共查询到20条相似文献，搜索用时 0 毫秒
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We present a method for estimating the parameters in random effects models for survival data when covariates are subject to missingness. Our method is more general than the usual frailty model as it accommodates a wide range of distributions for the random effects, which are included as an offset in the linear predictor in a manner analogous to that used in generalized linear mixed models. We propose using a Monte Carlo EM algorithm along with the Gibbs sampler to obtain parameter estimates. This method is useful in reducing the bias that may be incurred using complete-case methods in this setting. The methodology is applied to data from Eastern Cooperative Oncology Group melanoma clinical trials in which observations were believed to be clustered and several tumor characteristics were not always observed. 相似文献
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Summary . In clinical studies, longitudinal biomarkers are often used to monitor disease progression and failure time. Joint modeling of longitudinal and survival data has certain advantages and has emerged as an effective way to mutually enhance information. Typically, a parametric longitudinal model is assumed to facilitate the likelihood approach. However, the choice of a proper parametric model turns out to be more elusive than models for standard longitudinal studies in which no survival endpoint occurs. In this article, we propose a nonparametric multiplicative random effects model for the longitudinal process, which has many applications and leads to a flexible yet parsimonious nonparametric random effects model. A proportional hazards model is then used to link the biomarkers and event time. We use B-splines to represent the nonparametric longitudinal process, and select the number of knots and degrees based on a version of the Akaike information criterion (AIC). Unknown model parameters are estimated through maximizing the observed joint likelihood, which is iteratively maximized by the Monte Carlo Expectation Maximization (MCEM) algorithm. Due to the simplicity of the model structure, the proposed approach has good numerical stability and compares well with the competing parametric longitudinal approaches. The new approach is illustrated with primary biliary cirrhosis (PBC) data, aiming to capture nonlinear patterns of serum bilirubin time courses and their relationship with survival time of PBC patients. 相似文献
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We introduce a method of parameter estimation for a random effects cure rate model. We also propose a methodology that allows us to account for nonignorable missing covariates in this class of models. The proposed method corrects for possible bias introduced by complete case analysis when missing data are not missing completely at random and is motivated by data from a pair of melanoma studies conducted by the Eastern Cooperative Oncology Group in which clustering by cohort or time of study entry was suspected. In addition, these models allow estimation of cure rates, which is desirable when we do not wish to assume that all subjects remain at risk of death or relapse from disease after sufficient follow-up. We develop an EM algorithm for the model and provide an efficient Gibbs sampling scheme for carrying out the E-step of the algorithm. 相似文献
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Yang Yang Ira M. Longini Jr. M. Elizabeth Halloran Valerie Obenchain 《Biometrics》2012,68(4):1238-1249
Summary In epidemics of infectious diseases such as influenza, an individual may have one of four possible final states: prior immune, escaped from infection, infected with symptoms, and infected asymptomatically. The exact state is often not observed. In addition, the unobserved transmission times of asymptomatic infections further complicate analysis. Under the assumption of missing at random, data‐augmentation techniques can be used to integrate out such uncertainties. We adapt an importance‐sampling‐based Monte Carlo Expectation‐Maximization (MCEM) algorithm to the setting of an infectious disease transmitted in close contact groups. Assuming the independence between close contact groups, we propose a hybrid EM‐MCEM algorithm that applies the MCEM or the traditional EM algorithms to each close contact group depending on the dimension of missing data in that group, and discuss the variance estimation for this practice. In addition, we propose a bootstrap approach to assess the total Monte Carlo error and factor that error into the variance estimation. The proposed methods are evaluated using simulation studies. We use the hybrid EM‐MCEM algorithm to analyze two influenza epidemics in the late 1970s to assess the effects of age and preseason antibody levels on the transmissibility and pathogenicity of the viruses. 相似文献
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Multiple outcomes are often used to properly characterize an effect of interest. This paper proposes a latent variable model for the situation where repeated measures over time are obtained on each outcome. These outcomes are assumed to measure an underlying quantity of main interest from different perspectives. We relate the observed outcomes using regression models to a latent variable, which is then modeled as a function of covariates by a separate regression model. Random effects are used to model the correlation due to repeated measures of the observed outcomes and the latent variable. An EM algorithm is developed to obtain maximum likelihood estimates of model parameters. Unit-specific predictions of the latent variables are also calculated. This method is illustrated using data from a national panel study on changes in methadone treatment practices. 相似文献
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We consider estimation in generalized linear mixed models (GLMM) for longitudinal data with informative dropouts. At the time a unit drops out, time-varying covariates are often unobserved in addition to the missing outcome. However, existing informative dropout models typically require covariates to be completely observed. This assumption is not realistic in the presence of time-varying covariates. In this article, we first study the asymptotic bias that would result from applying existing methods, where missing time-varying covariates are handled using naive approaches, which include: (1) using only baseline values; (2) carrying forward the last observation; and (3) assuming the missing data are ignorable. Our asymptotic bias analysis shows that these naive approaches yield inconsistent estimators of model parameters. We next propose a selection/transition model that allows covariates to be missing in addition to the outcome variable at the time of dropout. The EM algorithm is used for inference in the proposed model. Data from a longitudinal study of human immunodeficiency virus (HIV)-infected women are used to illustrate the methodology. 相似文献
