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SUMMARY: In this article we investigate regression calibration methods to jointly model longitudinal and survival data using a semiparametric longitudinal model and a proportional hazards model. In the longitudinal model, a biomarker is assumed to follow a semiparametric mixed model where covariate effects are modeled parametrically and subject-specific time profiles are modeled nonparametrially using a population smoothing spline and subject-specific random stochastic processes. The Cox model is assumed for survival data by including both the current measure and the rate of change of the underlying longitudinal trajectories as covariates, as motivated by a prostate cancer study application. We develop a two-stage semiparametric regression calibration (RC) method. Two variations of the RC method are considered, risk set regression calibration and a computationally simpler ordinary regression calibration. Simulation results show that the two-stage RC approach performs well in practice and effectively corrects the bias from the naive method. We apply the proposed methods to the analysis of a dataset for evaluating the effects of the longitudinal biomarker PSA on the recurrence of prostate cancer. 相似文献
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Summary In studies involving functional data, it is commonly of interest to model the impact of predictors on the distribution of the curves, allowing flexible effects on not only the mean curve but also the distribution about the mean. Characterizing the curve for each subject as a linear combination of a high‐dimensional set of potential basis functions, we place a sparse latent factor regression model on the basis coefficients. We induce basis selection by choosing a shrinkage prior that allows many of the loadings to be close to zero. The number of latent factors is treated as unknown through a highly‐efficient, adaptive‐blocked Gibbs sampler. Predictors are included on the latent variables level, while allowing different predictors to impact different latent factors. This model induces a framework for functional response regression in which the distribution of the curves is allowed to change flexibly with predictors. The performance is assessed through simulation studies and the methods are applied to data on blood pressure trajectories during pregnancy. 相似文献
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A frequently encountered problem in longitudinal studies is data that are missing due to missed visits or dropouts. In the statistical literature, interest has primarily focused on monotone missing data (dropout) with much less work on intermittent missing data in which a subject may return after one or more missed visits. Intermittent missing data have broader applicability that can include the frequent situation in which subjects do not have common sets of visit times or they visit at nonprescheduled times. In this article, we propose a latent pattern mixture model (LPMM), where the mixture patterns are formed from latent classes that link the longitudinal response and the missingness process. This allows us to handle arbitrary patterns of missing data embodied by subjects' visit process, and avoids the need to specify the mixture patterns a priori. One assumption of our model is that the missingness process is assumed to be conditionally independent of the longitudinal outcomes given the latent classes. We propose a noniterative approach to assess this key assumption. The LPMM is illustrated with a data set from a health service research study in which homeless people with mental illness were randomized to three different service packages and measures of homelessness were recorded at multiple time points. Our model suggests the presence of four latent classes linking subject visit patterns to homeless outcomes. 相似文献
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A recurring objective in longitudinal studies on aging and longevity has been the investigation of the relationship between age-at-death and current values of a longitudinal covariate trajectory that quantifies reproductive or other behavioral activity. We propose a novel technique for predicting age-at-death distributions for situations where an entire covariate history is included in the predictor. The predictor trajectories up to current time are represented by time-varying functional principal component scores, which are continuously updated as time progresses and are considered to be time-varying predictor variables that are entered into a class of time-varying functional regression models that we propose. We demonstrate for biodemographic data how these methods can be applied to obtain predictions for age-at-death and estimates of remaining lifetime distributions, including estimates of quantiles and of prediction intervals for remaining lifetime. Estimates and predictions are obtained for individual subjects, based on their observed behavioral trajectories, and include a dimension-reduction step that is implemented by projecting on a single index. The proposed techniques are illustrated with data on longitudinal daily egg-laying for female medflies, predicting remaining lifetime and age-at-death distributions from individual event histories observed up to current time. 相似文献
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Miglioretti DL 《Biometrics》2003,59(3):710-720
