Logistic Regression with Missing Values in the Covariates by Werner VachLogistic Regression with Missing Values in the Covariates by Werner Vach

Logistic Regression with Missing Values in the Covariates

byWerner Vach

Paperback | April 8, 1994

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In many areas of science a basic task is to assess the influence of several factors on a quantity of interest. If this quantity is binary logistic, regression models provide a powerful tool for this purpose. This monograph presents an account of the use of logistic regression in the case where missing values in the variables prevent the use of standard techniques. Such situations occur frequently across a wide range of statistical applications.
The emphasis of this book is on methods related to the classical maximum likelihood principle. The author reviews the essentials of logistic regression and discusses the variety of mechanisms which might cause missing values while the rest of the book covers the methods which may be used to deal with missing values and their effectiveness. Researchers across a range of disciplines and graduate students in statistics and biostatistics will find this a readable account of this.
Title:Logistic Regression with Missing Values in the CovariatesFormat:PaperbackDimensions:148 pagesPublished:April 8, 1994Publisher:Springer New York

The following ISBNs are associated with this title:

ISBN - 10:0387942637

ISBN - 13:9780387942636

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Table of Contents

1. Introduction.- I: Logistic Regression with Two Categorical Covariates.- 2. The complete data case.- 3. Missing value mechanisms.- 4. Estimation methods.- 4.1 Maximum Likelihood (ML) Estimatio.- 4.2 Pseudo Maximum Likelihood (PML) Estimatio.- 4.3 The Filling metho.- 4.4 Complete Case Analysi.- 4.5 Additional Categor.- 4.6 Probability Imputatio.- 4.7 Omission of Covariat.- 5. Quantitative comparisons: Asymptotic results.- 5.1 Asymptotic relative efficiency: ML Estimation vs. PML Estimatio.- 5.2 Asymptotic relative efficiency: ML Estimation vs. Fillin.- 5.3 Asymptotic relative efficiency: PML Estimation vs. Fillin.- 5.4 Asymptotic relative efficiency: ML Estimation vs. Complete Case Analysi.- 5.5 Asymptotic relative efficiency: ML Estimation for complete data vs. ML Estimation for incomplete dat.- 5.6 Asymptotic relative efficiency: ML Estimation for complete data vs. Complete Case Analysi.- 5.7 Asymptotic relative efficiency: A summary of result.- 5.8 Asymptotic bias: Comparison of Probability Imputation, Additional Category and Omission of Covariat.- 5.9 Asymptotic bias: Evaluation of Conditional Probability Imputatio.- 5.10 Evaluating the underestimation of variance of Conditional Probability Imputatio.- 5.11 The importance of the variance correction of the Filling metho.- 6. Quantitative comparisons: Results from finite sample size simulation studies.- 6.1 Finite behavior of ML Estimation, PML Estimation, Filling and Complete Case Analysi.- 6.2 Power comparison.- 6.3 Evaluation of Conditional Probability Imputatio.- 7. Examples.- 7.1 Illustrating artificial example.- 7.2 An example with a real data se.- 8. Sensitivity analysis.- II: Generalizations.- 9. General regression models with missing values in one of two covariates.- 9.1 ML Estimatio.- 9.2 Semiparametric ML Estimatio.- 9.3 Estimation of the Score Functio.- 9.4 Complete Case Analysi.- 9.5 Mean Imputation and Additional Categor.- 9.6 The Cox proportional hazards mode.- 10. Generalizations for more than two covariates.- 10.1 One covariate with missing value.- 10.2 Missing values in more than one covariat.- 11. Missing values and subsampling.- 11.1 Two stage design.- 11.2 Surrogate covariates and validation samplin.- 11.3 Subsampling of the nonresponder.- 11.4 (Sub-)sampling of additional variable.- 12. Further Examples.- 12.1 Example 1: Risk factors for subsequent contralateral breast cance.- 12.2 Example 2: A study on the role of DNA content for the prognosis of ovarian cancer patient.- 13. Discussion.- 13.1 Statistical inference if the MAR assumption is satisfie.- 13.2 Statistical inference if the MAR assumption is questionabl.- 13.3 Topics of future researc.- 13.4 Final remar.- Appendices.- A. 1 ML Estimation in the presence of missing values A.2 The EM algorithm.- B. 1 Explicit representation of the score function of ML Estimation and the information matrix in the complete data case.- B. 2 Explicit representation of the score function of ML Estimation and the information matrix.- B. 3 Explicit representation of the quantities used for the asymptotic variance of the PML estimates.- B. 4 Explicit representation of the quantities used for the asymptotic variance of the estimates of the Filling method.- References.- Notation Index.