Wilson Confidence Intervals for Binomial Proportions With Multiple Imputation for Missing Data

ABSTRACT We present a Wilson interval for binomial proportions for use with multiple imputation for missing data. Using simulation studies, we show that it can have better repeated sampling properties than the usual confidence interval for binomial proportions based on Rubin’s combining rules. Further, in contrast to the usual multiple imputation confidence interval for proportions, the multiple imputation Wilson interval is always bounded by zero and one. Supplementary material is available online.

[1]  Guangliang Chen.  Interval Estimation , 2019, Bayesian Econometric Methods.

[2]  D. Rubin,et al.  Fully conditional specification in multivariate imputation , 2006 .

[3]  R. Newcombe.  Two-sided confidence intervals for the single proportion: comparison of seven methods. , 1998, Statistics in medicine.

[4]  L. Brown,et al.  Interval Estimation for a Binomial Proportion , 2001 .

[5]  Ofer Harel,et al.  Multiple imputation for correcting verification bias , 2006, Statistics in medicine.

[6]  Dandan Xu,et al.  Sequential BART for imputation of missing covariates. , 2016, Biostatistics.

[7]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[8]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[9]  Jerome P. Reiter,et al.  Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence , 2014, 1410.0438.

[10]  Jerome P. Reiter,et al.  Nonparametric Bayesian Multiple Imputation for Incomplete Categorical Variables in Large-Scale Assessment Surveys , 2013 .

[11]  susan. carter,et al.  Much Ado About Nothing ? , 2015 .

[12]  Jerome P. Reiter,et al.  An Empirical Comparison of Multiple Imputation Methods for Categorical Data , 2015, 1508.05918.

[13]  Sean Wallis,et al.  Binomial Confidence Intervals and Contingency Tests: Mathematical Fundamentals and the Evaluation of Alternative Methods , 2013, J. Quant. Linguistics.

[14]  E. B. Wilson.  Probable Inference, the Law of Succession, and Statistical Inference , 1927 .

[15]  Joseph G. Ibrahim,et al.  Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable , 1999 .

[16]  Devan V Mehrotra,et al.  Analysis of incomplete longitudinal binary data using multiple imputation , 2006, Statistics in medicine.

[17]  Ken P Kleinman,et al.  Much Ado About Nothing , 2007, The American statistician.

[18]  Jerome P. Reiter,et al.  Multiple imputation for missing data via sequential regression trees. , 2010, American journal of epidemiology.

[19]  Lena Osterhagen,et al.  Multiple Imputation For Nonresponse In Surveys , 2016 .

[20]  John Van Hoewyk,et al.  A multivariate technique for multiply imputing missing values using a sequence of regression models , 2001 .