Health status is a complex outcome, often characterized by multiple measures. When assessing changes in health status over time, multiple measures are typically collected longitudinally. Analytic challenges posed by these multivariate longitudinal data are further complicated when the outcomes are combinations of continuous, categorical, and count data. To address these challenges, we propose a fully Bayesian latent transition regression approach for jointly analyzing a mixture of longitudinal outcomes from any distribution. Health status is assumed to be a categorical latent variable, and the multiple outcomes are treated as surrogate measures of the latent health state, observed with error. Using this approach, both baseline latent health state prevalences and the probabilities of transitioning between the health states over time are modeled as functions of covariates. The observed outcomes are related to the latent health states through regression models that include subject-specific effects to account for residual correlation among repeated measures over time, and covariate effects to account for differential measurement of the latent health states. We illustrate our approach with data from a longitudinal study of back pain. 相似文献
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Nimisha Chaturvedi Renée X. de Menezes Jelle J. Goeman 《Biometrical journal. Biometrische Zeitschrift》2017,59(1):145-158
In high‐dimensional omics studies where multiple molecular profiles are obtained for each set of patients, there is often interest in identifying complex multivariate associations, for example, copy number regulated expression levels in a certain pathway or in a genomic region. To detect such associations, we present a novel approach to test for association between two sets of variables. Our approach generalizes the global test, which tests for association between a group of covariates and a single univariate response, to allow high‐dimensional multivariate response. We apply the method to several simulated datasets as well as two publicly available datasets, where we compare the performance of multivariate global test (G2) with univariate global test. The method is implemented in R and will be available as a part of the globaltest package in R. 相似文献
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Marginalized models (Heagerty, 1999, Biometrics 55, 688-698) permit likelihood-based inference when interest lies in marginal regression models for longitudinal binary response data. Two such models are the marginalized transition and marginalized latent variable models. The former captures within-subject serial dependence among repeated measurements with transition model terms while the latter assumes exchangeable or nondiminishing response dependence using random intercepts. In this article, we extend the class of marginalized models by proposing a single unifying model that describes both serial and long-range dependence. This model will be particularly useful in longitudinal analyses with a moderate to large number of repeated measurements per subject, where both serial and exchangeable forms of response correlation can be identified. We describe maximum likelihood and Bayesian approaches toward parameter estimation and inference, and we study the large sample operating characteristics under two types of dependence model misspecification. Data from the Madras Longitudinal Schizophrenia Study (Thara et al., 1994, Acta Psychiatrica Scandinavica 90, 329-336) are analyzed. 相似文献
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We consider the penalized generalized estimating equations (GEEs) for analyzing longitudinal data with high-dimensional covariates, which often arise in microarray experiments and large-scale health studies. Existing high-dimensional regression procedures often assume independent data and rely on the likelihood function. Construction of a feasible joint likelihood function for high-dimensional longitudinal data is challenging, particularly for correlated discrete outcome data. The penalized GEE procedure only requires specifying the first two marginal moments and a working correlation structure. We establish the asymptotic theory in a high-dimensional framework where the number of covariates p(n) increases as the number of clusters n increases, and p(n) can reach the same order as n. One important feature of the new procedure is that the consistency of model selection holds even if the working correlation structure is misspecified. We evaluate the performance of the proposed method using Monte Carlo simulations and demonstrate its application using a yeast cell-cycle gene expression data set. 相似文献
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Liang Zhu Hui Zhao Jianguo Sun Stanley Pounds Hui Zhang 《Biometrical journal. Biometrische Zeitschrift》2013,55(1):5-16
This paper discusses regression analysis of longitudinal data in which the observation process may be related to the longitudinal process of interest. Such data have recently attracted a great deal of attention and some methods have been developed. However, most of those methods treat the observation process as a recurrent event process, which assumes that one observation can immediately follow another. Sometimes, this is not the case, as there may be some delay or observation duration. Such a process is often referred to as a recurrent episode process. One example is the medical cost related to hospitalization, where each hospitalization serves as a single observation. For the problem, we present a joint analysis approach for regression analysis of both longitudinal and observation processes and a simulation study is conducted that assesses the finite sample performance of the approach. The asymptotic properties of the proposed estimates are also given and the method is applied to the medical cost data that motivated this study. 相似文献
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On modelling mean-covariance structures in longitudinal studies 总被引：4，自引：0，他引：4
