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Jonathan S Schildcrout - One of the best experts on this subject based on the ideXlab platform.
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outcome dependent sampling for longitudinal Binary Response data based on a time varying auxiliary variable
Statistics in Medicine, 2012Co-Authors: Jonathan S Schildcrout, Sunni L Mumford, Zhen Chen, Patrick J Heagerty, Paul J RathouzAbstract:Outcome-dependent sampling (ODS) study designs are commonly implemented with rare diseases or when prospective studies are infeasible. In longitudinal data settings, when a repeatedly measured Binary Response is rare, an ODS design can be highly efficient for maximizing statistical information subject to resource limitations that prohibit covariate ascertainment of all observations. This manuscript details an ODS design where individual observations are sampled with probabilities determined by an inexpensive, time-varying auxiliary variable that is related but is not equal to the Response. With the goal of validly estimating marginal model parameters based on the resulting biased sample, we propose a semi-parametric, sequential offsetted logistic regressions (SOLR) approach. The SOLR strategy first estimates the relationship between the auxiliary variable and the Response and covariate data by using an offsetted logistic regression analysis where the offset is used to adjust for the biased design. Results from the auxiliary variable model are then combined with the known or estimated sampling probabilities to formulate a second offset that is used to correct for the biased design in the ultimate target model relating the longitudinal Binary Response to covariates. Because the target model offset is estimated with SOLR, we detail asymptotic standard error estimates that account for uncertainty associated with the auxiliary variable model. Motivated by an analysis of the BioCycle Study (Gaskins et al., Effect of daily fiber intake on reproductive function: the BioCycle Study. American Journal of Clinical Nutrition 2009; 90(4): 1061–1069) that aims to describe the relationship between reproductive health (determined by luteinizing hormone levels) and fiber consumption, we examine properties of SOLR estimators and compare them with other common approaches. Copyright © 2011 John Wiley & Sons, Ltd.
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outcome dependent sampling for longitudinal Binary Response data based on a time varying auxiliary variable
Statistics in Medicine, 2012Co-Authors: Jonathan S Schildcrout, Sunni L Mumford, Zhen Chen, Patrick J Heagerty, Paul J RathouzAbstract:Outcome-dependent sampling (ODS) study designs are commonly implemented with rare diseases or when prospective studies are infeasible. In longitudinal data settings, when a repeatedly measured Binary Response is rare, an ODS design can be highly efficient for maximizing statistical information subject to resource limitations that prohibit covariate ascertainment of all observations. This manuscript details an ODS design where individual observations are sampled with probabilities determined by an inexpensive, time-varying auxiliary variable that is related but is not equal to the Response. With the goal of validly estimating marginal model parameters based on the resulting biased sample, we propose a semi-parametric, sequential offsetted logistic regressions (SOLR) approach. The SOLR strategy first estimates the relationship between the auxiliary variable and the Response and covariate data by using an offsetted logistic regression analysis where the offset is used to adjust for the biased design. Results from the auxiliary variable model are then combined with the known or estimated sampling probabilities to formulate a second offset that is used to correct for the biased design in the ultimate target model relating the longitudinal Binary Response to covariates. Because the target model offset is estimated with SOLR, we detail asymptotic standard error estimates that account for uncertainty associated with the auxiliary variable model. Motivated by an analysis of the BioCycle Study (Gaskins et al., Effect of daily fiber intake on reproductive function: the BioCycle Study. American Journal of Clinical Nutrition 2009; 90(4): 1061-1069) that aims to describe the relationship between reproductive health (determined by luteinizing hormone levels) and fiber consumption, we examine properties of SOLR estimators and compare them with other common approaches.
