The placenta forms in eutherian mammals, and is responsible for the nutrition of the developing fetus. However, maternal exposure to environmental pollutants both before and during pregnancy may result in the passage of toxins through the placental barrier and into fetal tissues. The placenta is the only organ derived from both maternal and fetal tissues, and establishes a link between the fetus and the environmental exposures of the mother. The analysis of placentae for the presence of environmental pollutants offers the possibility of exposure measurements in both the mother and the developing fetus. Specifically, trace element determination in human placentae may reveal fetal nutritional requirements, as well as identify potential indicators of negative health effects in both the mother and fetus. The principal goal of this project is to analyze approximately 160 archived human term placental tissues placenta body, placenta membrane, and umbilical cord) for essential trace elements, such as copper, zinc, and selenium, nonessential trace elements, including mercury, lead, and cadmium, and the rare earth elements of the lanthanide series. Sample preparation procedures focus on trace element homogeneity within the placenta, and contamination prevention. Analytical methodologies based on inductively coupled plasma mass spectrometry ICP-MS) and electrothermal atomic absorption spectrometry ETAAS) are developed and validated for all analytes of interest, using a variety of quality control materials. Subsequently, total element concentrations in each tissue component are measured and compared. Possible inter-element correlations within each tissue component are identified, as well as potential associations between analytical measurements and selected demographic and obstetric variables collected from the population studied. Results indicate that the placenta largely accumulates cadmium, an element strongly correlated with maternal smoking behavior. Lead and mercury are easily transported into fetal tissues. Placental concentrations of rare earth elements followed the typical abundance pattern of these elements in Earths crust, suggesting natural sources of exposure. Inter-element correlations were found for rubidium and cesium, as well as for aluminum and other bone-seeking elements, such as lead, lanthanum, uranium, barium, and strontium. Manganese in the placenta was positively correlated with infant growth variables, including birth weight, length, and head and chest circumference.

Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected Type I error, as well as the possibility of a costlier and lengthier trial. We develop several models that allow for the commensurability of the information in the historical and current data to determine how much historical information is used. First, we propose methods for univariate Gaussian data and provide an example analysis of data from two successive colon cancer trials that illustrates a linear models extension of our adaptive borrowing approach. Next, we extend the general method to linear and linear mixed models as well as generalized linear and generalized linear mixed models. We also provide two more sample analyses using the colon cancer data. Finally, we consider the effective historical sample size of our adaptive method for the case when historical data is available only for the concurrent control arm, and propose “optimal” use of new patients in the current trial using an adaptive randomization scheme that is balanced with respect to the amount of incorporated historical information. The approach is then demonstrated using data from a trial comparing antiretroviral strategies in HIV-1-infected persons. Throughout the thesis we present simulation studies that compare frequentist operating characteristics and highlight the advantages of our adaptive borrowing methods.

In this dissertation, we study statistical methodology for joint modeling that correctly controls for the interplay among longitudinal and counting processes and makes the most efficient use of data. Three types of joint modeling approaches are proposed based on three different purposes of studies. In the first topic, we develop a method for joint modeling of longitudinal data and recurrent events in the presence of an informative terminal event. We focus on data from patients who experience the same type of event at multiple times, such as multiple infection episodes or recurrent strokes, have longitudinal biomarkers, and may be subject to an event, for example death, that makes further observations impossible. To analyze such complicated data, we propose joint models based on a likelihood approach. A broad class of transformation models for the cumulative intensity of recurrent events and the cumulative hazard of the terminal event is considered. We propose to estimate all the parameters using nonparametric maximum likelihood estimators NPMLE), and we provide computationally efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we evaluate the performance of the proposed method through extensive simulations and application to real data. In the second topic, we develop a method for joint modeling of longitudinal and cure-survival data. By cure-survival data, we mean time-to-event data in which a certain proportion of patients never have any event during a sufficiently long follow-up period. These patients are believed to have been cured by treatment, such as radiation therapy or an initial surgery, and are often the source of heavy tail probabilities in survival curves. To take into account the possibility of patients being cured, we propose to model time-to-event through a transformed promotion time cure model, jointly with a linear mixed effects model for longitudinal data. Due to transformations applied to the promotion time cure model, the proposed method is able to be used in cases where the proportionality assumption does not hold. All the parameters are estimated using NPMLEs, and inference procedures are implemented via a simple EM algorithm. Asymptotic properties of the proposed NPMLEs are derived based on empirical process theory. Simulation studies are conducted and the method is applied to the ARIC data in order to demonstrate the small-sample performance of the proposed method. In the third topic, we develop a partially linear model for longitudinal data with informative censoring, where the main interest is in making inferences about the individuals trajectory of longitudinal responses, which may be informatively censored. Since a fully parameterized mean structure may be insufficient to capture the underlying patterns of longitudinal and event processes, we propose to use a partially linear model for longitudinal responses, where an unspecified underlying function is formulated along with linear covariate effects, and a transformation model is used for informative censoring times. We employ a sieve estimation for the nonparametric trajectory of longitudinal responses, where the unknown trajectory is approximated by cubic B-spline basis functions. All parameters are estimated based on a likelihood approach, and inference procedures are implemented via the EM algorithm. We also investigate a reliable way to select the number of knots and the best transformation. Through empirical process theory, asymptotic properties of the proposed estimators are shown to provide desirable properties. The validity of the proposed method is confirmed by simulated and real data examples.