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Articles 1 - 30 of 40
Full-Text Articles in Statistical Models
Shrinkage Priors For Isotonic Probability Vectors And Binary Data Modeling, Philip S. Boonstra, Daniel R. Owen, Jian Kang
Shrinkage Priors For Isotonic Probability Vectors And Binary Data Modeling, Philip S. Boonstra, Daniel R. Owen, Jian Kang
The University of Michigan Department of Biostatistics Working Paper Series
This paper outlines a new class of shrinkage priors for Bayesian isotonic regression modeling a binary outcome against a predictor, where the probability of the outcome is assumed to be monotonically non-decreasing with the predictor. The predictor is categorized into a large number of groups, and the set of differences between outcome probabilities in consecutive categories is equipped with a multivariate prior having support over the set of simplexes. The Dirichlet distribution, which can be derived from a normalized cumulative sum of gamma-distributed random variables, is a natural choice of prior, but using mathematical and simulation-based arguments, we show that …
Inferring A Consensus Problem List Using Penalized Multistage Models For Ordered Data, Philip S. Boonstra, John C. Krauss
Inferring A Consensus Problem List Using Penalized Multistage Models For Ordered Data, Philip S. Boonstra, John C. Krauss
The University of Michigan Department of Biostatistics Working Paper Series
A patient's medical problem list describes his or her current health status and aids in the coordination and transfer of care between providers, among other things. Because a problem list is generated once and then subsequently modified or updated, what is not usually observable is the provider-effect. That is, to what extent does a patient's problem in the electronic medical record actually reflect a consensus communication of that patient's current health status? To that end, we report on and analyze a unique interview-based design in which multiple medical providers independently generate problem lists for each of three patient case abstracts …
Default Priors For The Intercept Parameter In Logistic Regressions, Philip S. Boonstra, Ryan P. Barbaro, Ananda Sen
Default Priors For The Intercept Parameter In Logistic Regressions, Philip S. Boonstra, Ryan P. Barbaro, Ananda Sen
The University of Michigan Department of Biostatistics Working Paper Series
In logistic regression, separation refers to the situation in which a linear combination of predictors perfectly discriminates the binary outcome. Because finite-valued maximum likelihood parameter estimates do not exist under separation, Bayesian regressions with informative shrinkage of the regression coefficients offer a suitable alternative. Little focus has been given on whether and how to shrink the intercept parameter. Based upon classical studies of separation, we argue that efficiency in estimating regression coefficients may vary with the intercept prior. We adapt alternative prior distributions for the intercept that downweight implausibly extreme regions of the parameter space rendering less sensitivity to separation. …
Incorporating Historical Models With Adaptive Bayesian Updates, Philip S. Boonstra, Ryan P. Barbaro
Incorporating Historical Models With Adaptive Bayesian Updates, Philip S. Boonstra, Ryan P. Barbaro
The University of Michigan Department of Biostatistics Working Paper Series
This paper considers Bayesian approaches for incorporating information from a historical model into a current analysis when the historical model includes only a subset of covariates currently of interest. The statistical challenge is two-fold. First, the parameters in the nested historical model are not generally equal to their counterparts in the larger current model, neither in value nor interpretation. Second, because the historical information will not be equally informative for all parameters in the current analysis, additional regularization may be required beyond that provided by the historical information. We propose several novel extensions of the so-called power prior that adaptively …
A Pairwise Likelihood Augmented Estimator For The Cox Model Under Left-Truncation, Fan Wu, Sehee Kim, Jing Qin, Rajiv Saran, Yi Li
A Pairwise Likelihood Augmented Estimator For The Cox Model Under Left-Truncation, Fan Wu, Sehee Kim, Jing Qin, Rajiv Saran, Yi Li
The University of Michigan Department of Biostatistics Working Paper Series
Survival data collected from prevalent cohorts are subject to left-truncation and the analysis is challenging. Conditional approaches for left-truncated data under the Cox model are inefficient as they typically ignore the information in the marginal likelihood of the truncation times. Length-biased sampling methods can improve the estimation efficiency but only when the stationarity assumption of the disease incidence holds, i.e., the truncation distribution is uniform; otherwise they may generate biased estimates. In this paper, we propose a semi-parametric method for the Cox model under general left-truncation, where the truncation distribution is unspecified. Our approach is to make inference based on …
An Analysis Of Nonignorable Nonresponse In A Survey With A Rotating Panel Design, Caterina Giusti, Roderick J. Little