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longitudinal studies of Binary Response data following case control and stratified case control sampling design and analysis
Biometrics, 2010Co-Authors: Jonathan S Schildcrout, Paul J RathouzAbstract:We discuss design and analysis of longitudinal studies after case-control sampling, wherein interest is in the relationship between a longitudinal Binary Response that is related to the sampling (case-control) variable, and a set of covariates. We propose a semiparametric modeling framework based on a marginal longitudinal Binary Response model and an ancillary model for subjects' case-control status. In this approach, the analyst must posit the population prevalence of being a case, which is then used to compute an offset term in the ancillary model. Parameter estimates from this model are used to compute offsets for the longitudinal Response model. Examining the impact of population prevalence and ancillary model misspecification, we show that time-invariant covariate parameter estimates, other than the intercept, are reasonably robust, but intercept and time-varying covariate parameter estimates can be sensitive to such misspecification. We study design and analysis issues impacting study efficiency, namely: choice of sampling variable and the strength of its relationship to the Response, sample stratification, choice of working covariance weighting, and degree of flexibility of the ancillary model. The research is motivated by a longitudinal study following case-control sampling of the time course of attention deficit hyperactivity disorder (ADHD) symptoms.
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on outcome dependent sampling designs for longitudinal Binary Response data with time varying covariates
Biostatistics, 2008Co-Authors: Jonathan S Schildcrout, Patrick J HeagertyAbstract:A typical longitudinal study prospectively collects both repeated measures of a health status outcome as well as covariates that are used either as the primary predictor of interest or as important adjustment factors. In many situations, all covariates are measured on the entire study cohort. However, in some scenarios the primary covariates are time dependent yet may be ascertained retrospectively after completion of the study. One common example would be covariate measurements based on stored biological specimens such as blood plasma. While authors have previously proposed generalizations of the standard case-control design in which the clustered outcome measurements are used to selectively ascertain covariates (Neuhaus and Jewell, 1990) and therefore provide resource efficient collection of information, these designs do not appear to be commonly used. One potential barrier to the use of longitudinal outcome-dependent sampling designs would be the lack of a flexible class of likelihood-based analysis methods. With the relatively recent development of flexible and practical methods such as generalized linear mixed models (Breslow and Clayton, 1993) and marginalized models for categorical longitudinal data (see Heagerty and Zeger, 2000, for an overview), the class of likelihood-based methods is now sufficiently well developed to capture the major forms of longitudinal correlation found in biomedical repeated measures data. Therefore, the goal of this manuscript is to promote the consideration of outcome-dependent longitudinal sampling designs and to both outline and evaluate the basic conditional likelihood analysis allowing for valid statistical inference.
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Marginalized Models for Moderate to Long Series of Longitudinal Binary Response Data
Biometrics, 2006Co-Authors: Jonathan S Schildcrout, Patrick J HeagertyAbstract:Summary Marginalized models (Heagerty, 1999, Biometrics55, 688–698) permit likelihood-based inference when interest lies in marginal regression models for longitudinal Binary Response data. Two such models are the marginalized transition and marginalized latent variable models. The former captures within-subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing Response dependence using random intercepts. In this article, we extend the class of marginalized models by proposing a single unifying model that describes both serial and long-range dependence. This model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject, where both serial and exchangeable forms of Response correlation can be identified. We describe maximum likelihood and Bayesian approaches toward parameter estimation and inference, and we study the large sample operating characteristics under two types of dependence model misspecification. Data from the Madras Longitudinal Schizophrenia Study (Thara et al., 1994, Acta Psychiatrica Scandinavica90, 329–336) are analyzed.
Paul J Rathouz - One of the best experts on this subject based on the ideXlab platform.
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outcome dependent sampling for longitudinal Binary Response data based on a time varying auxiliary variable
Statistics in Medicine, 2012Co-Authors: Jonathan S Schildcrout, Sunni L Mumford, Zhen Chen, Patrick J Heagerty, Paul J RathouzAbstract:Outcome-dependent sampling (ODS) study designs are commonly implemented with rare diseases or when prospective studies are infeasible. In longitudinal data settings, when a repeatedly measured Binary Response is rare, an ODS design can be highly efficient for maximizing statistical information subject to resource limitations that prohibit covariate ascertainment of all observations. This manuscript details an ODS design where individual observations are sampled with probabilities determined by an inexpensive, time-varying auxiliary variable that is related but is not equal to the Response. With the goal of validly estimating marginal model parameters based on the resulting biased sample, we propose a semi-parametric, sequential offsetted logistic regressions (SOLR) approach. The SOLR strategy first estimates the relationship between the auxiliary variable and the Response and covariate data by using an offsetted logistic regression analysis where the offset is used to adjust for the biased design. Results from the auxiliary variable model are then combined with the known or estimated sampling probabilities to formulate a second offset that is used to correct for the biased design in the ultimate target model relating the longitudinal Binary Response to covariates. Because the target model offset is estimated with SOLR, we detail asymptotic standard error estimates that account for uncertainty associated with the auxiliary variable model. Motivated by an analysis of the BioCycle Study (Gaskins et al., Effect of daily fiber intake on reproductive function: the BioCycle Study. American Journal of Clinical Nutrition 2009; 90(4): 1061–1069) that aims to describe the relationship between reproductive health (determined by luteinizing hormone levels) and fiber consumption, we examine properties of SOLR estimators and compare them with other common approaches. Copyright © 2011 John Wiley & Sons, Ltd.
