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Articles 1 - 7 of 7
Full-Text Articles in Categorical Data Analysis
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. …
Survival Analysis Using Auxiliary Variables Via Nonparametric Multiple Imputation, Chiu-Hsieh Hsu, Jeremy Taylor, Susan Murray, Daniel Commenges
Survival Analysis Using Auxiliary Variables Via Nonparametric Multiple Imputation, Chiu-Hsieh Hsu, Jeremy Taylor, Susan Murray, Daniel Commenges
The University of Michigan Department of Biostatistics Working Paper Series
We develop an approach, based on multiple imputation, that estimates the marginal survival distribution in survival analysis using auxiliary variable to recover information for censored observations. To conduct the imputation, we use two working survival model to define the nearest neighbor imputing risk set. One model is for the event times and the other for the censoring times. Based on the imputing risk set, two nonparametric multiple imputation methods are considered: risk set imputation, and Kaplan-Meier estimator. For both methods a future event or censoring time is imputed for each censored observation. With a categorical auxiliary variable, we show that …
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 …
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 …
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 …
Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch
Maximum Likelihood Estimation Of Ordered Multinomial Parameters , Nicholas P. Jewell, Jack Kalbfleisch
The University of Michigan Department of Biostatistics Working Paper Series
The pool-adjacent violator-algorithm (Ayer et al., 1955) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see, Barlow et al., 1972). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of ‘ordered’ multinomial parameters pi = (p1i, p2i, . . . , pmi) for 1 < = I < = k, where ordered means that pj1 < = pj2 < = .. . < = pjk for each j with 1 < = j < = m-1. The data consist of k independent observations X1, . . . ,Xk where Xi has a multinomial distribution with probability parameter pi and known index ni > = 1. By making use of variants of the pool adjacent violator algorithm, …