Nonparametric analysis of treatment effects with missing observations

This paper develops a test for comparing treatment effects when observations are missing at random for repeated measures data on independent subjects. It is assumed that missingness at any occasion follows a Bernoulli distribution. It is shown that the distribution of the vector of linear rank statistics depends on the unknown parameters of the probability law that governs missingness, which is absent in the existing conditional methods employing rank statistics. This dependence is through the variance–covariance matrix of the vector of linear ranks. The test statistic is a quadratic form in the linear rank statistics when the variance–covariance matrix is estimated. The limiting distribution of the test statistic is derived under the null hypothesis. Several methods of estimating the unknown components of the variance–covariance matrix are considered. The estimate that produces stable empirical Type I error rate while maintaining the highest power among the competing tests is recommended for implementation in practice. Simulation studies are also presented to show the advantage of the proposed test over other rank-based tests that do not account for the randomness in the missing data pattern. Our method is shown to have the highest power while also maintaining near-nominal Type I error rates. Our results clearly illustrate that even for an ignorable missingness mechanism, the randomness in the pattern of missingness cannot be ignored. A real data example is presented to highlight the effectiveness of the proposed method.     

The impact of random machine unavailability on inventory policies in a continuous improvement environment

There are production situations where a production facility (e.g. a machine) is used intermittently to produce lot sizes of certain products. Upon completion of production run, the facility may not be available for a random amount of time due to several reasons, such as: the facility needs to be maintained and the maintenance time is random due to unforeseen circumstances; or that the facility is leased by different manufacturers and the demand for the facility is random. As a result of machine unavailability, stock-out situations might arise. This paper extends the work of Abboud et al . (2000, Computers and Operations Research , 27 , 335-351) by assuming learning and forgetting in production. A new mathematical model is developed with numerical examples and sensitivity analysis provided. Furthermore, this paper determines how the overall inventory cost is influenced by the nature of the random variable that represents the unavailability time of the production facility.     

The effects of learning and forgetting on the optimal lot size quantity of intermittent production runs

This paper studies the effects of learning and forgetting on the production lot size problem with infinite and finite planning horizons. It is assumed that the determination of the economic manufactured quantity (EMQ) in the succeeding production run is dependent on: (1) the maximum inventory accumulated prior to interruption; (2) the length of the interruption period which incurs total forgetting; and (3) the level of experience in equivalent units remembered at the start-up of the next production run. The optimum operating inventory doctrines is obtained by trading off procurement cost per unit time and the inventory carrying cost per unit time, so that their sum will be a minimum. A numerical example is presented to demonstrate the application of learning and forgetting to the determination of the EMQ.     

Estimation with unbalanced panel data having covariate measurement error

Panel data with covariate measurement error appear frequently in various studies. Due to the sampling design and/or missing data, panel data are often unbalanced in the sense that panels have different sizes. For balanced panel data (i.e., panels having the same size), there exists a generalized method of moments (GMM) approach for adjusting covariate measurement error, which does not require additional validation data. This paper extends the GMM approach of adjusting covariate measurement error to unbalanced panel data. Two health related longitudinal surveys are used to illustrate the implementation of the proposed method.     

Effects of correlation and missing data on sample size estimation in longitudinal clinical trials

In longitudinal clinical trials, a common objective is to compare the rates of changes in an outcome variable between two treatment groups. Generalized estimating equation (GEE) has been widely used to examine if the rates of changes are significantly different between treatment groups due to its robustness to misspecification of the true correlation structure and randomly missing data. The sample size formula for repeated outcomes is based on the assumption of missing completely at random and a large sample approximation. A simulation study is conducted to investigate the performance of GEE sample size formula with small sample sizes, damped exponential family of correlation structure and non‐ignorable missing data. Copyright © 2008 John Wiley & Sons, Ltd.     

