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Time-dependent Covariates (time-dependent + covariate)
Selected AbstractsCompeting Risks and Time-Dependent CovariatesBIOMETRICAL JOURNAL, Issue 1 2010Giuliana Cortese Abstract Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates are to be included in the modeling process, then it is still possible to estimate cause-specific hazards but prediction of the cumulative incidences and survival probabilities based on these is no longer feasible. This article aims at providing some possible strategies for dealing with these prediction problems. In a multi-state framework, a first approach uses internal covariates to define additional (intermediate) transient states in the competing risks model. Another approach is to apply the landmark analysis as described by van Houwelingen [Scandinavian Journal of Statistics 2007, 34, 70,85] in order to study cumulative incidences at different subintervals of the entire study period. The final strategy is to extend the competing risks model by considering all the possible combinations between internal covariate levels and cause-specific events as final states. In all of those proposals, it is possible to estimate the changes/differences of the cumulative risks associated with simple internal covariates. An illustrative example based on bone marrow transplant data is presented in order to compare the different methods. [source] Serum bilirubin levels and mortality after myeloablative allogeneic hematopoietic cell transplantation,HEPATOLOGY, Issue 2 2005Ted A. Gooley Many patients who undergo hematopoietic cell transplantation experience liver injury. We examined the association of serum bilirubin levels with nonrelapse mortality by day +200, testing the hypothesis that the duration of jaundice up to a given point in time provides more prognostic information than either the maximum bilirubin value or the value at that point in time. We studied 1,419 consecutive patients transplanted from allogeneic donors. Total serum bilirubin values up to day +100, death, or relapse were retrieved,along with nonrelapse mortality by day +200 as an outcome measure,using Cox regression models with each bilirubin measure modeled as a time-dependent covariate. The bilirubin value at a particular point in time provided the best fit to the model for mortality. With bilirubin at a point in time modeled as an 8th-degree polynomial, an increase in bilirubin from 1 to 3 mg/dL is associated with a mortality hazard ratio of 6.42. An increase from 4 to 6 mg/dL yields a hazard ratio of 2.05, and an increase from 10 to 12 mg/dL yields a hazard ratio of 1.17. Among patients who were deeply jaundiced, survival was related to the absence of multiorgan failure and to higher platelet counts. In conclusion, the value of total serum bilirubin at a particular point in time after transplant carries more informative prognostic information than does the maximum or average value up to that point in time. The increase in mortality for a given increase in bilirubin value is larger when the starting value is lower. (HEPATOLOGY 2005,41:345,352.) [source] Variability explained by covariates in linear mixed-effect models for longitudinal dataTHE CANADIAN JOURNAL OF STATISTICS, Issue 3 2010Bo Hu Abstract Variability explained by covariates or explained variance is a well-known concept in assessing the importance of covariates for dependent outcomes. In this paper we study R2 statistics of explained variance pertinent to longitudinal data under linear mixed-effect models, where the R2 statistics are computed at two different levels to measure, respectively, within- and between-subject variabilities explained by the covariates. By deriving the limits of R2 statistics, we find that the interpretation of explained variance for the existing R2 statistics is clear only in the case where the covariance matrix of the outcome vector is compound symmetric. Two new R2 statistics are proposed to address the effect of time-dependent covariate means. In the general case where the outcome covariance matrix is not compound symmetric, we introduce the concept of compound symmetry projection and use it to define level-one and level-two R2 statistics. Numerical results are provided to support the theoretical findings and demonstrate the performance of the R2 statistics. The Canadian Journal of Statistics 38: 352,368; 2010 © 2010 Statistical Society of Canada La variation expliquée par les covariables (ou la variance expliquée) est un concept bien connu pour mesurer l'importance de ces covariables sur la variable dépendante. Dans cet article, nous étudions la statistique du R carré pour la variance expliquée pertinente aux données longitudinales pour des modèles linéaires à effets mixtes. La statistique du R carré est calculée à deux niveaux différents pour mesurer la variation expliquée par les covariables à l'intérieur et entre les sujets. En obtenant des limites aux statistiques du R carré, nous trouvons que l'interprétation de la variance expliquée pour les statistiques du R carré existantes est claire seulement dans le cas où la matrice de variance-covariance des observations dépendantes est symétrique composée. Deux nouvelles statistiques du R carré sont proposées afin de prendre en compte les effets des moyennes des covariables pouvant dépendre du temps. Dans le cas général où la matrice de variance-covariance des observations n'est pas symétrique composée, nous introduisons le concept de projection symétrique composée et nous l'utilisons pour définir les statistiques du R carré de niveaux 1 et 2. Des résultats numériques appuient nos résultats théoriques et ils montrent la performance des statistiques du R carré. La revue canadienne de statistique 38: 352,368; 2010 © 2010 Société statistique du Canada [source] Violence from young women involuntarily admitted for severe drug abuseACTA PSYCHIATRICA SCANDINAVICA, Issue 1 2007T. Palmstierna Objective:, To simultaneously evaluate actuarial and dynamic predictors of severe in-patient violence among women involuntarily admitted for severe drug abuse. Method:, All patients admitted to special facilities for involuntary treatment of absconding-prone, previously violent, drug abusing women in Sweden were assessed with the Staff Observation Aggression Scale, revised. Actuarial data on risk factors for violence were collected and considered in an extended Cox proportional hazards model with multiple events and daily assessments of the Broset Violence Checklist as time-dependent covariates. Results:, Low-grade violence and being influenced by illicit drugs were the best predictors of severe violence within 24 h. Significant differences in risk for violence between different institutions were also found. Conclusion:, In-patient violence