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Conditional Independence (conditional + independence)
Selected AbstractsScore Test for Conditional Independence Between Longitudinal Outcome and Time to Event Given the Classes in the Joint Latent Class ModelBIOMETRICS, Issue 1 2010Hélène Jacqmin-Gadda Summary Latent class models have been recently developed for the joint analysis of a longitudinal quantitative outcome and a time to event. These models assume that the population is divided in,G,latent classes characterized by different risk functions for the event, and different profiles of evolution for the markers that are described by a mixed model for each class. However, the key assumption of conditional independence between the marker and the event given the latent classes is difficult to evaluate because the latent classes are not observed. Using a joint model with latent classes and shared random effects, we propose a score test for the null hypothesis of independence between the marker and the outcome given the latent classes versus the alternative hypothesis that the risk of event depends on one or several random effects from the mixed model in addition to the latent classes. A simulation study was performed to compare the behavior of the score test to other previously proposed tests, including situations where the alternative hypothesis or the baseline risk function are misspecified. In all the investigated situations, the score test was the most powerful. The methodology was applied to develop a prognostic model for recurrence of prostate cancer given the evolution of prostate-specific antigen in a cohort of patients treated by radiation therapy. [source] Association chain graphs: modelling etiological pathwaysINTERNATIONAL JOURNAL OF METHODS IN PSYCHIATRIC RESEARCH, Issue 2 2003Michael Höfler Abstract Multiple time-dynamic and interrelated risk factors are usually involved in the complex etiology of disorders. This paper presents a strategy to explore and display visually the relative importance of different association pathways for the onset of disorder over time. The approach is based on graphical chain models, a tool that is powerful but still under-utilized in most fields. Usually, the results of these models are displayed using directed acyclic graphs (DAGs). These draw an edge between a pair of variables whenever the assumption of conditional independence given variables on an earlier or equal temporal footing is violated to a statistically significant extent. In the present paper, the graphs are modified in that confidence intervals for the strengths of associations (statistical main effects) are visualized. These new graphs are called association chain graphs (ACGs). Statistical interactions cause ,edges' between the respective variables within the DAG framework (because the assumption of conditional independence is violated). In contrast they are represented as separate graphs within the subsample where the different association chains may work within the ACG framework. With this new type of graph, more specific information can be displayed whenever the data are essentially described only with statistical main- and two-way interaction effects. Copyright © 2003 Whurr Publishers Ltd. [source] Causality and Causal Models: A Conceptual Perspective,INTERNATIONAL STATISTICAL REVIEW, Issue 3 2006Benito V. Frosini Summary This paper aims at displaying a synthetic view of the historical development and the current research concerning causal relationships, starting from the Aristotelian doctrine of causes, following with the main philosophical streams until the middle of the twentieth century, and commenting on the present intensive research work in the statistical domain. The philosophical survey dwells upon various concepts of cause, and some attempts towards picking out spurious causes. Concerning statistical modelling, factorial models and directed acyclic graphs are examined and compared. Special attention is devoted to randomization and pseudo-randomization (for observational studies) in view of avoiding the effect of possible confounders. An outline of the most common problems and pitfalls, encountered in modelling empirical data, closes the paper, with a warning to be very cautious in modelling and inferring conditional independence between variables. Résumé Le but de cet article est d'offrir une vue d'ensemble sur le thème des relations causales, à partir de la doctrine philosophique aristotélique, et ensuite étendues et formalisées dans le champ de l'analyse statistique multivarée. Dans la revue philosophique on analyse plusieurs conceptions de cause, et les essais de reconnâtre les causes "fausses". La partie centrale du travail s'occupe de modèles causals en forme graphique, qui constituent l'instrument électif de plusieurs recherches causales, et met en evidence la différence entre conditionnement et intervention sur une variable. On a dedié une particulière attention aux procédures de randomization dans le but d'éviter de possible confusions. L'article termine en conseillant d'user de la prudence dans la modelage de l'independence conditionnelle et dans son contrôl empirique. [source] Forecast covariances in the linear multiregression dynamic modelJOURNAL OF FORECASTING, Issue 2 2008Catriona M. Queen Abstract The linear multiregression dynamic model (LMDM) is a Bayesian dynamic model which preserves any conditional independence and causal structure across a multivariate time series. The conditional independence structure is used to model the multivariate series by separate (conditional) univariate dynamic linear models, where each series has contemporaneous variables as regressors in its model. Calculating the forecast covariance matrix (which is required for calculating forecast variances in the LMDM) is not always straightforward in its current formulation. In this paper we introduce a simple