Inferences for joint modelling of repeated ordinal scores and time to event data
16 Aug 2010-Computational and Mathematical Methods in Medicine (Hindawi Publishing Corporation)-Vol. 11, Iss: 3, pp 281-295
TL;DR: This article has attempted to analyse clinical trials and other follow-up studies through a latent variable model to account for the dependence between ordered categorical responses and survival time for different causes due to unobserved factors.
Abstract: In clinical trials and other follow-up studies, it is natural that a response variable is repeatedly measured during follow-up and the occurrence of some key event is also monitored. There has been a considerable study on the joint modelling these measures together with information on covariates. But most of the studies are related to continuous outcomes. In many situations instead of observing continuous outcomes, repeated ordinal outcomes are recorded over time. The joint modelling of such serial outcomes and the time to event data then becomes a bit complicated. In this article we have attempted to analyse such models through a latent variable model. In view of the longitudinal variation on the ordinal outcome measure, it is desirable to account for the dependence between ordered categorical responses and survival time for different causes due to unobserved factors. A flexible Monte Carlo EM (MCEM) method based on exact likelihood is proposed that can simultaneously handle the longitudinal ordinal data and also the censored time to event data. A computationally more efficient MCEM method based on approximation of the likelihood is also proposed. The method is applied to a number of ordinal scores and survival data from trials of a treatment for children suffering from Duchenne Muscular Dystrophy. Finally, a simulation study is conducted to examine the finite sample properties of the proposed estimators in the joint model under two different methods.
Citations
More filters
TL;DR: Joint model analysis was more parsimonious as compared to separate analysis, as it reduces type I error and subject-specific analysis improved its model fit, and the observed correlation between the outcomes that have emerged from the association of intercepts is validated.
Abstract: Adherence and CD4 cell count change measure the progression of the disease in HIV patients after the commencement of HAART. Lack of information about associated factors on adherence to HAART and CD4 cell count reduction is a challenge for the improvement of cells in HIV positive adults. The main objective of adopting joint modeling was to compare separate and joint models of longitudinal repeated measures in identifying long-term predictors of the two longitudinal outcomes: CD4 cell count and adherence to HAART. A longitudinal retrospective cohort study was conducted to examine the joint predictors of CD4 cell count change and adherence to HAART among HIV adult patients enrolled in the first 10 months of the year 2008 and followed-up to June 2012. Joint model was employed to determine joint predictors of two longitudinal response variables over time. Furthermore, the generalized linear mixed effect model had been used for specification of the marginal distribution, conditional to correlated random effect. A total of 792 adult HIV patients were studied to analyze the longitudinal joint model study. The result from this investigation revealed that age, weight, baseline CD4 cell count, ownership of cell phone, visiting times, marital status, residence area and level of disclosure of the disease to family members had significantly affected both outcomes. From the two-way interactions, time * owner of cell phone, time * sex, age * sex, age * level of education as well as time * level of education were significant for CD4 cell count change in the longitudinal data analysis. The multivariate joint model with linear predictor indicates that CD4 cell count change was positively correlated (p ≤ 0.0001) with adherence to HAART. Hence, as adherence to HAART increased, CD4 cell count also increased; and those patients who had significant CD4 cell count change at each visiting time had been encouraged to be good adherents. Joint model analysis was more parsimonious as compared to separate analysis, as it reduces type I error and subject-specific analysis improved its model fit. The joint model operates multivariate analysis simultaneously; and it has great power in parameter estimation. Developing joint model helps validate the observed correlation between the outcomes that have emerged from the association of intercepts. There should be a special attention and intervention for HIV positive adults, especially for those who had poor adherence and with low CD4 cell count change. The intervention may be important for pre-treatment counseling and awareness creation. The study also identified a group of patients who were with maximum risk of CD4 cell count change. It is suggested that this group of patients needs high intervention for counseling.
27 citations
TL;DR: A joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event is proposed and is applied to the assessment of breast cancer risk in women attending a population‐based screening program.
