The Effect of Methods for Handling Missing Values on the Performance of the MEWMA Control Chart

This article is concerned with the effect of the methods for handling missing values in multivariate control charts. We discuss the complete case, mean substitution, regression, stochastic regression, and the expectation–maximization algorithm methods for handling missing values. Estimates of mean vector and variance–covariance matrix from the treated data set are used to build the multivariate exponentially weighted moving average (MEWMA) control chart. Based on a Monte Carlo simulation study, the performance of each of the five methods is investigated in terms of its ability to obtain the nominal in-control and out-of-control average run length (ARL). We consider three sample sizes, five levels of the percentage of missing values, and three types of variable numbers. Our simulation results show that imputation methods produce better performance than case deletion methods. The regression-based imputation methods have the best overall performance among all the competing methods.     

Local model uncertainty and incomplete-data bias (with discussion)

Summary.  Problems of the analysis of data with incomplete observations are all too familiar in statistics. They are doubly difficult if we are also uncertain about the choice of model. We propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small. Loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation: the increase in variance when an assumed model is correct; the bias in estimation when the model is incorrect. Examples include non-ignorable missing data, hidden confounders in observational studies and publication bias in meta-analysis. Doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model. The problem of assessing the risk of lung cancer from passive smoking is used as a motivating example.     

Nonparametric curve estimation with missing data: A general empirical process approach

A general nonparametric imputation procedure, based on kernel regression, is proposed to estimate points as well as set- and function-indexed parameters when the data are missing at random (MAR). The proposed method works by imputing a specific function of a missing value (and not the missing value itself), where the form of this specific function is dictated by the parameter of interest. Both single and multiple imputations are considered. The associated empirical processes provide the right tool to study the uniform convergence properties of the resulting estimators. Our estimators include, as special cases, the imputation estimator of the mean, the estimator of the distribution function proposed by Cheng and Chu [1996. Kernel estimation of distribution functions and quantiles with missing data. Statist. Sinica 6, 63–78], imputation estimators of a marginal density, and imputation estimators of regression functions.     

The robustness and optimality of response surface designs

Recent work on extended optimality criteria for robust designs is applied to response surface problems. Methods of calculation are described and the criteria illustrated with several examples. The extended criteria discriminate among designs equivalent by other criteria.     

Regression Analysis with Covariates Missing at Random: A Piece-wise Nonparametric Model for Missing Covariates

Statistical analysis for the regression model f _β(y | x, z) with missing values in the covariate vector X requires modeling of the covariate distribution g(x | z). Likelihood methods, including Ibrahim (1990 Ibrahim , J. G. ( 1990 ). Incomplete data in generalized linear models . J. Amer. Statist. Assoc. 85 : 765 – 769 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), Chen (2004 Chen , H. Y. (2004). Nonparametric and semiparametric models for missing covariates in parametric regression. J. Amer. Statist. Assoc. 99:1176–1189.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), and Zhao (2005 Zhao , Y. ( 2005 ). Design and Efficient Estimation in Regression Analysis with Missing Data in Two-Phase Studies. Ph.D. thesis , University of Waterloo . [Google Scholar]), need either X or Z to be discrete. This article considers extending the likelihood methods to deal with cases where both X and Z may be continuous. We propose modeling the covariate distribution g(x | z) using a piece-wise nonparametric model, then a maximum likelihood estimate (MLE) of β can be computed following the maximum likelihood estimating procedure of Chen (2004 Chen , H. Y. (2004). Nonparametric and semiparametric models for missing covariates in parametric regression. J. Amer. Statist. Assoc. 99:1176–1189.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) or Zhao (2005 Zhao , Y. ( 2005 ). Design and Efficient Estimation in Regression Analysis with Missing Data in Two-Phase Studies. Ph.D. thesis , University of Waterloo . [Google Scholar]). The resulting estimation method is easy to implement and the asymptotic properties of the MLE follow under certain conditions. Extensive simulation studies for different models indicate that the proposed method is acceptable for practical implementation. A real data example is used to illustrate the method.     

Application of Multiple Imputation in Analysis of Data from Clinical Trials with Treatment Related Dropouts

This article develops a functional form of the generalized Poisson regression model that parametrically nests the Poisson and the two well known generalized Poisson regression models (GP-1 and GP-2). The proposed model is applied on the Malaysian motor insurance claim count data.     

A Weighting Approach for GEE Analysis with Missing Data

We propose a new weighting (WT) method to handle missing categorical outcomes in longitudinal data analysis using generalized estimating equations (GEE). The proposed WT provides a valid GEE estimator when the data are missing at random (MAR), and has more stable weights and shows advantage in efficiency compared to the inverse probability weighing method in the presence of small observation probabilities. The WT estimator is similar to the stabilized weighting (SWT) estimator under mild conditions, but it is more stable and efficient than SWT when the associations of the outcome with the observation probabilities and the covariate are strong.     

Estimation Bias in Complete-Case Analysis in Crossover Studies with Missing Data

Crossover designs are used often in clinical trials. It is not uncommon that subjects discontinue before completing all treatment periods in a crossover study. Despite availability of statistical methodologies utilizing all available data and software for obtaining valid inferences under the assumption of missing at random (MAR), naïve approaches, such as the complete case (CC) analysis, which is only valid with a strong assumption of missing completely at random are still widely used in practice. In this article, we obtain the analytical form of the estimation bias of treatment effects with CC for linear mixed models. We use simulation studies to examine the inflation of Type I error and efficiency loss in the inferences with CC under MAR. Invalidity and inefficiency of two other commonly used approaches for defining analyzed data in the presence of missing data, including data from at least two periods in three period crossover and available cases for a specific comparison of interest, are also demonstrated through simulation studies.     

Statistical Inference on Partially Linear Additive Models with Missing Response Variables and Error-prone Covariates

This paper considers statistical inference for the partially linear additive models, which are useful extensions of additive models and partially linear models. We focus on the case where some covariates are measured with additive errors, and the response variable is sometimes missing. We propose a profile least-squares estimator for the parametric component and show that the resulting estimator is asymptotically normal. To construct a confidence region for the parametric component, we also propose an empirical-likelihood-based statistic, which is shown to have a chi-squared distribution asymptotically. Furthermore, a simulation study is conducted to illustrate the performance of the proposed methods.