An Analysis Of Nonignorable Nonresponse In A Survey With A Rotating Panel Design, Caterina Giusti, Roderick J. Little
The University of Michigan Department of Biostatistics Working Paper Series
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 …
Bayesian Bivariate Image Analysis With Application To Dual Autoradiography, Timothy D. Johnson, Morand Piert
Bayesian Bivariate Image Analysis With Application To Dual Autoradiography, Timothy D. Johnson, Morand Piert
The University of Michigan Department of Biostatistics Working Paper Series
We present a Bayesian bivariate image model and apply it to a study that was designed to investigate the relationship between hypoxia and angiogenesis in an animal tumor model. Two radiolabeled tracers (one measuring angio- genesis, the other measuring hypoxia) were simultaneously injected into the animals, the tumors removed and autoradiographic images of the tracer concentrations were obtained. We model correlation between tracers with a mixture of bivariate normal distributions and the spatial correlation inherent in the images by means of the celebrated Potts model. Although the Potts model is typically used for image segmentation, we use it solely as …
Quantitative Magnetic Resonance Image Analysis Via The Em Algorithm With Stochastic Variation, Xiaoxi Zhang, Timothy D. Johnson, Roderick J.A. Little
Quantitative Magnetic Resonance Image Analysis Via The Em Algorithm With Stochastic Variation, Xiaoxi Zhang, Timothy D. Johnson, Roderick J.A. Little
The University of Michigan Department of Biostatistics Working Paper Series
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 …
Bayesian Spatial Modeling Of Fmri Data: A Multiple-Subject Analysis, Lei Xu, Timothy Johnson, Thomas Nichols
Bayesian Spatial Modeling Of Fmri Data: A Multiple-Subject Analysis, Lei Xu, Timothy Johnson, Thomas Nichols
The University of Michigan Department of Biostatistics Working Paper Series
The aim of this work is to develop a spatial model for multi-subject fMRI data. While there has been much work on univariate modeling of each voxel for single- and multi-subject data, and some work on spatial modeling for single-subject data, there has been no work on spatial models that explicitly account for intersubject variability in activation location. We use a Bayesian hierarchical spatial model to fit the data. At the first level we model "population centers" that mark the centers of regions of activation. For a given population center each subject may have zero or more associated "individual components". …
A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan
A Hybrid Newton-Type Method For The Linear Regression In Case-Cohort Studies, Menggang Yu, Bin Nan
The University of Michigan Department of Biostatistics Working Paper Series
Case-cohort designs are increasingly commonly used in large epidemiological cohort studies. Nan, Yu, and Kalbeisch (2004) provided the asymptotic results for censored linear regression models in case-cohort studies. In this article, we consider computational aspects of their proposed rank based estimating methods. We show that the rank based discontinuous estimating functions for case-cohort studies are monotone, a property established for cohort data in the literature, when generalized Gehan type of weights are used. Though the estimating problem can be formulated to a linear programming problem as that for cohort data, due to its easily uncontrollable large scale even for a …
A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch
A Bayesian Mixture Model Relating Dose To Critical Organs And Functional Complication In 3d Conformal Radiation Therapy, Tim Johnson, Jeremy Taylor, Randall K. Ten Haken, Avraham Eisbruch
The University of Michigan Department of Biostatistics Working Paper Series
A goal of radiation therapy is to deliver maximum dose to the target tumor while minimizing complications due to irradiation of critical organs. Technological advances in 3D conformal radiation therapy has allowed great strides in realizing this goal, however complications may still arise. Critical organs may be adjacent to tumors or in the path of the radiation beam. Several mathematical models have been proposed that describe a relationship between dose and observed functional complication, however only a few published studies have successfully fit these models to data using modern statistical methods which make efficient use of the data. One complication …
Semiparametric Binary Regression Under Monotonicity Constraints, Moulinath Banerjee, Pinaki Biswas, Debashis Ghosh
Semiparametric Binary Regression Under Monotonicity Constraints, Moulinath Banerjee, Pinaki Biswas, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
Summary: We study a binary regression model where the response variable $\Delta$ is the indicator of an event of interest (for example, the incidence of cancer) and the set of covariates can be partitioned as $(X,Z)$ where $Z$ (real valued) is the covariate of primary interest and $X$ (vector valued) denotes a set of control variables. For any fixed $X$, the conditional probability of the event of interest is assumed to be a monotonic function of $Z$. The effect of the control variables is captured by a regression parameter $\beta$. We show that the baseline conditional probability function (corresponding to …