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outcome dependent sampling for longitudinal Binary Response data based on a time varying auxiliary variable
Statistics in Medicine, 2012Co-Authors: Jonathan S Schildcrout, Sunni L Mumford, Zhen Chen, Patrick J Heagerty, Paul J RathouzAbstract:Outcome-dependent sampling (ODS) study designs are commonly implemented with rare diseases or when prospective studies are infeasible. In longitudinal data settings, when a repeatedly measured Binary Response is rare, an ODS design can be highly efficient for maximizing statistical information subject to resource limitations that prohibit covariate ascertainment of all observations. This manuscript details an ODS design where individual observations are sampled with probabilities determined by an inexpensive, time-varying auxiliary variable that is related but is not equal to the Response. With the goal of validly estimating marginal model parameters based on the resulting biased sample, we propose a semi-parametric, sequential offsetted logistic regressions (SOLR) approach. The SOLR strategy first estimates the relationship between the auxiliary variable and the Response and covariate data by using an offsetted logistic regression analysis where the offset is used to adjust for the biased design. Results from the auxiliary variable model are then combined with the known or estimated sampling probabilities to formulate a second offset that is used to correct for the biased design in the ultimate target model relating the longitudinal Binary Response to covariates. Because the target model offset is estimated with SOLR, we detail asymptotic standard error estimates that account for uncertainty associated with the auxiliary variable model. Motivated by an analysis of the BioCycle Study (Gaskins et al., Effect of daily fiber intake on reproductive function: the BioCycle Study. American Journal of Clinical Nutrition 2009; 90(4): 1061-1069) that aims to describe the relationship between reproductive health (determined by luteinizing hormone levels) and fiber consumption, we examine properties of SOLR estimators and compare them with other common approaches.
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longitudinal studies of Binary Response data following case control and stratified case control sampling design and analysis
Biometrics, 2010Co-Authors: Jonathan S Schildcrout, Paul J RathouzAbstract:We discuss design and analysis of longitudinal studies after case-control sampling, wherein interest is in the relationship between a longitudinal Binary Response that is related to the sampling (case-control) variable, and a set of covariates. We propose a semiparametric modeling framework based on a marginal longitudinal Binary Response model and an ancillary model for subjects' case-control status. In this approach, the analyst must posit the population prevalence of being a case, which is then used to compute an offset term in the ancillary model. Parameter estimates from this model are used to compute offsets for the longitudinal Response model. Examining the impact of population prevalence and ancillary model misspecification, we show that time-invariant covariate parameter estimates, other than the intercept, are reasonably robust, but intercept and time-varying covariate parameter estimates can be sensitive to such misspecification. We study design and analysis issues impacting study efficiency, namely: choice of sampling variable and the strength of its relationship to the Response, sample stratification, choice of working covariance weighting, and degree of flexibility of the ancillary model. The research is motivated by a longitudinal study following case-control sampling of the time course of attention deficit hyperactivity disorder (ADHD) symptoms.
Patrick J Heagerty - One of the best experts on this subject based on the ideXlab platform.
