A Bayesian Image Analysis of the Change in Tumor/Brain Contrast Uptake Induced by Radiation via Reversible Jump Markov Chain Monte Carlo

This work is motivated by a pilot study on the change in tumor/brain contrast uptake induced by radiation via quantitative Magnetic Resonance Imaging. The results inform the optimal timing of administering chemotherapy in the context of radiotherapy. A noticeable feature of the data is spatial heterogeneity. The tumor is physiologically and pathologically distinct from surrounding healthy tissue. Also, the tumor itself is usually highly heterogeneous. We employ a Gaussian Hidden Markov Random Field model that respects the above features. The model introduces a latent layer of discrete labels from an Markov Random Field (MRF) governed by a spatial regularization parameter. We further assume that conditional on the hidden labels, the observed data are independent and normally distributed, We treat the regularization parameter of the MRF, as well as the number of states of the MRF as parameters, and estimate them via the Reversible Jump Markov chain Monte Carlo algorithm. We propose a novel and nontrivial implementation of the Reversible Jump moves. The performance of the method is examined in both simulation studies and real data analysis. We report the pixel-wise posterior mean and standard deviation of the change in contrast uptake marginalized over the number of states and hidden labels. We also compare the performance with a Markov chain with fixed number of states and a parallel Expectation-Maximization approach from a frequentist perspective

Quantitative Magnetic Resonance Image Analysis via the EM Algorithm with Stochastic Variation

Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight into pathological and physiological alterations of living tissue, with the help of which, researchers hope to predict (local) therapeutic efficacy early and determine optimal treatment schedule. However, the analysis of qMRI has been limited to ad-hoc heuristic methods. Our research provides a powerful statistical framework for image analysis and sheds light on future localized adaptive treatment regimes tailored to the individual’s response. We assume in an imperfect world we only observe a blurred and noisy version of the underlying “true” scene via qMRI, due to measurement errors or unpredictable influences. We use a hidden Markov Random Field to model the unobserved “true” scene and develop a maximum likelihood approach via the Expectation-Maximization algorithm with stochastic variation. An important improvement over previous work is the assessment of variability in parameter estimation, which is the valid basis for statistical inference. Moreover, we focus on recovering the “true” scene rather than segmenting the image. Our research has shown that the approach is powerful in both simulation studies and on a real dataset, while quite robust in the presence of some model assumption violations

Proxy Pattern-Mixture Analysis for a Binary Variable Subject to Nonresponse

Given increasing survey nonresponse, good measures of the potential impact of nonresponse on survey estimates are particularly important. Existing measures, such as the R-indicator, make the strong assumption that missingness is missing at random, meaning that it depends only on variables that are observed for respondents and nonrespondents. We consider assessment of the impact of nonresponse for a binary survey variable Y subject to nonresponse when missingness may be not at random, meaning that missingness may depend on Y itself. Our work is motivated by missing categorical income data in the 2015 Ohio Medicaid Assessment Survey (OMAS), where whether or not income is missing may be related to the income value itself, with low-income earners more reluctant to respond. We assume there is a set of covariates observed for nonrespondents and respondents, which for the item nonresponse (as in OMAS) is often a rich set of variables, but which may be potentially limited in cases of unit nonresponse. To reduce dimensionality and for simplicity we reduce these available covariates to a continuous proxy variable X, available for both respondents and nonrespondents, that has the highest correlation with Y, estimated from a probit regression analysis of respondent data. We extend the previously proposed proxy-pattern mixture (PPM) analysis for continuous outcomes to the binary outcome using a latent variable approach for modeling the joint distribution of Y and X. Our method does not assume data are missing at random but includes it as a special case, thus creating a convenient framework for sensitivity analyses. Maximum likelihood, Bayesian, and multiple imputation versions of PPM analysis are described, and robustness of these methods to model assumptions is discussed. Properties are demonstrated through simulation and with the 2015 OMAS data

Bayesian sensitivity analyses for longitudinal data with dropouts that are potentially missing not at random: A high dimensional pattern‐mixture model

Randomized clinical trials with outcome measured longitudinally are frequently analyzed using either random effect models or generalized estimating equations. Both approaches assume that the dropout mechanism is missing at random (MAR) or missing completely at random (MCAR). We propose a Bayesian pattern‐mixture model to incorporate missingness mechanisms that might be missing not at random (MNAR), where the distribution of the outcome measure at the follow‐up time tk, conditional on the prior history, differs across the patterns of missing data. We then perform sensitivity analysis on estimates of the parameters of interest. The sensitivity parameters relate the distribution of the outcome of interest between subjects from a missing‐data pattern at time tk with that of the observed subjects at time tk. The large number of the sensitivity parameters is reduced by treating them as random with a prior distribution having some pre‐specified mean and variance, which are varied to explore the sensitivity of inferences. The missing at random (MAR) mechanism is a special case of the proposed model, allowing a sensitivity analysis of deviations from MAR. The proposed approach is applied to data from the Trial of Preventing Hypertension.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/169265/1/sim9083.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/169265/2/sim9083_am.pd