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46
Adjusting for nonignorable dropout using semiparametric nonresponse models (with discussion
 Journal of the American Statistical Association
, 1999
"... Consider a study whose design calls for the study subjects to be followed from enrollment (time t = 0) to time t = T,at which point a primary endpoint of interest Y is to be measured. The design of the study also calls for measurements on a vector V(t) of covariates to be made at one or more times t ..."
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Cited by 39 (10 self)
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Consider a study whose design calls for the study subjects to be followed from enrollment (time t = 0) to time t = T,at which point a primary endpoint of interest Y is to be measured. The design of the study also calls for measurements on a vector V(t) of covariates to be made at one or more times t during the interval [0,T). We are interested in making inferences about the marginal mean µ0 of Y when some subjects drop out of the study at random times Q prior to the common fixed end of followup time T. The purpose of this article is to show how to make inferences about µ0 when the continuous dropout time Q is modeled semiparametrically and no restrictions are placed on the joint distribution of the outcome and other measured variables. In particular, we consider two models for the conditional hazard of dropout given ( ¯ V(T), Y), where ¯ V(t) denotes the history of the process V(t) through time t, t ∈ [0,T). In the first model, we assume that λQ(t  ¯ V(T), Y) = λ0(t  ¯ V(t)) exp(α0Y), where α0 is a scalar parameter and λ0(t  ¯ V(t)) is an unrestricted positive function of t and the process ¯ V(t). When the process ¯ V(t) is high dimensional, estimation in this model is not feasible with moderate sample sizes, due to the curse of dimensionality. For such situations, we consider a second model that imposes the additional restriction that λ0(t  ¯ V(t)) = λ0(t) exp(γ ′ 0W(t)), where λ0(t) is an unspecified baseline hazard function, W(t) = w(t, ¯ V(t)), w(·, ·) is a known function that maps (t, ¯ V(t)) to Rq, and γ0 is a q × 1 unknown parameter vector. When α0 � = 0, then dropout is nonignorable. On account of identifiability problems, joint estimation of the mean µ0 of Y and the selection bias parameter α0 may be difficult or impossible. Therefore, we propose regarding the selection bias parameter α0 as known, rather than estimating it from the data. We then perform a sensitivity analysis to see how inference about µ0 changes as we vary α0 over a plausible range of values. We apply our approach to the analysis of ACTG 175, an AIDS clinical trial. KEY WORDS: Augmented inverse probability of censoring weighted estimators; Cox proportional hazards model; Identification;
Statistical Themes and Lessons for Data Mining
, 1997
"... Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statist ..."
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Cited by 32 (3 self)
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Data mining is on the interface of Computer Science and Statistics, utilizing advances in both disciplines to make progress in extracting information from large databases. It is an emerging field that has attracted much attention in a very short period of time. This article highlights some statistical themes and lessons that are directly relevant to data mining and attempts to identify opportunities where close cooperation between the statistical and computational communities might reasonably provide synergy for further progress in data analysis.
Applications of randomeffects patternmixture models for missing data in longitudinal studies. Psychol Methods
, 1997
"... Randomeffects regression models have become increasingly popular for analysis of longitudinal data. A key advantage of the randomeffects approach is that it can be applied when subjects are not measured at the same number of timepoints. In this article we describe use of randomeffects patternmix ..."
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Cited by 25 (4 self)
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Randomeffects regression models have become increasingly popular for analysis of longitudinal data. A key advantage of the randomeffects approach is that it can be applied when subjects are not measured at the same number of timepoints. In this article we describe use of randomeffects patternmixture models to further handle and describe the influence of missing data in longitudinal studies. For this approach, subjects are first divided into groups depending on their missingdata pattern and then variables based on these groups are used as model covariates. Tn this way, researchers are able to examine the effect of missingdata patterns on the outcome (or outcomes) of interest. Furthermore, overall estimates can be obtained by averaging over the missingdata patterns. A psychiatric clinical trials data set is used to illustrate the randomeffects patternmixture approach to longitudinal data analysis with missing data. Longitudinal studies occupy an important role in psychological and psychiatric research. In these studies the same individuals are repeatedly measured on a number of important variables over a series of timepoints. As an example, a longitudinal design is often used to determine whether a particular therapeutic agent can produce changes in clinical status over the course of an illness. Another application for the longitudinal study is to assess potential indicators of a change, in the subject's clinical status; for example, the assessment of whether drug plasma level measurements indicate clinical outcome. Even in wellcontrolled situations, missing data invariably occur in longitudinal studies. Subjects can be
Mplus: Statistical Analysis with Latent Variables (Version 4.21) [Computer software
, 2007
"... Chapter 3: Regression and path analysis 19 Chapter 4: Exploratory factor analysis 43 ..."
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Cited by 23 (0 self)
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Chapter 3: Regression and path analysis 19 Chapter 4: Exploratory factor analysis 43
Optimal pricing of new subscription services: Analysis of a market experiment
 Marketing Science
, 2002
"... There are now available a number of new subscription services that comprise a dual pricing system of a monthly access fee (rental) and a perminute usage charge. Examples include cellular phones, the Internet, and pay TV. The usage and retention of such services depend on the absolute and relative p ..."