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outcome dependent sampling for longitudinal Binary Response data based on a time varying auxiliary variable
Statistics in Medicine, 2012Co-Authors: Jonathan S Schildcrout, Sunni L Mumford, Zhen Chen, Patrick J Heagerty, Paul J RathouzAbstract:Outcome-dependent sampling (ODS) study designs are commonly implemented with rare diseases or when prospective studies are infeasible. In longitudinal data settings, when a repeatedly measured Binary Response is rare, an ODS design can be highly efficient for maximizing statistical information subject to resource limitations that prohibit covariate ascertainment of all observations. This manuscript details an ODS design where individual observations are sampled with probabilities determined by an inexpensive, time-varying auxiliary variable that is related but is not equal to the Response. With the goal of validly estimating marginal model parameters based on the resulting biased sample, we propose a semi-parametric, sequential offsetted logistic regressions (SOLR) approach. The SOLR strategy first estimates the relationship between the auxiliary variable and the Response and covariate data by using an offsetted logistic regression analysis where the offset is used to adjust for the biased design. Results from the auxiliary variable model are then combined with the known or estimated sampling probabilities to formulate a second offset that is used to correct for the biased design in the ultimate target model relating the longitudinal Binary Response to covariates. Because the target model offset is estimated with SOLR, we detail asymptotic standard error estimates that account for uncertainty associated with the auxiliary variable model. Motivated by an analysis of the BioCycle Study (Gaskins et al., Effect of daily fiber intake on reproductive function: the BioCycle Study. American Journal of Clinical Nutrition 2009; 90(4): 1061–1069) that aims to describe the relationship between reproductive health (determined by luteinizing hormone levels) and fiber consumption, we examine properties of SOLR estimators and compare them with other common approaches. Copyright © 2011 John Wiley & Sons, Ltd.
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outcome dependent sampling for longitudinal Binary Response data based on a time varying auxiliary variable
Statistics in Medicine, 2012Co-Authors: Jonathan S Schildcrout, Sunni L Mumford, Zhen Chen, Patrick J Heagerty, Paul J RathouzAbstract:Outcome-dependent sampling (ODS) study designs are commonly implemented with rare diseases or when prospective studies are infeasible. In longitudinal data settings, when a repeatedly measured Binary Response is rare, an ODS design can be highly efficient for maximizing statistical information subject to resource limitations that prohibit covariate ascertainment of all observations. This manuscript details an ODS design where individual observations are sampled with probabilities determined by an inexpensive, time-varying auxiliary variable that is related but is not equal to the Response. With the goal of validly estimating marginal model parameters based on the resulting biased sample, we propose a semi-parametric, sequential offsetted logistic regressions (SOLR) approach. The SOLR strategy first estimates the relationship between the auxiliary variable and the Response and covariate data by using an offsetted logistic regression analysis where the offset is used to adjust for the biased design. Results from the auxiliary variable model are then combined with the known or estimated sampling probabilities to formulate a second offset that is used to correct for the biased design in the ultimate target model relating the longitudinal Binary Response to covariates. Because the target model offset is estimated with SOLR, we detail asymptotic standard error estimates that account for uncertainty associated with the auxiliary variable model. Motivated by an analysis of the BioCycle Study (Gaskins et al., Effect of daily fiber intake on reproductive function: the BioCycle Study. American Journal of Clinical Nutrition 2009; 90(4): 1061-1069) that aims to describe the relationship between reproductive health (determined by luteinizing hormone levels) and fiber consumption, we examine properties of SOLR estimators and compare them with other common approaches.
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on outcome dependent sampling designs for longitudinal Binary Response data with time varying covariates
Biostatistics, 2008Co-Authors: Jonathan S Schildcrout, Patrick J HeagertyAbstract:A typical longitudinal study prospectively collects both repeated measures of a health status outcome as well as covariates that are used either as the primary predictor of interest or as important adjustment factors. In many situations, all covariates are measured on the entire study cohort. However, in some scenarios the primary covariates are time dependent yet may be ascertained retrospectively after completion of the study. One common example would be covariate measurements based on stored biological specimens such as blood plasma. While authors have previously proposed generalizations of the standard case-control design in which the clustered outcome measurements are used to selectively ascertain covariates (Neuhaus and Jewell, 1990) and therefore provide resource efficient collection of information, these designs do not appear to be commonly used. One potential barrier to the use of longitudinal outcome-dependent sampling designs would be the lack of a flexible class of likelihood-based analysis methods. With the relatively recent development of flexible and practical methods such as generalized linear mixed models (Breslow and Clayton, 1993) and marginalized models for categorical longitudinal data (see Heagerty and Zeger, 2000, for an overview), the class of likelihood-based methods is now sufficiently well developed to capture the major forms of longitudinal correlation found in biomedical repeated measures data. Therefore, the goal of this manuscript is to promote the consideration of outcome-dependent longitudinal sampling designs and to both outline and evaluate the basic conditional likelihood analysis allowing for valid statistical inference.
