Comment: Struggles with Survey Weighting and Regression Modeling

Comment: Struggles with Survey Weighting and Regression Modeling [arXiv:0710.5005]Comment: Published in at http://dx.doi.org/10.1214/088342307000000186 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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

Turning marketing promises into business value: The experience of an industrial SME

The article studies the value that businesses should have for their customers and shareholders. It explains how to develop such value to meet or exceed customer's expectations through the application of the promise framework. The promise model includes promises made to customers, promises kept, and promises that involve a synchronized effort from the whole firm to create and deliver value to customers

AN ANALYSIS OF NONIGNORABLE NONRESPONSE IN A SURVEY WITH A ROTATING PANEL DESIGN

Missing values to income questions are common in survey data. When the probabilities of nonresponse are assumed to depend on the observed information and not on the underlining unobserved amounts, the missing income values are missing at random (MAR), and methods such as sequential multiple imputation can be applied. However, the MAR assumption is often considered questionable in this context, since missingness of income is thought to be related to the value of income itself, after conditioning on available covariates. In this article we describe a sensitivity analysis based on a pattern-mixture model for deviations from MAR, in the context of missing income values in a rotating panel survey. The sensitivity analysis avoids the well-known problems of underidentification of parameters of non-MAR models, is easy to carry out using existing sequential multiple imputation software and has a number of novel features

MISSING AT RANDOM AND IGNORABILITY FOR INFERENCES ABOUT SUBSETS OF PARAMETERS WITH MISSING DATA

For likelihood-based inferences from data with missing values, Rubin (1976) showed that the missing data mechanism can be ignored when (a) the missing data are missing at random (MAR), in the sense that missingness does not depend on the missing values after conditioning on the observed data, and (b) the parameters of the data model and the missing-data mechanism are distinct; that is, there are no a priori ties, via parameter space restrictions or prior distributions, between the parameters of the data model and the parameters of the model for the mechanism. Rubin described (a) and (b) as the weakest simple and general conditions under which it is always appropriate to ignore the process that causes missing data . However, these conditions are not always necessary. Also, they relate to the complete set of parameters in the model, but we argue that it would be useful to have definitions of MAR and ignorability for a subset of parameters of substantive interest. We propose such definitions, and apply them to a variety of examples where the missing data mechanism is missing not at random, but MAR or ignorable for the parameter subset

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

Estimating Causal Effects in Trials Involving Multi-treatment Arms Subject to Non-compliance: A Bayesian Frame-work

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

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

We consider assessment of the impact of nonresponse for a binary survey variable Y subject to nonresponse, when there is a set of covariates observed for nonrespondents and respondents. To reduce dimensionality and for simplicity we reduce the covariates to a continuous proxy variable X that has the highest correlation with Y, estimated from a probit regression analysis of respondent data. We extend our previously proposed proxy-pattern mixture analysis (PPMA) for continuous outcomes to the binary outcome using a latent variable approach. The method does not assume data are missing at random, and creates a framework for sensitivity analyses. Maximum likelihood, Bayesian, and multiple imputation versions of PPMA are described, and robustness of these methods to model assumptions are discussed. Properties are demonstrated through simulation and with data from the Ohio Family Health Survey (OFHS)