Effectively Selecting a Target Population for a Future Comparative Study

When comparing a new treatment with a control in a randomized clinical study, the treatment effect is generally assessed by evaluating a summary measure over a specific study population. The success of the trial heavily depends on the choice of such a population. In this paper, we show a systematic, effective way to identify a promising population, for which the new treatment is expected to have a desired benefit, using the data from a current study involving similar comparator treatments. Specifically, with the existing data we first create a parametric scoring system using multiple covariates to estimate subject-specific treatment differences. Using this system, we specify a desired level of treatment difference and create a subgroup of patients, defined as those whose estimated scores exceed this threshold. An empirically calibrated group-specific treatment difference curve across a range of threshold values is constructed. The population of patients with any desired level of treatment benefit can then be identified accordingly. To avoid any ``self-serving'' bias, we utilize a cross-training-evaluation method for implementing the above two-step procedure. Lastly, we show how to select the best scoring system among all competing models. The proposals are illustrated with the data from two clinical trials in treating AIDS and cardiovascular diseases. Note that if we are not interested in designing a new study for comparing similar treatments, the new procedure can also be quite useful for the management of future patients who would receive nontrivial benefits to compensate for the risk or cost of the new treatment.

Designed Extension of Survival Studies: Application to Clinical Trials with Unrecognized Heterogeneity

It is well known that unrecognized heterogeneity among patients, such as is conferred by genetic subtype, can undermine the power of randomized trial, designed under the assumption of homogeneity, to detect a truly beneficial treatment. We consider the conditional power approach to allow for recovery of power under unexplained heterogeneity. While Proschan and Hunsberger (1995) confined the application of conditional power design to normally distributed observations, we consider more general and difficult settings in which the data are in the framework of continuous time and are subject to censoring. In particular, we derive a procedure appropriate for the analysis of the weighted log rank test under the assumption of a proportional hazards frailty model. The proposed method is illustrated through application to a brain tumor trial.

Analyzing Panel Count Data with Informative Observation Times

In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying recurrent event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the recurrent event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximizing a conditional likelihood function of observed event counts and solving estimation equations. Large sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumor study is presented to illustrate the use of the proposed methods.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

ON THE MERITS OF VOXEL-BASED MORPHOMETRIC PATH-ANALYSIS FOR INVESTIGATING VOLUMETRIC MEDIATION OF A TOXICANT'S INFLUENCE ON COGNITIVE FUNCTION

We previously showed that lifetime cumulative lead dose, measured as lead concentration in the tibia bone by X-ray fluorescence, was associated with persistent and progressive declines in cognitive function and with decreases in MRI-based brain volumes in former lead workers. Moreover, larger region-specific brain volumes were associated with better cognitive function. These findings motivated us to explore a novel application of path analysis to evaluate effect mediation. Voxel-wise path analysis, at face value, represents the natural evolution of voxel-based morphometry methods to answer questions of mediation. Application of these methods to the former lead worker data demonstrated potential limitations in this approach where there was a tendency for results to be strongly biased towards the null hypothesis (lack of mediation). Moreover, a complimentary analysis using anatomically-derived regions of interest volumes yielded opposing results, suggesting evidence of mediation. Specifically, in the ROI-based approach, there was evidence that the association of tibia lead with function in three cognitive domains was mediated through the volumes of total brain, frontal gray matter, and/or possibly cingulate. A simulation study was conducted to investigate whether the voxel-wise results arose from an absence of localized mediation, or more subtle defects in the methodology. The simulation results showed the same null bias evidenced as seen in the lead workers data. Both the lead worker data results and the simulation study suggest that a null-bias in voxel-wise path analysis limits its inferential utility for producing confirmatory results.

Optimal game theoretic distributed control methodologies in small scale power systems

This dissertation presents the competitive control methodologies for small-scale power system (SSPS). A SSPS is a collection of sources and loads that shares a common network which can be isolated during terrestrial disturbances. Micro-grids, naval ship electric power systems (NSEPS), aircraft power systems and telecommunication system power systems are typical examples of SSPS. The analysis and development of control systems for small-scale power systems (SSPS) lacks a defined slack bus. In addition, a change of a load or source will influence the real time system parameters of the system. Therefore, the control system should provide the required flexibility, to ensure operation as a single aggregated system. In most of the cases of a SSPS the sources and loads must be equipped with power electronic interfaces which can be modeled as a dynamic controllable quantity. The mathematical formulation of the micro-grid is carried out with the help of game theory, optimal control and fundamental theory of electrical power systems. Then the micro-grid can be viewed as a dynamical multi-objective optimization problem with nonlinear objectives and variables. Basically detailed analysis was done with optimal solutions with regards to start up transient modeling, bus selection modeling and level of communication within the micro-grids. In each approach a detail mathematical model is formed to observe the system response. The differential game theoretic approach was also used for modeling and optimization of startup transients. The startup transient controller was implemented with open loop, PI and feedback control methodologies. Then the hardware implementation was carried out to validate the theoretical results. The proposed game theoretic controller shows higher performances over traditional the PI controller during startup. In addition, the optimal transient surface is necessary while implementing the feedback controller for startup transient. Further, the experimental results are in agreement with the theoretical simulation. The bus selection and team communication was modeled with discrete and continuous game theory models. Although players have multiple choices, this controller is capable of choosing the optimum bus. Next the team communication structures are able to optimize the players’ Nash equilibrium point. All mathematical models are based on the local information of the load or source. As a result, these models are the keys to developing accurate distributed controllers.

Red blood cell lifespan, erythropoiesis and hemoglobin control

Erythropoietin (EPO) and iron deficiency as causes of anemia in patients with limited renal function or end-stage renal disease are well addressed. The concomitant impairment of red blood cell (RBC) survival has been largely neglected. Properties of the uremic environment like inflammation, increased oxidative stress and uremic toxins seem to be responsible for the premature changes in RBC membrane and cytoskeleton. The exposure of antigenic sites and breakdown of the phosphatidylserine asymmetry promote RBC phagocytosis. While the individual response to treatment with EPO-stimulating agents (ESA) depends on both the RBC's lifespan and the production rate, uniform dosing algorithms do not meet that demand. The clinical use of mathematical models predicting ESA-induced changes in hematocrit might be greatly improved once independent estimates of RBC production rate and/or lifespan become available, thus making the concomitant estimation of both parameters unnecessary. Since heme breakdown by the hemoxygenase pathway results in carbon monoxide (CO) which is exhaled, a simple CO breath test has been used to calculate hemoglobin turnover and therefore RBC survival and lifespan. Future research will have to be done to validate and implement this method in patients with kidney failure. This will result in new insights into RBC kinetics in renal patients. Eventually, these findings are expected to improve our understanding of the hemoglobin variability in response to ESA.