A Bayesian Method For Finding Interactions In Genomic Studies, Wei Chen, Debashis Ghosh, Trivellore E. Raghuanthan, Sharon Kardia
A Bayesian Method For Finding Interactions In Genomic Studies, Wei Chen, Debashis Ghosh, Trivellore E. Raghuanthan, Sharon Kardia
The University of Michigan Department of Biostatistics Working Paper Series
An important step in building a multiple regression model is the selection of predictors. In genomic and epidemiologic studies, datasets with a small sample size and a large number of predictors are common. In such settings, most standard methods for identifying a good subset of predictors are unstable. Furthermore, there is an increasing emphasis towards identification of interactions, which has not been studied much in the statistical literature. We propose a method, called BSI (Bayesian Selection of Interactions), for selecting predictors in a regression setting when the number of predictors is considerably larger than the sample size with a focus …
Finding Cancer Subtypes In Microarray Data Using Random Projections, Debashis Ghosh
Finding Cancer Subtypes In Microarray Data Using Random Projections, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
One of the benefits of profiling of cancer samples using microarrays is the generation of molecular fingerprints that will define subtypes of disease. Such subgroups have typically been found in microarray data using hierarchical clustering. A major problem in interpretation of the output is determining the number of clusters. We approach the problem of determining disease subtypes using mixture models. A novel estimation procedure of the parameters in the mixture model is developed based on a combination of random projections and the expectation-maximization algorithm. Because the approach is probabilistic, our approach provides a measure for the number of true clusters …
Semiparametric Methods For The Binormal Model With Multiple Biomarkers, Debashis Ghosh
Semiparametric Methods For The Binormal Model With Multiple Biomarkers, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
Abstract: In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We also discuss adjustment for covariates in this class of models and provide a simple …
Censored Linear Regression For Case-Cohort Studies, Bin Nan, Menggang Yu, Jack Kalbfleisch
Censored Linear Regression For Case-Cohort Studies, Bin Nan, Menggang Yu, Jack Kalbfleisch
The University of Michigan Department of Biostatistics Working Paper Series
Right censored data from a classical case-cohort design and a stratified case-cohort design are considered. In the classical case-cohort design, the subcohort is obtained as a simple random sample of the entire cohort, whereas in the stratified design, the subcohort is selected by independent Bernoulli sampling with arbitrary selection probabilities. For each design and under a linear regression model, methods for estimating the regression parameters are proposed and analyzed. These methods are derived by modifying the linear ranks tests and estimating equations that arise from full-cohort data using methods that are similar to the "pseudo-likelihood" estimating equation that has been …
Nonparametric Methods For Analyzing Replication Origins In Genomewide Data, Debashis Ghosh
Nonparametric Methods For Analyzing Replication Origins In Genomewide Data, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
Due to the advent of high-throughput genomic technology, it has become possible to globally monitor cellular activities on a genomewide basis. With these new methods, scientists can begin to address important biological questions. One such question involves the identification of replication origins, which are regions in chromosomes where DNA replication is initiated. In addition, one hypothesis regarding replication origins is that their locations are non-random throughout the genome. In this article, we develop methods for identification of and cluster inference regarding replication origins involving genomewide expression data. We compare several nonparametric regression methods for the identification of replication origin locations. …
Semiparametric Methods For Identification Of Tumor Progression Genes From Microarray Data, Debashis Ghosh, Arul Chinnaiyan
Semiparametric Methods For Identification Of Tumor Progression Genes From Microarray Data, Debashis Ghosh, Arul Chinnaiyan
The University of Michigan Department of Biostatistics Working Paper Series
The use of microarray data has become quite commonplace in medical and scientific experiments. We focus here on microarray data generated from cancer studies. It is potentially important for the discovery of biomarkers to identify genes whose expression levels correlate with tumor progression. In this article, we develop statistical procedures for the identification of such genes, which we term tumor progression genes. Two methods are considered in this paper. The first is use of a proportional odds procedure, combined with false discovery rate estimation techniques to adjust for the multiple testing problem. The second method is based on order-restricted estimation …
The False Discovery Rate: A Variable Selection Perspective, Debashis Ghosh, Wei Chen, Trivellore E. Raghuanthan