algebraic form for calculating LMDM forecast covariances. Calculation of the covariance between model regression components can also be useful and we shall present a simple algebraic method for calculating these component covariances. In the LMDM formulation, certain pairs of series are constrained to have zero forecast covariance. We shall also introduce a possible method to relax this restriction. Copyright © 2008 John Wiley & Sons, Ltd. [source] Stochastic Model Reduction by Maximizing IndependenceASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 3-4 2005Hui Zhang By analysing information descriptions in state space models of linear stochastic systems, this paper proposes two model reduction methods via principles of maximizing independence and conditional independence among the reduced state vector, respectively. These methods are based on state aggregation. The independence and conditional independence are measured by the Kullback-Leibler information distance. It is demonstrated that the maximum conditional independence method is not only applicable to stable systems, but also applicable to unstable systems. Simulation results illustrate the efficiency of the present methods. [source] ELICITING A DIRECTED ACYCLIC GRAPH FOR A MULTIVARIATE TIME SERIES OF VEHICLE COUNTS IN A TRAFFIC NETWORKAUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 3 2007Catriona M. Queen Summary The problem of modelling multivariate time series of vehicle counts in traffic networks is considered. It is proposed to use a model called the linear multiregression dynamic model (LMDM). The LMDM is a multivariate Bayesian dynamic model which uses any conditional independence and causal structure across the time series to break down the complex multivariate model into simpler univariate dynamic linear models. The conditional independence and causal structure in the time series can be represented by a directed acyclic graph (DAG). The DAG not only gives a useful pictorial representation of the multivariate structure, but it is also used to build the LMDM. Therefore, eliciting a DAG which gives a realistic representation of the series is a crucial part of the modelling process. A DAG is elicited for the multivariate time series of hourly vehicle counts at the junction of three major roads in the UK. A flow diagram is introduced to give a pictorial representation of the possible vehicle routes through the network. It is shown how this flow diagram, together with a map of the network, can suggest a DAG for the time series suitable for use with an LMDM. [source] Score Test for Conditional Independence Between Longitudinal Outcome and Time to Event Given the Classes in the Joint Latent Class ModelBIOMETRICS, Issue 1 2010Hélène Jacqmin-Gadda Summary Latent class models have been recently developed for the joint analysis of a longitudinal quantitative outcome and a time to event. These models assume that the population is divided in,G,latent classes characterized by different risk functions for the event, and different profiles of evolution for the markers that are described by a mixed model for each class. However, the key assumption of conditional independence between the marker and the event given the latent classes is difficult to evaluate because the latent classes are not observed. Using a joint model with latent classes and shared random effects, we propose a score test for the null hypothesis of independence between the marker and the outcome given the latent classes versus the alternative hypothesis that the risk of event depends on one or several random effects from the mixed model in addition to the latent classes. A simulation study was performed to compare the behavior of the score test to other previously proposed tests, including situations where the alternative hypothesis or the baseline risk function are misspecified. In all the investigated situations, the score test was the most powerful. The methodology was applied to develop a prognostic model for recurrence of prostate cancer given the evolution of prostate-specific antigen in a cohort of patients treated by radiation therapy. [source] Related Causal Frameworks for Surrogate OutcomesBIOMETRICS, Issue 2 2009Marshall M. Joffe Summary Four major frameworks have been developed for evaluating surrogate markers in randomized trials: one based on conditional independence of observable variables, another based on direct and indirect effects, a third based on a meta-analysis, and a fourth based on principal stratification. The first two of these fit into a paradigm we call the causal-effects (CE) paradigm, in which, for a good surrogate, the effect of treatment on the surrogate, combined with the effect of the surrogate on the clinical outcome, allow prediction of the effect of the treatment on the clinical outcome. The last two approaches fall into the causal-association (CA) paradigm, in which the effect of the treatment on the surrogate is associated with its effect on the clinical outcome. We consider the CE paradigm first, and consider identifying assumptions and some simple estimation procedures; we then consider the CA paradigm. We examine the relationships among these approaches and associated estimators. We perform a small simulation study to illustrate properties of the various estimators under different scenarios, and conclude with a discussion of the applicability of both paradigms. [source] Binary models for marginal independenceJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 2 2008Mathias Drton Summary., Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach that is taken is graphical and draws on analogies with multivariate Gaussian models for marginal independence. For the graphical model representation we use bidirected graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm. Finally we consider combining these models with symmetry restrictions. [source] | ||||||||||