A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

Behavioral and psychosocial factors associated with sexual risk in a population of crack cocaine users

The purpose of this dissertation was to examine the relationship between key psychosocial and behavioral components of the Transtheoretical Model and the Theory of Reasoned Action for sexual risk reduction in a population of crack cocaine smokers and sex workers, not in drug treatment. ^ The first study examined the results of an analysis of the association between two principal constructs in the Transtheoretical Model, the processes of change and the stages of change for condom use, in a high risk population. In the analysis of variance for all respondents, the overall F-test revealed that people in different stages have different levels of experiential process use, F(3,317) = 17.79, p = 0.0001 and different levels of behavioral process use, F(3,317) = 28.59, p = .0001. For the experiential processes, there was a significant difference between the precontemplation/contemplation stage, and both the action, and maintenance, stages.^ The second study explored the relationship between the Theory of Reasoned Action “beliefs” and the stages-of-change in the same population. In the analysis of variance for all participants, the results indicate that people in different stages did value the positive beliefs differently, F(3,502) = 15.38, p = .0001 but did not value the negative beliefs differently, F(3,502) = 2.08, p = .10. ^ The third study explored differences in stage-of-change by gender, partner type drug use, and HIV status. Three discriminant functions emerged, with a combined χ2(12) = 139.57, p = <.0001. The loading matrix of correlations between predictors and discriminant functions demonstrate that the strongest predictor for distinguishing between the precontemplation/contemplation stage and the preparation, action, and maintenance stages (first function) is partner type (.962). The loadings on the second discriminant function suggest that once partner type has been accounted for, ever having HIV/AIDS (.935) was the best predictor for distinguishing between the first three stages and the maintenance stage. ^ These studies demonstrate that behavioral change theories can contribute important insight to researchers and program planners attempting to alter HIV risk behavior in high-risk populations. ^

Procedure for the identification of population characteristics for targeting intervention services on the basis of outcome-goal priorities: Case management services for the chronic mentally ill

Although the processes involved in rational patient targeting may be obvious for certain services, for others, both the appropriate sub-populations to receive services and the procedures to be used for their identification may be unclear. This project was designed to address several research questions which arise in the attempt to deliver appropriate services to specific populations. The related difficulties are particularly evident for those interventions about which findings regarding effectiveness are conflicting. When an intervention clearly is not beneficial (or is dangerous) to a large, diverse population, consensus regarding withholding the intervention from dissemination can easily be reached. When findings are ambiguous, however, conclusions may be impossible.^ When characteristics of patients likely to benefit from an intervention are not obvious, and when the intervention is not significantly invasive or dangerous, the strategy proposed herein may be used to identify specific characteristics of sub-populations which may benefit from the intervention. The identification of these populations may be used both in further informing decisions regarding distribution of the intervention and for purposes of planning implementation of the intervention by identifying specific target populations for service delivery.^ This project explores a method for identifying such sub-populations through the use of related datasets generated from clinical trials conducted to test the effectiveness of an intervention. The method is specified in detail and tested using the example intervention of case management for outpatient treatment of populations with chronic mental illness. These analyses were applied in order to identify any characteristics which distinguish specific sub-populations who are more likely to benefit from case management service, despite conflicting findings regarding its effectiveness for the aggregate population, as reported in the body of related research. However, in addition to a limited set of characteristics associated with benefit, the findings generated, a larger set of characteristics of patients likely to experience greater improvement without intervention. ^

Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^