Progressive multi-state models for informatively incomplete longitudinal data

Progressive multi-state models provide a convenient framework for characterizing chronic disease processes where the states represent the degree of damage resulting from the disease. Incomplete data often arise in studies of such processes, and standard methods of analysis can lead to biased parameter estimates when observation of data is response-dependent. This paper describes a joint analysis useful for fitting progressive multi-state models to data arising in longitudinal studies in such settings. Likelihood based methods are described and parameters are shown to be identifiable. An EM algorithm is described for parameter estimation, and variance estimation is carried out using the Louis’ method. Simulation studies demonstrate that the proposed method works well in practice under a variety of settings. An application to data from a smoking prevention study illustrates the utility of the method.     

Variable selection for high-dimensional generalized linear model with block-missing data

In modern scientific research, multiblock missing data emerges with synthesizing information across multiple studies. However, existing imputation methods for handling block-wise missing data either focus on the single-block missing pattern or heavily rely on the model structure. In this study, we propose a single regression-based imputation algorithm for multiblock missing data. First, we conduct a sparse precision matrix estimation based on the structure of block-wise missing data. Second, we impute the missing blocks with their means conditional on the observed blocks. Theoretical results about variable selection and estimation consistency are established in the context of a generalized linear model. Moreover, simulation studies show that compared with existing methods, the proposed imputation procedure is robust to various missing mechanisms because of the good properties of regression imputation. An application to Alzheimer's Disease Neuroimaging Initiative data also confirms the superiority of our proposed method.     

百泉泉水变迁初探

百泉是我国北方岩溶性上升泉的典型代表,是卫河水系的源头。历史时期百泉泉水在卫河漕运中发挥了重要作用,时至解放后其天然流量仍能灌溉农田8万余亩。但自1979年开始至今,百泉出现了长期的间歇性断流现象。从其泉域内地下水开采过量且不断增加、泉域补给区内连年干旱少雨等方面来分析泉水间歇性断流的原因,并从改善泉域补给区内的地表植被状况、合理控制泉域内地下水的开采、加强对泉域的正确管理等方面入手,对百泉的资源利用前景做几点简略的思考。     

Pseudo likelihood-based estimation and testing of missingness mechanism function in nonignorable missing data problems

In nonignorable missing response problems, we study a semiparametric model with unspecified missingness mechanism model and a exponential family model for response conditional density. Even though existing methods are available to estimate the parameters in exponential family, estimation or testing of the missingness mechanism model nonparametrically remains to be an open problem. By defining a “synthesis" density involving the unknown missingness mechanism model and the known baseline “carrier" density in the exponential family model, we treat this “synthesis" density as a legitimate one with biased sampling version. We develop maximum pseudo likelihood estimation procedures and the resultant estimators are consistent and asymptotically normal. Since the “synthesis" cumulative distribution is a functional of the missingness mechanism model and the known carrier density, proposed method can be used to test the correctness of the missingness mechanism model nonparametrically andindirectly. Simulation studies and real example demonstrate the proposed methods perform very well.     

Modeling Longitudinal Obesity Data with Intermittent Missingness Using a New Latent Variable Model

We propose a latent variable model for informative missingness in longitudinal studies which is an extension of latent dropout class model. In our model, the value of the latent variable is affected by the missingness pattern and it is also used as a covariate in modeling the longitudinal response. So the latent variable links the longitudinal response and the missingness process. In our model, the latent variable is continuous instead of categorical and we assume that it is from a normal distribution. The EM algorithm is used to obtain the estimates of the parameter we are interested in and Gauss–Hermite quadrature is used to approximate the integration of the latent variable. The standard errors of the parameter estimates can be obtained from the bootstrap method or from the inverse of the Fisher information matrix of the final marginal likelihood. Comparisons are made to the mixed model and complete-case analysis in terms of a clinical trial dataset, which is Weight Gain Prevention among Women (WGPW) study. We use the generalized Pearson residuals to assess the fit of the proposed latent variable model.