The False Discovery Rate: A Variable Selection Perspective, Debashis Ghosh, Wei Chen, Trivellore E. Raghuanthan
The University of Michigan Department of Biostatistics Working Paper Series
In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to …
Semiparametic Models And Estimation Procedures For Binormal Roc Curves With Multiple Biomarkers, Debashis Ghosh
Semiparametic Models And Estimation Procedures For Binormal Roc Curves With Multiple Biomarkers, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
In diagnostic medicine, there is great interest in developing strategies for combining biomarkers in order to optimize classification accuracy. A popular model that has been used for receiver operating characteristic (ROC) curve modelling when one biomarker is available is the binormal model. Extension of the model to accommodate multiple biomarkers has not been considered in this literature. Here, we consider a multivariate binormal framework for combining biomarkers using copula functions that leads to a natural multivariate extension of the binormal model. Estimation in this model will be done using rank-based procedures. We show that the Van der Waerden rank score …
Nonparametric And Semiparametric Inference For Models Of Tumor Size And Metastasis, Debashis Ghosh
Nonparametric And Semiparametric Inference For Models Of Tumor Size And Metastasis, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
There has been some recent work in the statistical literature for modelling the relationship between the size of primary cancers and the occurrences of metastases. While nonparametric methods have been proposed for estimation of the tumor size distribution at which metastatic transition occurs, their asymptotic properties have not been studied. In addition, no testing or regression methods are available so that potential confounders and prognostic factors can be adjusted for. We develop a unified approach to nonparametric and semiparametric analysis of modelling tumor size-metastasis data in this article. An equivalence between the models considered by previous authors with survival data …
Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh
Model Checking Techniques For Regression Models In Cancer Screening, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
There has been much work on developing statistical procedures for associating tumor size with the probability of detecting a metastasis. Recently, Ghosh (2004) developed a unified statistical framework in which equivalences with censored data structures and models for tumor size and metastasis were examined. Based on this framework, we consider model checking techniques for semiparametric regression models in this paper. The procedures are for checking the additive hazards model. Goodness of fit methods are described for assessing functional form of covariates as well as the additive hazards assumption. The finite-sample properties of the methods are assessed using simulation studies.
Binary Isotonic Regression Procedures, With Application To Cancer Biomarkers, Debashis Ghosh, Moulinath Banerjee, Pinaki Biswas
Binary Isotonic Regression Procedures, With Application To Cancer Biomarkers, Debashis Ghosh, Moulinath Banerjee, Pinaki Biswas
The University of Michigan Department of Biostatistics Working Paper Series
There is a lot of interest in the development and characterization of new biomarkers for screening large populations for disease. In much of the literature on diagnostic testing, increased levels of a biomarker correlate with increased disease risk. However, parametric forms are typically used to associate these quantities. In this article, we specify a monotonic relationship between biomarker levels with disease risk. This leads to consideration of a nonparametric regression model for a single biomarker. Estimation results using isotonic regression-type estimators and asymptotic results are given. We also discuss confidence set estimation in this setting and propose three procedures for …
Covariate Adjustment In The Analysis Of Microarray Data From Clinical Studies, Debashis Ghosh, Arul Chinnaiyan
Covariate Adjustment In The Analysis Of Microarray Data From Clinical Studies, Debashis Ghosh, Arul Chinnaiyan
The University of Michigan Department of Biostatistics Working Paper Series
There is tremendous scientific interest in the analysis of gene expression data in clinical settings, such as oncology. In this paper, we describe the importance of adjusting for confounders and other prognostic factors in order to select for differentially expressed genes for followup validation studies. We develop two approaches to the analysis of microarray data in nonrandomized clinical settings. The first is an extension of the current significance analysis of microarray procedures, where other covariates are taken into account. The second is a novel covariate-adjusted regression modelling based on the receiver operating characteristic curve for the analysis of gene expression …
A Bayesian Hierarchical Approach To Multirater Correlated Roc Analysis, Tim Johnson, Valen Johnson
A Bayesian Hierarchical Approach To Multirater Correlated Roc Analysis, Tim Johnson, Valen Johnson
The University of Michigan Department of Biostatistics Working Paper Series