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When novel scientific questions arise after longitudinal binary data have been collected, the subsequent selection of subjects from the cohort for whom further detailed assessment will be undertaken is often necessary to efficiently collect new information. Key examples of additional data collection include retrospective questionnaire data, novel data linkage, or evaluation of stored biological specimens. In such cases, all data required for the new analyses are available except for the new target predictor or exposure. We propose a class of longitudinal outcome-dependent sampling schemes and detail a design corrected conditional maximum likelihood analysis for highly efficient estimation of time-varying and time-invariant covariate coefficients when resource limitations prohibit exposure ascertainment on all participants. Additionally, we detail an important study planning phase that exploits available cohort data to proactively examine the feasibility of any proposed substudy as well as to inform decisions regarding the most desirable study design. The proposed designs and associated analyses are discussed in the context of a study that seeks to examine the modifying effect of an interleukin-10 cytokine single nucleotide polymorphism on asthma symptom regression in adolescents participating Childhood Asthma Management Program Continuation Study. Using this example we assume that all data necessary to conduct the study are available except subject-specific genotype data. We also assume that these data would be ascertained by analyzing stored blood samples, the cost of which limits the sample size. 相似文献
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SUMMARY: We propose a general multistate transition model. The model is developed for the analysis of repeated episodes of multiple states representing different health status. Transitions among multiple states are modeled jointly using multivariate latent traits with factor loadings. Different types of state transition are described by flexible transition-specific nonparametric baseline intensities. A state-specific latent trait is used to capture individual tendency of the sojourn in the state that cannot be explained by covariates and to account for correlation among repeated sojourns in the same state within an individual. Correlation among sojourns across different states within an individual is accounted for by the correlation between the different latent traits. The factor loadings for a latent trait accommodate the dependence of the transitions to different competing states from a same state. We obtain the semiparametric maximum likelihood estimates through an expectation-maximization (EM) algorithm. The method is illustrated by studying repeated transitions between independence and disability states of activities of daily living (ADL) with death as an absorbing state in a longitudinal aging study. The performance of the estimation procedure is assessed by simulation studies. 相似文献
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Summary Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row–column associations within high‐dimensional data matrices. SSVD seeks a low‐rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left‐ and right‐singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity‐inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets. 相似文献
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Edward J. Bedrick 《Biometrics》2020,76(2):508-517
Researchers often use a two-step process to analyze multivariate data. First, dimensionality is reduced using a technique such as principal component analysis, followed by a group comparison using a -test or analysis of variance. Although this practice is often discouraged, the statistical properties of this procedure are not well understood, starting with the hypothesis being tested. We suggest that this approach might be considering two distinct hypotheses, one of which is a global test of no differences in the mean vectors, and the other being a focused test of a specific linear combination where the coefficients have been estimated from the data. We study the asymptotic properties of the two-sample -statistic for these two scenarios, assuming a nonsparse setting. We show that the size of the global test agrees with the presumed level but that the test has poor power. In contrast, the size of the focused test can be arbitrarily distorted with certain mean and covariance structures. A simple method is provided to correct the size of the focused test. Data analyses and simulations are used to illustrate the results. Recommendations on the use of this two-step method and the related use of principal components for prediction are provided. 相似文献
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Mareike Kohlmann Leonhard Held Veit Peter Grunert 《Biometrical journal. Biometrische Zeitschrift》2009,51(4):610-626
To classify patients either as resistant or non‐resistant to HIV therapy based on longitudinal viral load profiles, we applied longitudinal quadratic discriminant analysis and examined various measures, mainly derived from the Brier Score, to assess the biomarker performance in terms of discrimination and calibration. The analysis of the application data revealed an increase in performance by using longer profiles instead of single biomarker measurements. Simulations showed that the selection of mixed models for the estimation of the group‐specific discriminant rule parameters should be based on BIC, rather than on the best performance measure. An incorrect model selection can lead to spuriously better or worse performance as misclassification and classification certainty regards, especially with increasing length of the profiles and for more complex models with random slopes. 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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Donald Hedeker Stephen H. C. du Toit Hakan Demirtas Robert D. Gibbons 《Biometrics》2018,74(1):354-361
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