Bayesian semi‐parametric ROC analysis

This paper describes a semi-parametric Bayesian approach for estimating receiver operating characteristic (ROC) curves based on mixtures of Dirichlet process priors (MDP). We address difficulties in modelling the underlying distribution of screening scores due to non-normality that may lead to incorrect choices of diagnostic cut-offs and unreliable estimates of prevalence of the disease. MDP is a robust tool for modelling non-standard diagnostic distributions associated with imperfect classification of an underlying diseased population, for example, when a diagnostic test is not a gold standard. For posterior computations, we propose an efficient Gibbs sampling framework based on a finite-dimensional approximation to MDP. We show, using both simulated and real data sets, that MDP modelling for ROC curve estimation closely parallels the frequentist kernel density estimation (KDE) approach.

[1]  Lancelot F. James,et al.  Approximate Dirichlet Process Computing in Finite Normal Mixtures , 2002 .

[2]  Peter Congdon.  Bayesian statistical modelling , 2002 .

[3]  C. Antoniak.  Mixtures of Dirichlet Processes with Applications to Bayesian Nonparametric Problems , 1974 .

[4]  T. Ferguson.  BAYESIAN DENSITY ESTIMATION BY MIXTURES OF NORMAL DISTRIBUTIONS , 1983 .

[5]  M. Tan,et al.  Random effects models in latent class analysis for evaluating accuracy of diagnostic tests. , 1996, Biometrics.

[6]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[7]  Lancelot F. James,et al.  Gibbs Sampling Methods for Stick-Breaking Priors , 2001 .

[8]  P. Müller,et al.  Bayesian curve fitting using multivariate normal mixtures , 1996 .

[9]  J A Hanley,et al.  The use of the 'binormal' model for parametric ROC analysis of quantitative diagnostic tests. , 1996, Statistics in medicine.

[10]  D.Sc. Joseph Berkson.  Are there Two Regressions , 1950 .

[11]  Albert Sorribas,et al.  A new parametric method based on S-distributions for computing receiver operating characteristic curves for continuous diagnostic tests. , 2002, Statistics in medicine.

[12]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[13]  H. Müller,et al.  Estimating regression functions and their derivatives by the kernel method , 1984 .

[14]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[15]  T. Marill.  Detection theory and psychophysics , 1956 .

[16]  S. MacEachern,et al.  Estimating mixture of dirichlet process models , 1998 .

[17]  Chris Lloyd,et al.  Using Smoothed Receiver Operating Characteristic Curves to Summarize and Compare Diagnostic Systems , 1998 .

[18]  I Yang,et al.  Latent variable modeling of diagnostic accuracy. , 1997, Biometrics.

[19]  Alan Gelfand.  Approaches for Semiparametric Bayesian Regression , 1997 .

[20]  M. Escobar.  Estimating Normal Means with a Dirichlet Process Prior , 1994 .

[21]  E. Costello,et al.  A test–retest reliability study of child-reported psychiatric symptoms and diagnoses using the Child and Adolescent Psychiatric Assessment (CAPA-C) , 1995, Psychological Medicine.

[22]  M. Escobar,et al.  Bayesian Density Estimation and Inference Using Mixtures , 1995 .

[23]  Eberhard O. Voit,et al.  The S‐Distribution A Tool for Approximation and Classification of Univariate, Unimodal Probability Distributions , 1992 .

[24]  Lynn Kuo,et al.  Bayesian semiparametric inference for the accelerated failure‐time model , 1997 .

[25]  Lancelot F. James,et al.  Bayesian Model Selection in Finite Mixtures by Marginal Density Decompositions , 2001 .

[26]  A. Erkanli,et al.  The Great Smoky Mountains Study of Youth. Goals, design, methods, and the prevalence of DSM-III-R disorders. , 1996, Archives of general psychiatry.

[27]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[28]  Michael A. West,et al.  Computing Nonparametric Hierarchical Models , 1998 .

[29]  Michael A. West,et al.  Hierarchical priors and mixture models, with applications in regression and density estimation , 2006 .

[30]  Jun S. Liu.  Nonparametric hierarchical Bayes via sequential imputations , 1996 .

[31]  Dalene Stangl,et al.  A Bayesian Analysis of Ordinal Data Using Mixtures , 2007 .

[32]  J G Ibrahim,et al.  A semiparametric Bayesian approach to the random effects model. , 1998, Biometrics.

[33]  K. Zou,et al.  Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests. , 1997, Statistics in medicine.

[34]  Andrew Gelman,et al.  General methods for monitoring convergence of iterative simulations , 1998 .

[35]  T. Achenbach.  Integrative Guide for the 1991 CBCL/4-18, Ysr, and Trf Profiles , 1991 .

[36]  J. Sethuraman,et al.  Convergence of Dirichlet Measures and the Interpretation of Their Parameter. , 1981 .