Two stage adaptive optimal design with applications to dose-finding clinical trials

In adaptive optimal designs, each stage uses an estimate of the locally optimal design derived using cumulative data from all prior stages. This dependency on prior stages a ffects the properties of maximum likelihood estimates. To illuminate the eff ects, we assume for simplicity a nonlinear regression model with normal errors and that there are only two stages with a fixed first stage design point. Fisher's information is motivated for adaptive designs by deriving the Cram er-Rao lower bound for such experiments. Then the usefulness of Fisher's information is shown from both a design and analysis perspective. From a design perspective Fisher's information is used in a procedure that is developed to select the proportion of observations assigned to the first stage. From an analysis perspective the information measure most commonly used in the optimal design literature is compared with Fisher's information. Several estimates of information are compared and a procedure for selecting the proportion of subjects allocated to stage 1 is recommended. Asymptotics for regular models with fixed number of stages are typically motivated by assuming the sample size of each stage goes to infi nity as the overall sample size goes to in finity. However, it is not uncommon for a small pilot study of fixed size to be followed by a much larger experiment. We show that the distribution of the maximum likelihood estimates converges to a scale mixture family of normal random variables

Bayesian non-linear methods for survival analysis and structural equation models

"July 2014."Dissertation Co-adviser: Dr. Sounak Chakraborty.Dissertation Co-adviser: Dr. (Tony) Jianguo Sun.Includes vita.High dimensional data are more common nowadays, because the collection of such data becomes larger and more complex due to the technology advance of the computer science, biology, etc. The analysis of high dimensional data is different from traditional data analysis, and variable selection for high dimensional data becomes very challenging. Structural equation modeling (SEM) analyzes the relationship between manifest variables and latent variables. The structural equation focuses on analyzing the relationship between latent variables. New proposed methods of these topics are discussed in the dissertation. In the first chapter, we review the basic concept of survival analysis, SEM, and current method of variable selection in those two scenarios. We also introduce the available software package for current methods and relevant data set. In the second chapter, we develop a Bayesian kernel machine model with incorporating existing information on pathways and gene networks in the analysis of DNA microarray data. Each pathway is modeled nonparametrically using reproducing kernel Hilbert space. The pathways and the genes are selected via assigning mixture priors on the pathway indicator variable and the gene indicator variable. This approach helped us in flexible modeling of the pathway effects, which can capture both linear and non-linear effect. Moreover, the model can also pinpoint the important pathways and the important active genes within each pathway. We have also developed an efficient Markov Chain Monte Carlo (MCMC) algorithm to fit our model. We used simulations and a real data analysis, [van 't Veer et al., 2002] breast cancer microarray data, to illustrate the proposed method. In the third chapter, we extend the idea of semiparametric structural equation model where the nonlinear functional relationships are approximated using basis expansions [Guo et al., 2012]. Many basis expansion methods, including cubic splines, are known to induce correlations. In this chapter we compare standard Lasso, Fused Lasso anIncludes bibliographical references (pages 115-122)

Declining HIV-1 Prevalence and Incidence among Police Officers - A potential Cohort for HIV Vaccine Trials, in Dar es Salaam, Tanzania.

A safe effective and affordable HIV vaccine is the most cost effective way to prevent HIV infection worldwide. Current studies of HIV prevalence and incidence are needed to determine potentially suitable cohorts for vaccine studies. The prevalence and incidence of HIV-1 infection among the police in Dar es Salaam in 1996 were 13.8% and 19.6/1000 PYAR respectively. This study aimed at determining the current prevalence and incidence of HIV in a police cohort 10 years after a similar study was conducted. Police officers in Dar es Salaam, Tanzania were prospectively enrolled into the study from 2005 and followed-up in an incidence study three years later. HIV infection was determined by two sequential enzyme linked immunosorbent assays (ELISAs) in the prevalence study and discordant results between two ELISAs were resolved by a Western blot assay. Rapid HIV assays (SD Bioline and Determine) were used for the incidence study. A total of 1,240 police participated in the HIV prevalence study from August 2005 to November 2008. Of these, 1101 joined the study from August 2005-September 2007 and an additional 139 were recruited between October 2007 to November 2008 while conducting the incidence study. A total of 726 (70%) out of the 1043 eligible police participated in the incidence study.The overall HIV-1 prevalence was 65/1240 (5.2%). Females had a non-statistically significant higher prevalence of HIV infection compared to males 19/253, (7.5%) vs. 46/987 (4.7%) respectively (p = 0.07). The overall incidence of HIV-1 was 8.4 per 1000 PYAR (95% CI 4.68-14.03), and by gender was 8.8 and 6.9 per 1000 PYAR, among males and females respectively, (p = 0.82). The HIV prevalence and incidence among the studied police has declined over the past 10 years, and therefore this cohort is better suited for phase I/II HIV vaccine studies than for efficacy trials

Trends in Weekly Reported Net use by Children During and after Rainy Season in Central Tanzania.

The use of long-lasting insecticidal nets (LLINs) is one of the principal interventions to prevent malaria in young children, reducing episodes of malaria by 50% and child deaths by one fifth. Prioritizing young children for net use is important to achieve mortality reductions, particularly during transmission seasons. Households were followed up weekly from January through June 2009 to track net use among children under seven under as well as caretakers. Net use rates for children and caretakers in net-owning households were calculated by dividing the number of person-weeks of net use by the number of person-weeks of follow-up. Use was stratified by age of the child or caretaker status. Determinants of ownership and of use were assessed using multivariate models. Overall, 60.1% of the households reported owning a bed net at least once during the study period. Among net owners, use rates remained high during and after the rainy season. Rates of use per person-week decreased as the age of the child rose from 0 to six years old; at ages 0-23 months and 24-35 months use rates per person-week were 0.93 and 0.92 respectively during the study period, while for children ages 3 and 4 use rates per person-week were 0.86 and 0.80. For children ages 5-6 person-week ratios dropped to 0.55. This represents an incidence rate ratio of 1.67 for children ages 0-23 months compared to children aged 5-6. Caretakers had use rates similar to those of children age 0-35 months. Having fewer children under age seven in the household also appeared to positively impact net use rates for individual children. In this area of Tanzania, net use is very high among net-owning households, with no variability either at the beginning or end of the rainy season high transmission period. The youngest children are prioritized for sleeping under the net and caretakers also have high rates of use. Given the high use rates, increasing the number of nets available in the household is likely to boost use rates by older children