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Cited by 18 (0 self)
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There are now available a number of new subscription services that comprise a dual pricing system of a monthly access fee (rental) and a perminute usage charge. Examples include cellular phones, the Internet, and pay TV. The usage and retention of such services depend on the absolute and relative prices of this dual system. For instance, a moderate access fee but a lowusage charge might initially appeal to customers, but later a lowusage customer might find the monthly fee unjustified and thereby relinquish the service. Providers of such services, therefore, usually offer several pricing packages to cater to differing customer needs. The purpose of this study is to derive a revenuemaximizing strategy for subscription services, that is, the combination of access and usage price that maximizes revenue over a specified
Multiple imputation for model checking: Completeddata plots with missing and latent data
 Biometrics
, 2005
"... Summary. In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset—corresponding to the observed data and imputed unobserved data—using standard procedures for completedata inference. Here, we ..."
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Cited by 11 (3 self)
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Summary. In problems with missing or latent data, a standard approach is to first impute the unobserved data, then perform all statistical analyses on the completed dataset—corresponding to the observed data and imputed unobserved data—using standard procedures for completedata inference. Here, we extend this approach to model checking by demonstrating the advantages of the use of completeddata model diagnostics on imputed completed datasets. The approach is set in the theoretical framework of Bayesian posterior predictive checks (but, as with missingdata imputation, our methods of missingdata model checking can also be interpreted as “predictive inference ” in a nonBayesian context). We consider the graphical diagnostics within this framework. Advantages of the completeddata approach include: (1) One can often check model fit in terms of quantities that are of key substantive interest in a natural way, which is not always possible using observed data alone. (2) In problems with missing data, checks may be devised that do not require to model the missingness or inclusion mechanism; the latter is useful for the analysis of ignorable but unknown data collection mechanisms, such as are often assumed in the analysis of sample surveys and observational studies. (3) In many problems with latent data, it is possible to check qualitative features of the model (for example, independence of two variables) that can be naturally formalized with the help of the latent data. We illustrate with several applied examples.
Much Ado About Nothing: A Comparison of Missing Data Methods and Software to Fit Incomplete Data Regression Models
"... Missing data are a recurring problem that can cause bias or lead to inefficient analyses. Statistical methods to address missingness have been actively pursued in recent years, including imputation, likelihood, and weighting approaches. Each approach is more complicated when there are many patterns ..."
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Cited by 10 (0 self)
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Missing data are a recurring problem that can cause bias or lead to inefficient analyses. Statistical methods to address missingness have been actively pursued in recent years, including imputation, likelihood, and weighting approaches. Each approach is more complicated when there are many patterns of missing values, or when both categorical and continuous random variables are involved. Implementations of routines to incorporate observations with incomplete variables in regression models are now widely available. We review these routines in the context of a motivating example from a large health services research dataset. While there are still limitations to the current implementations, and additional efforts are required of the analyst, it is feasible to incorporate partially observed values, and these methods should be used in practice.
Simultaneous Modelling of the Cholesky Decomposition of Several Covariance Matrices
 J. Multivar. Anal
, 2006
"... A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the classical ..."
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Cited by 8 (3 self)
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A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the classical spectral (eigenvalue) and variancecorrelation decompositions. All these methods amount to decomposing complicated covariance matrices into “dependence” and “variance” components, and then modelling them virtually separately using regression techniques. The entries of the “dependence” component of the Cholesky decomposition have the unique advantage of being unconstrained so that further reduction of the dimension of its parameter space is fairly simple. Normal theory maximum likelihood estimates for complete and incomplete data are presented using iterative methods such as EM (ExpectationMaximization) algorithm and their improvements. These procedures are illustrated using a dataset from a growth hormone longitudinal clinical trial.
Methods for Conducting Sensitivity Analysis of Trials with Potentially Nonignorable Competing Causes of Censoring
"... : We consider inference for the treatmentarm mean difference of an outcome that would have been measured at the end of a randomized followup study if, during the course of the study, patients had not initiated a nonrandomized therapy or dropped out. We argue that the treatmentarm mean difference ..."
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Cited by 7 (3 self)
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: We consider inference for the treatmentarm mean difference of an outcome that would have been measured at the end of a randomized followup study if, during the course of the study, patients had not initiated a nonrandomized therapy or dropped out. We argue that the treatmentarm mean difference is not identified unless unverifiable assumptions are made. We describe identifying assumptions that are tantamount to postulating relationships between the components of a patternmixture model, but can also be interpreted as imposing restrictions on the causespecific censoring probabilities of a selection model. We then argue that although sufficient for identification, these assumptions are insufficient for inference due to the curse of dimensionality. We propose reducing dimensionality by specifying semiparametric causespecific selection models. These models are useful for conducting a sensitivity analysis to examine how inference for the treatmentarm mean difference changes as one v...
Diagnostics for Multivariate Imputations ∗
, 2007
"... We consider three sorts of diagnostics for random imputations: (a) displays of the completed data, intended to reveal unusual patterns that might suggest problems with the imputations, (b) comparisons of the distributions of observed and imputed data values, and (c) checks of the fit of observed dat ..."
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Cited by 6 (2 self)
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We consider three sorts of diagnostics for random imputations: (a) displays of the completed data, intended to reveal unusual patterns that might suggest problems with the imputations, (b) comparisons of the distributions of observed and imputed data values, and (c) checks of the fit of observed data to the model used to create the imputations. We formulate these methods in terms of sequential regression multivariate imputation [Van Buuren and Oudshoom 2000, and Raghunathan, Van Hoewyk, and Solenberger 2001], an iterative procedure in which the missing values of each variable are randomly imputed conditional on all the other variables in the completed data matrix. We also consider a recalibration procedure for sequential regression imputations. We apply these methods to the 2002 Environmental Sustainability Index (ESI), a linear aggregation of 64 environmental variables on 142 countries. 1