含不可忽略缺失数据非线性再生散度模型参数的Bayes估计

给出协变量带有不可忽略缺失数据的非线性再生散度模型的Bayes方法,缺失数据机制由Logistic回归模型来确定.Gibbs抽样技术和Metropolis-Hastings算法(简称MH算法)用来得到模型参数、缺失数据机制中回归系数的联合Bayes估计,并用实例加以说明.     

Cox model with interval‐censored covariate in cohort studies

In cohort studies the outcome is often time to a particular event, and subjects are followed at regular intervals. Periodic visits may also monitor a secondary irreversible event influencing the event of primary interest, and a significant proportion of subjects develop the secondary event over the period of follow‐up. The status of the secondary event serves as a time‐varying covariate, but is recorded only at the times of the scheduled visits, generating incomplete time‐varying covariates. While information on a typical time‐varying covariate is missing for entire follow‐up period except the visiting times, the status of the secondary event are unavailable only between visits where the status has changed, thus interval‐censored. One may view interval‐censored covariate of the secondary event status as missing time‐varying covariates, yet missingness is partial since partial information is provided throughout the follow‐up period. Current practice of using the latest observed status produces biased estimators, and the existing missing covariate techniques cannot accommodate the special feature of missingness due to interval censoring. To handle interval‐censored covariates in the Cox proportional hazards model, we propose an available‐data estimator, a doubly robust‐type estimator as well as the maximum likelihood estimator via EM algorithm and present their asymptotic properties. We also present practical approaches that are valid. We demonstrate the proposed methods using our motivating example from the Northern Manhattan Study.     

Doubly robust estimates for binary longitudinal data analysis with missing response and missing covariates

Longitudinal studies often feature incomplete response and covariate data. Likelihood-based methods such as the expectation-maximization algorithm give consistent estimators for model parameters when data are missing at random (MAR) provided that the response model and the missing covariate model are correctly specified; however, we do not need to specify the missing data mechanism. An alternative method is the weighted estimating equation, which gives consistent estimators if the missing data and response models are correctly specified; however, we do not need to specify the distribution of the covariates that have missing values. In this article, we develop a doubly robust estimation method for longitudinal data with missing response and missing covariate when data are MAR. This method is appealing in that it can provide consistent estimators if either the missing data model or the missing covariate model is correctly specified. Simulation studies demonstrate that this method performs well in a variety of situations.     

Model misspecification in proportional hazards regression

The proportional hazards model is frequently used to evaluatethe effect of treatment on failure time events in randomisedclinical trials. Concomitant variables are usually availableand may be considered for use in the primary analyses underthe assumption that incorporating them may reduce bias or improveefficiency. In this paper we consider two approaches to includingcovariate information: regression modelling and stratification.We focus on the setting where covariate effects are nonproportionaland we compare the bias, efficiency and coverage propertiesof these approaches. These results indicate that our intuitionbased on linear model analysis of covariance is misleading.Covariate adjustment in proportional hazards models has littleeffect on the variance but may significantly improve the accuracyof the treatment effect estimator.     

Covariate and multinomial: Accounting for distance in movement in capture–recapture analyses

Many biological quantities cannot be measured directly but rather need to be estimated from models. Estimates from models are statistical objects with variance and, when derived simultaneously, covariance. It is well known that their variance–covariance (VC) matrix must be considered in subsequent analyses. Although it is always preferable to carry out the proposed analyses on the raw data themselves, a two‐step approach cannot always be avoided. This situation arises when the parameters of a multinomial must be regressed against a covariate. The Delta method is an appropriate and frequently recommended way of deriving variance approximations of transformed and correlated variables. Implementing the Delta method is not trivial, and there is a lack of a detailed information on the procedure in the literature for complex situations such as those involved in constraining the parameters of a multinomial distribution. This paper proposes a how‐to guide for calculating the correct VC matrices of dependant estimates involved in multinomial distributions and how to use them for testing the effects of covariates in post hoc analyses when the integration of these analyses directly into a model is not possible. For illustrative purpose, we focus on variables calculated in capture–recapture models, but the same procedure can be applied to all analyses dealing with correlated estimates with multinomial distribution and their variances and covariances.     

Sensitivity analysis for trend tests: application to the risk of radiation exposure

Trend tests are used to assess the relationship between multiple level treatment X and binary response R. In observational studies, however, there may be a confounder U that is associated with treatment X and causally related to response R. When the data for the confounder U are not observed, an approach for assessing the sensitivity of test results to U is provided. Its use is illustrated by examining data from a study of mutation rate after the Chernobyl accident.     

Testing for bias in weighted estimating equations

It is very common in regression analysis to encounter incompletely observed covariate information. A recent approach to analyse such data is weighted estimating equations (Robins, J. M., Rotnitzky, A. and Zhao, L. P. (1994), JASA, 89, 846-866, and Zhao, L. P., Lipsitz, S. R. and Lew, D. (1996), Biometrics, 52, 1165-1182). With weighted estimating equations, the contribution to the estimating equation from a complete observation is weighted by the inverse of the probability of being observed. We propose a test statistic to assess if the weighted estimating equations produce biased estimates. Our test statistic is similar to the test statistic proposed by DuMouchel and Duncan (1983) for weighted least squares estimates for sample survey data. The method is illustrated using data from a randomized clinical trial on chemotherapy for multiple myeloma.     

Borrowing strength with nonexchangeable priors over subpopulations

We introduce a nonparametric Bayesian model for a phase II clinical trial with patients presenting different subtypes of the disease under study. The objective is to estimate the success probability of an experimental therapy for each subtype. We consider the case when small sample sizes require extensive borrowing of information across subtypes, but the subtypes are not a priori exchangeable. The lack of a priori exchangeability hinders the straightforward use of traditional hierarchical models to implement borrowing of strength across disease subtypes. We introduce instead a random partition model for the set of disease subtypes. This is a variation of the product partition model that allows us to model a nonexchangeable prior structure. Like a hierarchical model, the proposed clustering approach considers all observations, across all disease subtypes, to estimate individual success probabilities. But in contrast to standard hierarchical models, the model considers disease subtypes a priori nonexchangeable. This implies that when assessing the success probability for a particular type our model borrows more information from the outcome of the patients sharing the same prognosis than from the others. Our data arise from a phase II clinical trial of patients with sarcoma, a rare type of cancer affecting connective or supportive tissues and soft tissue (e.g., cartilage and fat). Each patient presents one subtype of the disease and subtypes are grouped by good, intermediate, and poor prognosis. The prior model should respect the varying prognosis across disease subtypes. The practical motivation for the proposed approach is that the number of accrued patients within each disease subtype is small. Thus it is not possible to carry out a clinical study of possible new therapies for rare conditions, because it would be impossible to plan for sufficiently large sample size to achieve the desired power. We carry out a simulation study to compare the proposed model with a model that assumes similar success probabilities for all subtypes with the same prognosis, i.e., a fixed partition of subtypes by prognosis. When the assumption is satisfied the two models perform comparably. But the proposed model outperforms the competing model when the assumption is incorrect.