Statistical ConsultantAmerican College of Radiology Jan 2017 - Present
Joint Estimation of Mammographic Sensitivity and Tumor Growth
This dissertation develops two Bayesian models for jointly estimating mammographic sensitivity and tumor growth rates. First, we fit a two-measurement design, where each patient has exactly two tumor measurements, and provide a basic model for such data. Using a Metropolis-Hastings step to update values of the parameters, we utilized a Markov Chain Monte Carlo algorithm to sample iteratively from our posterior distribution. We then present our complete-measurement design. Its data would include all past negative mammograms and ages, symptomatic status at detection, and number of looks at each mammogram. We propose a joint likelihood to fit such an ideal dataset. In the cases of missing information or only one tumor measurement, we provide a marginal likelihood as well. Within our complete-measurement design, we require the probability of a woman being symptomatic given her age and tumor size. We present a non-parametric method to interpolate symptomatic counts of bivariate categorical data into finer bins of equal size. By assigning each symptomatic count a growth rate, we multiply-impute associated asymptomatic counts. Using these counts, we create a table of symptomatic probabilities over age and tumor size. We then generate twelve sets of 1000 patients, using pre-set values for our five parameters. Using the same MCMC approach with a Metropolis-Hastings step, we fit our complete-measurement design to each of the twelve sets of data. We present a comparison of our posterior MCMC means and pre-set values for the parameters of interest, and discuss possible bias issues.