some of the benefits of the approach in terms of statistical and economic interpretations as well as improved predictions. Supplementary materials for this article are available online. © 2013 Copyright Taylor and Francis Group, LLC.

Sexual selection and canine dimorphism in New World monkeys.

Social and ecological factors are important in shaping sexual dimorphism in Anthropoidea, but there is also a tendency for body-size dimorphism and canine dimorphism to increase with increased body size (Rensch's rule) (Rensch: Evolution Above the Species Level. London: Methuen, 1959.) Most ecologist interpret Rensch's rule to be a consequence of social and ecological selective factors that covary with body size, but recent claims have been advanced that dimorphism is principally a consequence of selection for increased body size alone. Here we assess the effects of body size, body-size dimorphism, and social structure on canine dimorphism among platyrrhine monkeys. Platyrrhine species examined are classified into four behavioral groups reflecting the intensity of intermale competition for access to females or to limiting resources. As canine dimorphism increases, so does the level of intermale competition. Those species with monogamous and polyandrous social structures have the lowest canine dimorphism, while those with dominance rank hierarchies of males have the most canine dimorphism. Species with fission-fusion social structures and transitory intermale breeding-season competition fall between these extremes. Among platyrrhines there is a significant positive correlation between body size and canine dimorphism However, within levels of competition, no significant correlation was found between the two. Also, with increased body size, body-size dimorphism tends to increase, and this correlation holds in some cases within competition levels. In an analysis of covariance, once the level of intermale competition is controlled for, neither molar size nor molar-size dimorphism accounts for a significant part of the variance in canine dimorphism. A similar analysis using body weight as a measure of size and dimorphism yields a less clear-cut picture: body weight contributes significantly to the model when the effects of the other factors are controlled. Finally, in a model using head and body length as a measure of size and dimorphism, all factors and the interactions between them are significant. We conclude that intermale competition among platyrrhine species is the most important factor explaining variations in canine dimorphism. The significant effects of size and size dimorphism in some models may be evidence that natural (as opposed to sexual) selection also plays a role in the evolution of increased canine dimorphism.

Sociocultural and socioeconomic influences on type 2 diabetes risk in overweight/obese African-American and Latino-American children and adolescents.

PURPOSE: It is unclear whether sociocultural and socioeconomic factors are directly linked to type 2 diabetes risk in overweight/obese ethnic minority children and adolescents. This study examines the relationships between sociocultural orientation, household social position, and type 2 diabetes risk in overweight/obese African-American (n = 43) and Latino-American (n = 113) children and adolescents. METHODS: Sociocultural orientation was assessed using the Acculturation, Habits, and Interests Multicultural Scale for Adolescents (AHIMSA) questionnaire. Household social position was calculated using the Hollingshead Two-Factor Index of Social Position. Insulin sensitivity (SI), acute insulin response (AIRG) and disposition index (DI) were derived from a frequently sampled intravenous glucose tolerance test (FSIGT). The relationships between AHIMSA subscales (i.e., integration, assimilation, separation, and marginalization), household social position and FSIGT parameters were assessed using multiple linear regression. RESULTS: For African-Americans, integration (integrating their family's culture with those of mainstream white-American culture) was positively associated with AIRG (β = 0.27 ± 0.09, r = 0.48, P < 0.01) and DI (β = 0.28 ± 0.09, r = 0.55, P < 0.01). For Latino-Americans, household social position was inversely associated with AIRG (β = -0.010 ± 0.004, r = -0.19, P = 0.02) and DI (β = -20.44 ± 7.50, r = -0.27, P < 0.01). CONCLUSIONS: Sociocultural orientation and household social position play distinct and opposing roles in shaping type 2 diabetes risk in African-American and Latino-American children and adolescents.

Bioburden after Staphylococcus aureus inoculation in type 1 diabetic rats undergoing internal fixation.

