Baojiang Chen

Weighted Generalized Estimating Functions for Longitudinal Response and Covariate Data That Are Missing at Random

Longitudinal studies often feature incomplete response and covariate data. It is well known that biases can arise from naive analyses of available data, but the precise impact of incomplete data depends on the frequency of missing data and the strength of the association between the response variables and covariates and the missing-data indicators. Various factors may influence the availability of response and covariate data at scheduled assessment times, and at any given assessment time the response may be missing, covariate data may be missing, or both response and covariate data may be missing. Here we show that it is important to take the association between the missing data indicators for these two processes into account through joint models. Inverse probability-weighted generalized estimating equations offer an appealing approach for doing this. Here we develop these equations for a particular model generating intermittently missing-at-random data. Empirical studies demonstrate that the consistent estimators arising from the proposed methods have very small empirical biases in moderate samples. Supplemental materials are available online.

Analysis of interval‐censored disease progression data via multi‐state models under a nonignorable inspection process

Irreversible multi-state models provide a convenient framework for characterizing disease processes that arise when the states represent the degree of organ or tissue damage incurred by a progressive disease. In many settings, however, individuals are only observed at periodic clinic visits and so the precise times of the transitions are not observed. If the life history and observation processes are not independent, the observation process contains information about the life history process, and more importantly, likelihoods based on the disease process alone are invalid. With interval-censored failure time data, joint models are nonidentifiable and data analysts must rely on sensitivity analyses to assess the effect of the dependent observation times. This paper is concerned, however, with the analysis of data from progressive multi-state disease processes in which individuals are scheduled to be seen at periodic pre-scheduled assessment times. We cast the problem in the framework used for incomplete longitudinal data problems. Maximum likelihood estimation via an EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well under a variety of situations. Data from a cohort of patients with psoriatic arthritis are analyzed for illustration.

Variable selection using the optimal ROC curve: An application to a traditional Chinese medicine study on osteoporosis disease

In biomedical studies, there are multiple sources of information available of which only a small number of them are associated with the diseases. It is of importance to select and combine these factors that are associated with the disease in order to predict the disease status of a new subject. The receiving operating characteristic (ROC) technique has been widely used in disease classification, and the classification accuracy can be measured with area under the ROC curve (AUC). In this article, we combine recent variable selection methods with AUC methods to optimize diagnostic accuracy of multiple risk factors. We first describe one new and some recent AUC-based methods for effectively combining multiple risk factors for disease classification. We then apply them to analyze the data from a new clinical study, investigating whether a combination of traditional Chinese medicine symptoms and standard Western medicine risk factors can increase discriminative accuracy in diagnosing osteoporosis (OP). Based on the results, we conclude that we can make a better diagnosis of primary OP by combining traditional Chinese medicine symptoms with Western medicine risk factors.

Shrinkage and pretest estimators for longitudinal data analysis under partially linear models

In this paper, we develop marginal analysis methods for longitudinal data under partially linear models. We employ the pretest and shrinkage estimation procedures to estimate the mean response parameters as well as the association parameters, which may be subject to certain restrictions. We provide the analytic expressions for the asymptotic biases and risks of the proposed estimators, and investigate their relative performance to the unrestricted semiparametric least-squares estimator (USLSE). We show that if the dimension of association parameters exceeds two, the risk of the shrinkage estimators is strictly less than that of the USLSE in most of the parameter space. On the other hand, the risk of the pretest estimator depends on the validity of the restrictions of association parameters. A simulation study is conducted to evaluate the performance of the proposed estimators relative to that of the USLSE. A real data example is applied to illustrate the practical usefulness of the proposed estimation procedures.

Strategies for Bias Reduction in Estimation of Marginal Means with Data Missing at Random

Incomplete data are common in many fields of research, and interest often lies in estimating a marginal mean based on available information. This paper is concerned with the comparison of different strategies for estimating the marginal mean of a response when data are missing at random. We evaluate these methods based on the asymptotic bias, empirical bias and efficiency. We show that complete case analysis gives biased results when data are missing at random, but inverse probability weighted estimating equations (IPWEE) and a method based on the expected conditional mean (ECM) yield consistent estimators.. While these methods give estimators which behave similarly in the contexts studied they are based on quite different assumptions. The IPWEE approach requires analysts to specify a model for the missing data mechanism whereas the ECM approach requires a model for the distribution of auxiliary variables driving the missing data mechanism. The latter can be a challenge in practice, particularly when the covariates are of high dimension or are a mixture of continuous and categorical variables. The IPWEE approach therefore has considerable appeal in many practical settings.