risk is rapidly varying over time with being influenced by illicit drugs and exhibiting low-grade violence being significant dynamic predictors. Differences in violence between patients could not be explained by patient characteristics. [source] Graphing survival curve estimates for time-dependent covariatesINTERNATIONAL JOURNAL OF METHODS IN PSYCHIATRIC RESEARCH, Issue 2 2002Lonni R. Schultz Abstract Graphical representation of statistical results is often used to assist readers in the interpretation of the findings. This is especially true for survival analysis where there is an interest in explaining the patterns of survival over time for specific covariates. For fixed categorical covariates, such as a group membership indicator, Kaplan-Meier estimates (1958) can be used to display the curves. For time-dependent covariates this method may not be adequate. Simon and Makuch (1984) proposed a technique that evaluates the covariate status of the individuals remaining at risk at each event time. The method takes into account the change in an individual's covariate status over time. The survival computations are the same as the Kaplan-Meier method, in that the conditional survival estimates are the function of the ratio of the number of events to the number at risk at each event time. The difference between the two methods is that the individuals at risk within each level defined by the covariate is not fixed at time 0 in the Simon and Makuch method as it is with the Kaplan-Meier method. Examples of how the two methods can differ for time dependent covariates in Cox proportional hazards regression analysis are presented. Copyright © 2002 Whurr Publishers Ltd. [source] Modelling survival in acute severe illness: Cox versus accelerated failure time modelsJOURNAL OF EVALUATION IN CLINICAL PRACTICE, Issue 1 2008John L. Moran MBBS FRACP FJFICM MD Abstract Background, The Cox model has been the mainstay of survival analysis in the critically ill and time-dependent covariates have infrequently been incorporated into survival analysis. Objectives, To model 28-day survival of patients with acute lung injury (ALI) and acute respiratory distress syndrome (ARDS), and compare the utility of Cox and accelerated failure time (AFT) models. Methods, Prospective cohort study of 168 adult patients enrolled at diagnosis of ALI in 21 adult ICUs in three Australian States with measurement of survival time, censored at 28 days. Model performance was assessed as goodness-of-fit [GOF, cross-products of quantiles of risk and time intervals (P , 0.1), Cox model] and explained variation (,R2', Cox and ATF). Results, Over a 2-month study period (October,November 1999), 168 patients with ALI were identified, with a mean (SD) age of 61.5 (18) years and 30% female. Peak mortality hazard occurred at days 7,8 after onset of ALI/ARDS. In the Cox model, increasing age and female gender, plus interaction, were associated with an increased mortality hazard. Time-varying effects were established for patient severity-of-illness score (decreasing hazard over time) and multiple-organ-dysfunction score (increasing hazard over time). The Cox model was well specified (GOF, P > 0.34) and R2 = 0.546, 95% CI: 0.390, 0.781. Both log-normal (R2 = 0.451, 95% CI: 0.321, 0.695) and log-logistic (R2 0.470, 95% CI: 0.346, 0.714) AFT models identified the same predictors as the Cox model, but did not demonstrate convincingly superior overall fit. Conclusions, Time dependence of predictors of survival in ALI/ARDS exists and must be appropriately modelled. The Cox model with time-varying covariates remains a flexible model in survival analysis of patients with acute severe illness. [source] Competing Risks and Time-Dependent CovariatesBIOMETRICAL JOURNAL, Issue 1 2010Giuliana Cortese Abstract Time-dependent covariates are frequently encountered in regression analysis for event history data and competing risks. They are often essential predictors, which cannot be substituted by time-fixed covariates. This study briefly recalls the different types of time-dependent covariates, as classified by Kalbfleisch and Prentice [The Statistical Analysis of Failure Time Data, Wiley, New York, 2002] with the intent of clarifying their role and emphasizing the limitations in standard survival models and in the competing risks setting. If random (internal) time-dependent covariates are to be included in the modeling process, then it is still possible to estimate cause-specific hazards but prediction of the cumulative incidences and survival probabilities based on these is no longer feasible. This article aims at providing some possible strategies for dealing with these prediction problems. In a multi-state framework, a first approach uses internal covariates to define additional (intermediate) transient states in the competing risks model. Another approach is to apply the landmark analysis as described by van Houwelingen [Scandinavian Journal of Statistics 2007, 34, 70,85] in order to study cumulative incidences at different subintervals of the entire study period. The final strategy is to extend the competing risks model by considering all the possible combinations between internal covariate levels and cause-specific events as final states. In all of those proposals, it is possible to estimate the changes/differences of the cumulative risks associated with simple internal covariates. An illustrative example based on bone marrow transplant data is presented in order to compare the different methods. [source] A Semiparametric Joint Model for Longitudinal and Survival Data with Application to Hemodialysis StudyBIOMETRICS, Issue 3 2009Liang Li Summary In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkers on each subject quantify the severity of the disease and that subject's susceptibility to progression of the disease. It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival. This is usually done with a shared parameter model. In such models, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independent given subject-level severity or susceptibility (also called frailty in statistical terms). In this article, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox proportional hazard model. We allow unknown regression coefficients and time-dependent covariates in both models. The proposed estimators are maximizers of an exact correction to the joint log likelihood with the frailties eliminated as nuisance parameters, an idea that originated from correction of covariate measurement error in measurement error models. The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators. Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties. The proposed method was studied in simulations and applied to a data set from the Hemodialysis Study. [source] | |||||||||||||