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Summary It is a common practice to analyze complex longitudinal data using semiparametric nonlinear mixed-effects (SNLME) models with a normal distribution. Normality assumption of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models, but some covariates may often be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. Inferential procedures can be complicated dramatically when data with skewness, missing values, and measurement error are observed. In the literature, there has been considerable interest in accommodating either skewness, incompleteness or covariate measurement error in such models, but there has been relatively little study concerning all three features simultaneously. In this article, our objective is to address the simultaneous impact of skewness, missingness, and covariate measurement error by jointly modeling the response and covariate processes based on a flexible Bayesian SNLME model. The method is illustrated using a real AIDS data set to compare potential models with various scenarios and different distribution specifications. 相似文献
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Jeffrey M. Albert Cuiyu Geng Suchitra Nelson 《Biometrical journal. Biometrische Zeitschrift》2016,58(3):535-548
Health researchers are often interested in assessing the direct effect of a treatment or exposure on an outcome variable, as well as its indirect (or mediation) effect through an intermediate variable (or mediator). For an outcome following a nonlinear model, the mediation formula may be used to estimate causally interpretable mediation effects. This method, like others, assumes that the mediator is observed. However, as is common in structural equations modeling, we may wish to consider a latent (unobserved) mediator. We follow a potential outcomes framework and assume a generalized structural equations model (GSEM). We provide maximum‐likelihood estimation of GSEM parameters using an approximate Monte Carlo EM algorithm, coupled with a mediation formula approach to estimate natural direct and indirect effects. The method relies on an untestable sequential ignorability assumption; we assess robustness to this assumption by adapting a recently proposed method for sensitivity analysis. Simulation studies show good properties of the proposed estimators in plausible scenarios. Our method is applied to a study of the effect of mother education on occurrence of adolescent dental caries, in which we examine possible mediation through latent oral health behavior. 相似文献
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Semiparametric nonlinear mixed-effects (NLME) models are flexible for modeling complex longitudinal data. Covariates are usually introduced in the models to partially explain interindividual variations. Some covariates, however, may be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. We propose two approximate likelihood methods for semiparametric NLME models with covariate measurement errors and nonignorable missing responses. The methods are illustrated in a real data example. Simulation results show that both methods perform well and are much better than the commonly used naive method. 相似文献
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In this paper we present an extension of cure models: to incorporate a longitudinal disease progression marker. The model is motivated by studies of patients with prostate cancer undergoing radiation therapy. The patients are followed until recurrence of the prostate cancer or censoring, with the PSA marker measured intermittently. Some patients are cured by the treatment and are immune from recurrence. A joint-cure model is developed for this type of data, in which the longitudinal marker and the failure time process are modeled jointly, with a fraction of patients assumed to be immune from the endpoint. A hierarchical nonlinear mixed-effects model is assumed for the marker and a time-dependent Cox proportional hazards model is used to model the time to endpoint. The probability of cure is modeled by a logistic link. The parameters are estimated using a Monte Carlo EM algorithm. Importance sampling with an adaptively chosen t-distribution and variable Monte Carlo sample size is used. We apply the method to data from prostate cancer and perform a simulation study. We show that by incorporating the longitudinal disease progression marker into the cure model, we obtain parameter estimates with better statistical properties. The classification of the censored patients into the cure group and the susceptible group based on the estimated conditional recurrence probability from the joint-cure model has a higher sensitivity and specificity, and a lower misclassification probability compared with the standard cure model. The addition of the longitudinal data has the effect of reducing the impact of the identifiability problems in a standard cure model and can help overcome biases due to informative censoring. 相似文献
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Two-level data with hierarchical structure and mixed continuous and polytomous data are very common in biomedical research. In this article, we propose a maximum likelihood approach for analyzing a latent variable model with these data. The maximum likelihood estimates are obtained by a Monte Carlo EM algorithm that involves the Gibbs sampler for approximating the E-step and the M-step and the bridge sampling for monitoring the convergence. The approach is illustrated by a two-level data set concerning the development and preliminary findings from an AIDS preventative intervention for Filipina commercial sex workers where the relationship between some latent quantities is investigated. 相似文献
