B Nandram | PubMed Health

PubMed1997

Bayesian analysis for a single 2 x 2 table.

The simple comparison of two binomial populations is frequently of interest in epidemiology when the domains are large. For small domains, however, there are no exact methods except Fisher's exact test. A basic problem, therefore, is to compare two populations by assessing the difference between the proportions of individuals who possess a characteristic in the first and second populations. When there is prior information, we take the proportions to have independent conjugate beta distributions with known parameters, thereby facilitating a Bayesian analysis. We consider Bayesian inference on functions of the proportions, and the three most common scalar measures used in epidemiology and health services research, namely relative risk, odds ratio and attributable risk. We develop the highest density regions (both exact and approximate) for relative risk, odds ratio and attributable risk. In addition, we consider the Bayes factor for testing whether the model with a common proportion holds rather than one with distinct proportions. Using data from the population-based Worcester Heart Attack Study, we apply our methodology to study gender differences in the therapeutic management of patients with acute myocardial infarction (AMI) by selected demographic and clinical characteristics. The Bayes factor, the approximate and exact intervals generally suggest that there are no substantial differences in the pharmacologic management of males and females hospitalized with AMI.

Adult↗

PubMed1995

Collimator optimization for lesion detection incorporating prior information about lesion size.

A Bayesian estimator has been developed as a paradigm for human observer performance in detecting lesions of unknown size in a uniform noisy background. The Bayesian observer used knowledge of the range of possible lesion sizes as a prior; its predictions agreed well with the results of a six-observer perceptual study. The average human response to changes in collimator resolution, as measured by the detectability index, dA, was tracked by the Bayesian detector's signal-to-noise ratio (SNR) somewhat better than by two other estimation models based, respectively, on lesser and greater degrees of lesion size uncertainty. As the range of possible lesion sizes increased, the Bayesian detector's SNR decreased and the optimal collimator resolution shifted towards better resolution. An analytic approximation for the variance of lesion activity estimates (which included the same prior) was shown to predict the variance of the Bayesian estimator over a wide range of collimator resolution values. Because the bias of the Bayesian estimator was small (< 1%), the analytic variance estimate permitted a rapid and convenient prediction of the Bayesian detection SNR. This calculation was then used to optimize the geometric parameters of a two-layer tungsten collimator being constructed from crossed grids for a new imaging detector. A Monte Carlo program was first run to estimate all contributions to the radial point-spread function for collimators of differing tungsten contents and spatial resolution values, imaging 140-keV photons emitted from the center of a 15-cm-diameter, water-filled attenuator. The optimal collimator design for detecting lesions with unknown diameters in the range 2.5-7.5 mm yielded a system resolution of approximately 8.5-mm FWHM, a geometric collimator efficiency of 1.21 x 10(-4), and a single-septum penetration probability of 1%.

Bayes Theorem↗