In a common ROC study design, several readers are asked to rate diagnostics of the same cases processed under different modalities. We describe a Bayesian hierarchical model that facilitates the analysis of this study design by explicitly modeling the three sources of variation inherent to it. In so doing, we achieve substantial reductions in the posterior uncertainty associated with estimates of the differences in areas under the estimated ROC curves and corresponding reductions in the mean squared error (MSE) of these estimates. Based on simulation studies, both the widths of confidence intervals and MSE of estimates of differences in the …
A Bayesian Chi-Squared Test For Goodness Of Fit, Valen Johnson
A Bayesian Chi-Squared Test For Goodness Of Fit, Valen Johnson
The University of Michigan Department of Biostatistics Working Paper Series
This article describes an extension of classical x 2 goodness-of-fit tests to Bayesian model assessment. The extension, which essentially involvesevaluating Pearson's goodness-of-fit statistic at a parameter value drawn from its posterior distribution, has the important property that it is asymptoti-cally distributed as a x2 random variable on K-1 degrees of freedom, indepen-dently of the dimension of the underlying parameter vector. By averaging over the posterior distribution of this statistic, a global goodness-of-fit diagnostic is obtained. Advantages of this diagnostic{which may be interpreted as the area under an ROC curve{include ease of interpretation, computational conve-nience, and favorable power properties. The proposed …
Individual Prediction In Prostate Cancer Studies Using A Joint Longitudinal-Survival-Cure Model, Menggang Yu, Jeremy Taylor, Howard M. Sandler
Individual Prediction In Prostate Cancer Studies Using A Joint Longitudinal-Survival-Cure Model, Menggang Yu, Jeremy Taylor, Howard M. Sandler
The University of Michigan Department of Biostatistics Working Paper Series
For monitoring patients treated for prostate cancer, Prostate Specific Antigen (PSA) is measured periodically after they receive treatment. Increases in PSA are suggestive of recurrence of the cancer and are used in making decisions about possible new treatments. The data from studies of such patients typically consist of longitudinal PSA measurements, censored event times and baseline covariates. Methods for the combined analysis of both longitudinal and survival data have been developed in recent years, with the main emphasis being on modeling and estimation. We analyze data from a prostate cancer study that has been extended by adding a mixture structure …
Mixture Models For Assessing Differential Expression In Complex Tissues Using Microarray Data, Debashis Ghosh
Mixture Models For Assessing Differential Expression In Complex Tissues Using Microarray Data, Debashis Ghosh
The University of Michigan Department of Biostatistics Working Paper Series
The use of DNA microarrays has become quite popular in many scientific and medical disciplines, such as in cancer research. One common goal of these studies is to determine which genes are differentially expressed between cancer and healthy tissue, or more generally, between two experimental conditions. A major complication in the molecular profiling of tumors using gene expression data is that the data represent a combination of tumor and normal cells. Much of the methodology developed for assessing differential expression with microarray data has assumed that tissue samples are homogeneous. In this article, we outline a general framework for determining …
Robust Likelihood-Based Analysis Of Multivariate Data With Missing Values, Rod Little, An Hyonggin
Robust Likelihood-Based Analysis Of Multivariate Data With Missing Values, Rod Little, An Hyonggin
The University of Michigan Department of Biostatistics Working Paper Series
The model-based approach to inference from multivariate data with missing values is reviewed. Regression prediction is most useful when the covariates are predictive of the missing values and the probability of being missing, and in these circumstances predictions are particularly sensitive to model misspecification. The use of penalized splines of the propensity score is proposed to yield robust model-based inference under the missing at random (MAR) assumption, assuming monotone missing data. Simulation comparisons with other methods suggest that the method works well in a wide range of populations, with little loss of efficiency relative to parametric models when the latter …
To Model Or Not To Model? Competing Modes Of Inference For Finite Population Sampling, Rod Little
To Model Or Not To Model? Competing Modes Of Inference For Finite Population Sampling, Rod Little
The University of Michigan Department of Biostatistics Working Paper Series
Finite population sampling is perhaps the only area of statistics where the primary mode of analysis is based on the randomization distribution, rather than on statistical models for the measured variables. This article reviews the debate between design and model-based inference. The basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples. Strengths and weakness of design-based and model-based inference for surveys are discussed. It is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings. …