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We develop an approach, based on multiple imputation, to using auxiliary variables to recover information from censored observations in survival analysis. We apply the approach to data from an AIDS clinical trial comparing ZDV and placebo, in which CD4 count is the time-dependent auxiliary variable. To facilitate imputation, a joint model is developed for the data, which includes a hierarchical change-point model for CD4 counts and a time-dependent proportional hazards model for the time to AIDS. Markov chain Monte Carlo methods are used to multiply impute event times for censored cases. The augmented data are then analyzed and the results combined using standard multiple-imputation techniques. A comparison of our multiple-imputation approach to simply analyzing the observed data indicates that multiple imputation leads to a small change in the estimated effect of ZDV and smaller estimated standard errors. A sensitivity analysis suggests that the qualitative findings are reproducible under a variety of imputation models. A simulation study indicates that improved efficiency over standard analyses and partial corrections for dependent censoring can result. An issue that arises with our approach, however, is whether the analysis of primary interest and the imputation model are compatible. 相似文献
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This paper develops a model for repeated binary regression when a covariate is measured with error. The model allows for estimating the effect of the true value of the covariate on a repeated binary response. The choice of a probit link for the effect of the error-free covariate, coupled with normal measurement error for the error-free covariate, results in a probit model after integrating over the measurement error distribution. We propose a two-stage estimation procedure where, in the first stage, a linear mixed model is used to fit the repeated covariate. In the second stage, a model for the correlated binary responses conditional on the linear mixed model estimates is fit to the repeated binary data using generalized estimating equations. The approach is demonstrated using nutrient safety data from the Diet Intervention of School Age Children (DISC) study. 相似文献
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Aitkin M 《Biometrics》1999,55(1):117-128
This paper describes an EM algorithm for nonparametric maximum likelihood (ML) estimation in generalized linear models with variance component structure. The algorithm provides an alternative analysis to approximate MQL and PQL analyses (McGilchrist and Aisbett, 1991, Biometrical Journal 33, 131-141; Breslow and Clayton, 1993; Journal of the American Statistical Association 88, 9-25; McGilchrist, 1994, Journal of the Royal Statistical Society, Series B 56, 61-69; Goldstein, 1995, Multilevel Statistical Models) and to GEE analyses (Liang and Zeger, 1986, Biometrika 73, 13-22). The algorithm, first given by Hinde and Wood (1987, in Longitudinal Data Analysis, 110-126), is a generalization of that for random effect models for overdispersion in generalized linear models, described in Aitkin (1996, Statistics and Computing 6, 251-262). The algorithm is initially derived as a form of Gaussian quadrature assuming a normal mixing distribution, but with only slight variation it can be used for a completely unknown mixing distribution, giving a straightforward method for the fully nonparametric ML estimation of this distribution. This is of value because the ML estimates of the GLM parameters can be sensitive to the specification of a parametric form for the mixing distribution. The nonparametric analysis can be extended straightforwardly to general random parameter models, with full NPML estimation of the joint distribution of the random parameters. This can produce substantial computational saving compared with full numerical integration over a specified parametric distribution for the random parameters. A simple method is described for obtaining correct standard errors for parameter estimates when using the EM algorithm. Several examples are discussed involving simple variance component and longitudinal models, and small-area estimation. 相似文献
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Summary Traditional latent class modeling has been widely applied to assess the accuracy of dichotomous diagnostic tests. These models, however, assume that the tests are independent conditional on the true disease status, which is rarely valid in practice. Alternative models using probit analysis have been proposed to incorporate dependence among tests, but these models consider restricted correlation structures. In this article, we propose a probit latent class model that allows a general correlation structure. When combined with some helpful diagnostics, this model provides a more flexible framework from which to evaluate the correlation structure and model fit. Our model encompasses several other PLC models but uses a parameter‐expanded Monte Carlo EM algorithm to obtain the maximum‐likelihood estimates. The parameter‐expanded EM algorithm was designed to accelerate the convergence rate of the EM algorithm by expanding the complete‐data model to include a larger set of parameters and it ensures a simple solution in fitting the PLC model. We demonstrate our estimation and model selection methods using a simulation study and two published medical studies. 相似文献
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Albert PS 《Biometrics》2000,56(2):602-608
Binary longitudinal data are often collected in clinical trials when interest is on assessing the effect of a treatment over time. Our application is a recent study of opiate addiction that examined the effect of a new treatment on repeated urine tests to assess opiate use over an extended follow-up. Drug addiction is episodic, and a new treatment may affect various features of the opiate-use process such as the proportion of positive urine tests over follow-up and the time to the first occurrence of a positive test. Complications in this trial were the large amounts of dropout and intermittent missing data and the large number of observations on each subject. We develop a transitional model for longitudinal binary data subject to nonignorable missing data and propose an EM algorithm for parameter estimation. We use the transitional model to derive summary measures of the opiate-use process that can be compared across treatment groups to assess treatment effect. Through analyses and simulations, we show the importance of properly accounting for the missing data mechanism when assessing the treatment effect in our example. 相似文献