Longitudinal data analysis / mixed effects model 1
Presenter: Freedom Gumedze
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Saanich 1-2 (Level 1)
Session Synopsis:
Robust joint modeling of longitudinal data and clustered competing risks data by downweighting of outlying longitudinal measurements
Joint models for longitudinal data and competing risk survival data usually assume Gaussian random errors for the longitudinal sub-model which is not robust to outliers. This paper proposes a joint model for the analysis of longitudinal data and clustered competing risk survival data which downweights outliers or outlying subject profiles with respect to the longitudinal measurements. Our proposed model consists of a linear mixed effects sub-model for the longitudinal measurements and a proportional cause-specific hazard frailty sub-model, linked together by latent random effects. The inclusion of random effects in the cause-specific hazard sub-model accounts for the correlation induced by the clustering of patients within centres. A frailty model for the subdistribution hazard could be used instead of the inclusion of random effects in the cause-specific hazard sub-model. The proposed linear mixed effects sub-model considers an outlying subject as a subject whose profile has an inflated random effects variance-covariance matrix. A measure of the shift or inflation in the random effects variance-covariance matrix for a subject gives an indication of the outlyingness of that subject. We use a likelihood ratio test statistic to determine whether the ith subject has an inflated variance-covariance matrix and is therefore a possible outlier. The joint model can then be fitted to downweight the subject in the analysis, if desired. The proposed methodology is illustrated using a real dataset from TB pericarditis multicentre clinical trial and a simulation.
Longitudinal data analysis / mixed effects model 1
Presenter: Hélène Jacqmin-Gadda
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Saanich 1-2 (Level 1)
Session Synopsis:
Population-averaged versus subject-specific approaches for longitudinal data with follow-up truncated by death
Mixed models estimated by maximum likelihood (Laird & Ware, 1982) and marginal models estimated by Generalized Estimating Equations (GEE, Liang & Zeger, 1986) are the two main methods for the analysis of longitudinal data in epidemiology. They differ with regards to underlying hypotheses (covariance structure modeling vs completely at random missingness assumption) and parameter interpretation (subject-specific vs population averaged). However, parameters from linear models have both subject-specific and population averaged interpretations when missing data are completely at random. As mixed models are robust to missing at random data, they are favored for the analysis of cohort studies with attrition, but weighted GEE (Robins et al, 1995) can provide unbiased population-averaged estimates under the missing at random assumption. When attrition may be due to death, as in cohort of elderly subjects, the use of mixed model is debated because some authors consider they can be interpreted only in an immortal cohort (Kurland et al, 2009). We investigate the interpretation and robustness of estimators from mixed models and joint models obtained by maximum likelihood and from marginal models obtained by GEE or two weighted GEE approaches, when follow-up may be truncated by death. Using both formal calculations and a simulation study, we advocate that the subject-specific interpretation of linear mixed model parameters holds when death is at random while the population-averaged interpretation in the alive population does not hold. The marginal expectation in the alive population may be obtained by weighted GEE if weights are correctly defined as the inverse probability of observation given alive. In a more realistic framework where death depends on unobserved values of the response variable, well specified joint models may provide valid subject-specific estimates.
Longitudinal data analysis / mixed effects model 1
Presenter: Francesca Little
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Saanich 1-2 (Level 1)
Session Synopsis:
Joint models for nonlinear longitudinal profiles in the presence of informative censoring.
Malaria clinical trials are typically designed to determine the efficacy of malaria drugs in eliminating asexual parasites. However, it is the gametocytes, or sexual parasites that are the agents of transmission. Several problems related to the design and conduct of the trials make it difficult to estimate overall gametocytemia related to an infection accurately. These include informative censoring of subjects due to subjects being rescued when parasites do not clear by day 7. One way of overcoming this problem is through the joint modeling of the gametocyte densities and the time to censoring due to either lost to follow up or failure or administrative censoring. The nonlinear nature of the gametocyte density profile over time, the underlying zero-inflated and skew distribution of gametocyte densities and the competing risk nature of different reasons for terminating follow-up all contribute to the complexity of the joint modeling. We present a joint model that combines a modified critical exponential model for the gametocyte density profiles and a Weibull model for the time to censoring through the use of shared random effects. We model time-varying covariates like drug concentrations and parasite density using bi-exponential models and include the estimated/smooth profiles from these models as predictors in the gametocyte model. We compare this to a model where we use splines for the nonlinear gametocyte profile and combine this with a competing risk model for the different censoring mechanisms. In addition we look at a model for gametocyte prevalence using an underlying binomial distribution. Both frequentist and Bayesian estimation approaches are used.
