Block-Conditional Missing at Random Models for Missing Data

Two major ideas in the analysis of missing data are (a) the EM algorithm [Dempster, Laird and Rubin, J. Roy. Statist. Soc. Ser. B 39 (1977) 1--38] for maximum likelihood (ML) estimation, and (b) the formulation of models for the joint distribution of the data ${Z}$ and missing data indicators ${M}$, and associated "missing at random"; (MAR) condition under which a model for ${M}$ is unnecessary [Rubin, Biometrika 63 (1976) 581--592]. Most previous work has treated ${Z}$ and ${M}$ as single blocks, yielding selection or pattern-mixture models depending on how their joint distribution is factorized. This paper explores "block-sequential"; models that interleave subsets of the variables and their missing data indicators, and then make parameter restrictions based on assumptions in each block. These include models that are not MAR. We examine a subclass of block-sequential models we call block-conditional MAR (BCMAR) models, and an associated block-monotone reduced likelihood strategy that typically yields consistent estimates by selectively discarding some data. Alternatively, full ML estimation can often be achieved via the EM algorithm. We examine in some detail BCMAR models for the case of two multinomially distributed categorical variables, and a two block structure where the first block is categorical and the second block arises from a (possibly multivariate) exponential family distribution.Comment: Published in at http://dx.doi.org/10.1214/10-STS344 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Meta-Analysis of Studies with Missing Data

Consider a meta-analysis of studies with varying proportions of patient-level missing data, and assume that each primary study has made certain missing data adjustments so that the reported estimates of treatment effect size and variance are valid. These estimates of treatment effects can be combined across studies by standard meta-analytic methods, employing a random-effects model to account for heterogeneity across studies. However, we note that a meta-analysis based on the standard random-effects model will lead to biased estimates when the attrition rates of primary studies depend on the size of the underlying study-level treatment effect. Perhaps ignorable within each study, these types of missing data are in fact not ignorable in a meta-analysis. We propose three methods to correct the bias resulting from such missing data in a meta-analysis: reweighting the DerSimonian–Laird estimate by the completion rate; incorporating the completion rate into a Bayesian random-effects model; and inference based on a Bayesian shared-parameter model that includes the completion rate. We illustrate these methods through a meta-analysis of 16 published randomized trials that examined combined pharmacotherapy and psychological treatment for depression.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66327/1/j.1541-0420.2008.01068.x.pd

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 pathological/physiological changes via qMRI, due to measurement errors or unpredictable influences. We use a hidden Markov random field to model the spatial dependence in the data 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. More importantly, we focus on the expected changes rather than image segmentation. 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.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS157 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Mixed-Effect Hybrid Models for Longitudinal Data with Nonignorable Dropout

Selection models and pattern-mixture models are often used to deal with nonignorable dropout in longitudinal studies. These two classes of models are based on different factorizations of the joint distribution of the outcome process and the dropout process. We consider a new class of models, called mixed-effect hybrid models (MEHMs), where the joint distribution of the outcome process and dropout process is factorized into the marginal distribution of random effects, the dropout process conditional on random effects, and the outcome process conditional on dropout patterns and random effects. MEHMs combine features of selection models and pattern-mixture models: they directly model the missingness process as in selection models, and enjoy the computational simplicity of pattern-mixture models. The MEHM provides a generalization of shared-parameter models (SPMs) by relaxing the conditional independence assumption between the measurement process and the dropout process given random effects. Because SPMs are nested within MEHMs, likelihood ratio tests can be constructed to evaluate the conditional independence assumption of SPMs. We use data from a pediatric AIDS clinical trial to illustrate the models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66099/1/j.1541-0420.2008.01102.x.pd

Estimating causal effects in trials involving multitreatment arms subject to non-compliance: a Bayesian framework

Data analysis for randomized trials including multitreatment arms is often complicated by subjects who do not comply with their treatment assignment. We discuss here methods of estimating treatment efficacy for randomized trials involving multitreatment arms subject to non-compliance. One treatment effect of interest in the presence of non-compliance is the complier average causal effect, which is defined as the treatment effect for subjects who would comply regardless of the treatment assigned. Following the idea of principal stratification, we define principal compliance in trials with three treatment arms, extend the complier average causal effect and define causal estimands of interest in this setting. In addition, we discuss structural assumptions that are needed for estimation of causal effects and the identifiability problem that is inherent in this setting from both a Bayesian and a classical statistical perspective. We propose a likelihood-based framework that models potential outcomes in this setting and a Bayes procedure for statistical inference. We compare our method with a method-of-moments approach that was proposed by Cheng and Small in 2006 by using a hypothetical data set, and we further illustrate our approach with an application to a behavioural intervention study.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79224/1/j.1467-9876.2009.00709.x.pd

A Case Study of Nonresponse Bias Analysis

Nonresponse bias is a widely prevalent problem for data collections. We develop a ten-step exemplar to guide nonresponse bias analysis (NRBA) in cross-sectional studies, and apply these steps to the Early Childhood Longitudinal Study, Kindergarten Class of 2010-11. A key step is the construction of indices of nonresponse bias based on proxy pattern-mixture models for survey variables of interest. A novel feature is to characterize the strength of evidence about nonresponse bias contained in these indices, based on the strength of relationship of the characteristics in the nonresponse adjustment with the key survey variables. Our NRBA incorporates missing at random and missing not at random mechanisms, and all analyses can be done straightforwardly with standard statistical software

Longitudinal image analysis of tumour–healthy brain change in contrast uptake induced by radiation

The work is motivated by a quantitative magnetic resonance imaging study of the differential tumour–healthy tissue change in contrast uptake induced by radiation. The goal is to determine the time in which there is maximal contrast uptake (a surrogate for permeability) in the tumour relative to healthy tissue. A notable feature of the data is its spatial heterogeneity. Zhang and co-workers have discussed two parallel approaches to ‘denoise’ a single image of change in contrast uptake from baseline to one follow-up visit of interest. In this work we extend the image model to explore the longitudinal profile of the tumour–healthy tissue contrast uptake in multiple images over time. We fit a two-stage model. First, we propose a longitudinal image model for each subject. This model simultaneously accounts for the spatial and temporal correlation and denoises the observed images by borrowing strength both across neighbouring pixels and over time. We propose to use the Mann–Whitney U -statistic to summarize the tumour contrast uptake relative to healthy tissue. In the second stage, we fit a population model to the U -statistic and estimate when it achieves its maximum. Our initial findings suggest that the maximal contrast uptake of the tumour core relative to healthy tissue peaks around 3 weeks after initiation of radiotherapy, though this warrants further investigation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79255/1/j.1467-9876.2010.00718.x.pd

Indices of nonâ ignorable selection bias for proportions estimated from nonâ probability samples

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151805/1/rssc12371_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151805/2/rssc12371.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151805/3/rssc12371-sup-0001-SupInfo.pd

Evaluation of a brief tailored motivational intervention to prevent early childhood caries

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87108/1/j.1600-0528.2011.00613.x.pd