-
Marginalized Models for Moderate to Long Series of Longitudinal Binary Response Data
Biometrics, 2006Co-Authors: Jonathan S Schildcrout, Patrick J HeagertyAbstract:Summary Marginalized models (Heagerty, 1999, Biometrics55, 688–698) permit likelihood-based inference when interest lies in marginal regression models for longitudinal Binary Response data. Two such models are the marginalized transition and marginalized latent variable models. The former captures within-subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing Response dependence using random intercepts. In this article, we extend the class of marginalized models by proposing a single unifying model that describes both serial and long-range dependence. This model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject, where both serial and exchangeable forms of Response correlation can be identified. We describe maximum likelihood and Bayesian approaches toward parameter estimation and inference, and we study the large sample operating characteristics under two types of dependence model misspecification. Data from the Madras Longitudinal Schizophrenia Study (Thara et al., 1994, Acta Psychiatrica Scandinavica90, 329–336) are analyzed.
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marginalized transition models and likelihood inference for longitudinal categorical data
Biometrics, 2002Co-Authors: Patrick J HeagertyAbstract:Summary. Marginal generalized linear models are now frequently used for the analysis of longitudinal data. Semiparametric inference for marginal models was introduced by Liang and Zeger (1986, Biometrics73, 13–22). This article develops a general parametric class of serial dependence models that permits likelihood-based marginal regression analysis of Binary Response data. The methods naturally extend the first-order Markov models of Azzalini (1994, Biometrika81, 767–775) and prove computationally feasible for long series.
Gary Chamberlain - One of the best experts on this subject based on the ideXlab platform.
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Binary Response models for panel data identification and information
Econometrica, 2010Co-Authors: Gary ChamberlainAbstract:This paper considers a panel data model for predicting a Binary outcome. The conditional probability of a positive Response is obtained by evaluating a given distribution function (F) at a linear combination of the predictor variables. One of the predictor variables is unobserved. It is a random effect that varies across individuals but is constant over time. The semiparametric aspect is that the conditional distribution of the random effect, given the predictor variables, is unrestricted. Copyright 2010 The Econometric Society.
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Binary Response models for panel data identification and information
Econometrica, 2010Co-Authors: Gary ChamberlainAbstract:This paper considers a panel data model for predicting a Binary outcome. The conditional probability of a positive Response is obtained by evaluating a given distribution function (F) at a linear combination of the predictor variables. One of the predictor variables is unobserved. It is a random effect that varies across individuals but is constant over time. The semiparametric aspect is that the conditional distribution of the random effect, given the predictor variables, is unrestricted. This paper has two results. If the support of the observed predictor variables is bounded, then identification is possible only in the logistic case. Even if the support is unbounded, so that (from Manski (1987)) identification holds quite generally, the information bound is zero unless F is logistic. Hence consistent estimation at the standard pn rate is possible only in the logistic case.
Roger Koenker - One of the best experts on this subject based on the ideXlab platform.
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nonparametric maximum likelihood methods for Binary Response models with random coefficients
Research Papers in Economics, 2018Co-Authors: Roger KoenkerAbstract:Single index linear models for Binary Response with random coefficients have been extensively employed in many econometric settings under various parametric specifications of the distribution of the random coefficients. Nonparametric maximum likelihood estimation (NPMLE) as proposed by Cosslett (1983) and Ichimura and Thompson (1998), in contrast, has received less attention in applied work due primarily to computational difficulties. We propose a new approach to computation of NPMLEs for Binary Response models that significantly increase their computational tractability thereby facilitating greater flexibility in applications. Our approach, which relies on recent developments involving the geometry of hyperplane arrangements, is contrasted with the recently proposed deconvolution method of Gautier and Kitamura (2013). An application to modal choice for the journey to work in the Washington DC area illustrates the methods.
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nonparametric maximum likelihood methods for Binary Response models with random coefficients
Journal of the American Statistical Association, 2018Co-Authors: Roger KoenkerAbstract:The venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities. For mixture models the nonparametric max...