Longitudinal data analysis / mixed effects model 1
Presenter: Tea Uggen
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Saanich 1-2 (Level 1)
Session Synopsis:
SELECTING OUTCOME MEASURES AND STATISTICAL MODELS IN NEUROLOGICAL CLINICAL TRIALS THAT MEASURE FUNCTIONAL OUTCOMES
In clinical trials that assess recovery or management of a neurological condition, it is common to use a variety of outcome variables to assess functional recovery. For example, a clinical trial may involve the assessment of aphasia, a communication disorder that is caused by a stroke or traumatic brain injury. Aphasia recovery is assessed using the Western Aphasia Battery Aphasia Quotient (AQ) and Discourse Analysis (DA), in addition to other measures. A number of alternative measures have also been derived from these, to facilitate statistical analysis. While determining the most appropriate measure to use is a clinical issue, statistical considerations can inform the use of the most appropriate models to assess these measures. However, the problem of determining the most appropriate variant of an outcome measure to model is non-trivial. Although Information Criteria (eg. AIC, BIC) are commonly used in model selection, these criteria focus on the selection of predictors rather than on the selection of outcome variables. In this work, we demonstrate that Information Criteria cannot be used to select the best variant of an outcome variable since their values are scale-dependant and can change dramatically when a variable is transformed. A more appropriate method to achieve this involves the examination of model residual plots. However, residual plots are not commonly used to assess the fits of longitudinal models such as generalized estimating equations (GEE) or linear mixed models, which are used to analyse functional recovery. In this work, we demonstrate the use of model diagnostic plots that were proposed by Park and Lee (2004) for GEE models, to determine the most appropriate variant of discourse analysis (a measure of aphasia recovery after a stroke). While our focus is on selecting the best model to assess aphasia recovery using discourse analysis, the method is general enough to be applied to the selection of the appropriate variant of an outcome measure in any clinical trial that uses GEE models to assess functional recovery.
Longitudinal data analysis / mixed effects model 1
Presenter: Sean Yiu
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Saanich 1-2 (Level 1)
Session Synopsis:
Two-part models with stochastic processes for modelling longitudinal semi continuous data: exact likelihood inference and modelling the overall marginal mean
Several authors have described two-part models with patient-specific stochastic processes for analysing longitudinal semi continuous data. In theory, such models can offer greater flexibility than the standard two-part model with patient-specific random effects. However, in practice the high dimensional integrations involved in the marginal likelihood (over the stochastic processes) significantly complicates model fitting. Thus non-standard computationally intensive procedures based on simulating the marginal likelihood have so far only been proposed. In this presentation, we demonstrate how the high dimensional integrations involved in the marginal likelihood can be computed exactly. Specifically, by using newly obtained results on the skew normal distribution, the marginal likelihood is transformed so that the high dimensional integrations are contained in the cumulative distribution function of a multivariate normal distribution, which can be efficiently evaluated. Hence maximum likelihood estimation can be used to obtain parameter estimates and asymptotic standard errors (from the observed information matrix) of model parameters. We describe our proposed efficient implementation procedure for the standard two-part model parameterization and when it is of interest to directly model the overall marginal mean. The methodology is applied on a psoriatic arthritis data set concerning functional disability.
Longitudinal data analysis / mixed effects model 1
Presenter: Virginie Rondeau
When: Tuesday, July 12, 2016 Time: 11:00 AM - 12:30 PM
Room: Saanich 1-2 (Level 1)
Session Synopsis:
Multivariate Joint Models for Longitudinal and Survival Data: Predictive Abilities of Tumor Burden in Advanced Colorectal Cancer
The RECIST criteria are used as standard guidelines for the clinical evaluation of cancer treatments. In clinical trials of phase III, it is the time to the development of disease progression that defines the clinical endpoint related to overall survival (OS). The assessment is based on the anatomical tumor burden: change in the sum of the longest diameters of target lesions, appearance of new lesions (NL) and unequivocal progression of non-target lesions (NTL). Despite indisputable advantages of this standard tool, RECIST are subject to some limits such as categorization of continuous tumor size or negligence of its longitudinal trajectory. In particular, it is of interest to capture the tendency of short-term decrease and long-term re-growth of tumor size that is often present under an advanced cancer treatment and model it simultaneously with time to appearance of NL and/or progression of NTL and OS. This complex analysis is achievable using multivariate joint models for longitudinal and survival data. Using statistical tools such as Brier Score and EPOCE, the predictive abilities for OS of tumor size, appearance of NL and progression of NTL can be evaluated. We propose a new multivariate joint model for longitudinal biomarker (SLD) and two types of survival data (death and jointly appearance of NL and progression of NTL). In the model it is assumed that the tumor size trajectory is divided into three phases: the baseline level, the short-term and long-term evolution. We perform a simulation study to validate the proposed method and apply the model to a real dataset of a phase III clinical trial for metastatic colorectal cancer. In the results of the analysis, we will determine on which component: tumor size (in all the phases), appearance of NL and progression of NTL or death, the treatment acts mostly and evaluate the predictive abilities of the components for death. Concluding whether the short-term tumor size evolution is predictive on OS will be an important step in the research on early tumor response as a surrogate endpoint for OS.