SUMMARY: Fracture stabilization in the diabetic patient is associated with higher complication rates, particularly infection and impaired wound healing, which can lead to major tissue damage, osteomyelitis, and higher amputation rates. With an increasing prevalence of diabetes and an aging population, the risks of infection of internal fixation devices are expected to grow. Although numerous retrospective clinical studies have identified a relationship between diabetes and infection, currently there are few animal models that have been used to investigate postoperative surgical-site infections associated with internal fixator implantation and diabetes. The authors therefore refined the protocol for inducing hyperglycemia and compared the bacterial burden in controls to pharmacologically induced type 1 diabetic rats after undergoing internal fracture plate fixation and Staphylococcus aureus surgical-site inoculation. Using an initial series of streptozotocin doses, followed by optional additional doses to reach a target blood glucose range of 300 to 600 mg/dl, the authors reliably induced diabetes in 100 percent of the rats (n = 16), in which a narrow hyperglycemic range was maintained 14 days after onset of diabetes (mean ± SEM, 466 ± 16 mg/dl; coefficient of variation, 0.15). With respect to their primary endpoint, the authors quantified a significantly higher infectious burden in inoculated diabetic animals (median, 3.2 × 10 colony-forming units/mg dry tissue) compared with inoculated nondiabetic animals (7.2 × 10 colony-forming units/mg dry tissue). These data support the authors' hypothesis that uncontrolled diabetes adversely affects the immune system's ability to clear Staphylococcus aureus associated with internal hardware.

The upstream enhancer elements of the G6PC promoter are critical for optimal G6PC expression in murine glycogen storage disease type Ia.

Glycogen storage disease type-Ia (GSD-Ia) patients deficient in glucose-6-phosphatase-α (G6Pase-α or G6PC) manifest impaired glucose homeostasis characterized by fasting hypoglycemia, growth retardation, hepatomegaly, nephromegaly, hyperlipidemia, hyperuricemia, and lactic acidemia. Two efficacious recombinant adeno-associated virus pseudotype 2/8 (rAAV8) vectors expressing human G6Pase-α have been independently developed. One is a single-stranded vector containing a 2864-bp of the G6PC promoter/enhancer (rAAV8-GPE) and the other is a double-stranded vector containing a shorter 382-bp minimal G6PC promoter/enhancer (rAAV8-miGPE). To identify the best construct, a direct comparison of the rAAV8-GPE and the rAAV8-miGPE vectors was initiated to determine the best vector to take forward into clinical trials. We show that the rAAV8-GPE vector directed significantly higher levels of hepatic G6Pase-α expression, achieved greater reduction in hepatic glycogen accumulation, and led to a better toleration of fasting in GSD-Ia mice than the rAAV8-miGPE vector. Our results indicated that additional control elements in the rAAV8-GPE vector outweigh the gains from the double-stranded rAAV8-miGPE transduction efficiency, and that the rAAV8-GPE vector is the current choice for clinical translation in human GSD-Ia.

Evaluating marker-guided treatment selection strategies

© 2014, The International Biometric Society.A potential venue to improve healthcare efficiency is to effectively tailor individualized treatment strategies by incorporating patient level predictor information such as environmental exposure, biological, and genetic marker measurements. Many useful statistical methods for deriving individualized treatment rules (ITR) have become available in recent years. Prior to adopting any ITR in clinical practice, it is crucial to evaluate its value in improving patient outcomes. Existing methods for quantifying such values mainly consider either a single marker or semi-parametric methods that are subject to bias under model misspecification. In this article, we consider a general setting with multiple markers and propose a two-step robust method to derive ITRs and evaluate their values. We also propose procedures for comparing different ITRs, which can be used to quantify the incremental value of new markers in improving treatment selection. While working models are used in step I to approximate optimal ITRs, we add a layer of calibration to guard against model misspecification and further assess the value of the ITR non-parametrically, which ensures the validity of the inference. To account for the sampling variability of the estimated rules and their corresponding values, we propose a resampling procedure to provide valid confidence intervals for the value functions as well as for the incremental value of new markers for treatment selection. Our proposals are examined through extensive simulation studies and illustrated with the data from a clinical trial that studies the effects of two drug combinations on HIV-1 infected patients.