Abstract: We propose a joint model to analyze the structure and intensity of the association between longitudinal measurements of an ordinal marker and time to a relevant event. The longitudinal process is defined in terms of a proportional-odds cumulative logit model. Time-to-event is modeled through a left-truncated proportional-hazards model, which incorporates information of the longitudinal marker as well as baseline covariates. Both longitudinal and survival processes are connected by means of a common vector of random effects. General inferences are discussed under the Bayesian approach and include the posterior distribution of the probabilities associated to each longitudinal category and the assessment of the impact of the baseline covariates and the longitudinal marker on the hazard function. The flexibility provided by the joint model makes possible to dynamically estimate individual event-free probabilities and predict future longitudinal marker values. The model is applied to the assessment of breast cancer risk in women attending a population-based screening program. The longitudinal ordinal marker is mammographic breast density measured with the Breast Imaging Reporting and Data System (BI-RADS) scale in biennial screening exams. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.
22 citations
TL;DR: This work proposes to simultaneously model the survival time with a stratified Cox proportional hazards model and the longitudinal categorical outcomes with a generalized linear mixed model to address the dependence between survival time and longitudinal outcomes due to unobserved factors.
Abstract: In biomedical or public health research, it is common for both survival time and longitudinal categorical outcomes to be collected for a subject, along with the subject’s characteristics or risk factors. Investigators are often interested in finding important variables for predicting both survival time and longitudinal outcomes which could be correlated within the same subject. Existing approaches for such joint analyses deal with continuous longitudinal outcomes. New statistical methods need to be developed for categorical longitudinal outcomes. We propose to simultaneously model the survival time with a stratified Cox proportional hazards model and the longitudinal categorical outcomes with a generalized linear mixed model. Random effects are introduced to account for the dependence between survival time and longitudinal outcomes due to unobserved factors. The Expectation–Maximization (EM) algorithm is used to derive the point estimates for the model parameters, and the observed information matrix is adopted to estimate their asymptotic variances. Asymptotic properties for our proposed maximum likelihood estimators are established using the theory of empirical processes. The method is demonstrated to perform well in finite samples via simulation studies. We illustrate our approach with data from the Carolina Head and Neck Cancer Study (CHANCE) and compare the results based on our simultaneous analysis and the separately conducted analyses using the generalized linear mixed model and the Cox proportional hazards model. Our proposed method identifies more predictors than by separate analyses.
6 citations
TL;DR: PA had the smallest AB-PE and ASE-PE for the longitudinal submodel among the three approaches for the small and moderate sample sizes and JLCM was desirable for the none-association and the large sample size.
Abstract: In recent years, the joint models have been widely used for modeling the longitudinal and time-to-event data simultaneously. In this study, we proposed an approach (PA) to study the longitudinal and survival outcomes simultaneously in heterogeneous populations. PA relaxes the assumption of conditional independence (CI). We also compared PA with joint latent class model (JLCM) and separate approach (SA) for various sample sizes (150, 300, and 600) and different association parameters (0, 0.2, and 0.5). The average bias of parameters estimation (AB-PE), average SE of parameters estimation (ASE-PE), and coverage probability of the 95% confidence interval (CP) among the three approaches were compared. In most cases, when the sample sizes increased, AB-PE and ASE-PE decreased for the three approaches, and CP got closer to the nominal level of 0.95. When there was a considerable association, PA in comparison with SA and JLCM performed better in the sense that PA had the smallest AB-PE and ASE-PE for the longitudinal submodel among the three approaches for the small and moderate sample sizes. Moreover, JLCM was desirable for the none-association and the large sample size. Finally, the evaluated approaches were applied on a real HIV/AIDS dataset for validation, and the results were compared.
5 citations
TL;DR: A large number of clinical applications and methodological development in the area of joint models of longitudinal and time-to-event outcomes have come up in the last 20 or more years.
Abstract: Over the last 20 or more years a lot of clinical applications and methodological development in the area of joint models of longitudinal and time-to-event outcomes have come up. In these studies, p...
4 citations
References
More filters
TL;DR: A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects and an approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations.
Abstract: A procedure is derived for computing standard errors of EM estimates in generalized linear models with random effects. Quadrature formulas are used to approximate the integrals in the EM algorithm, where two different approaches are pursued, i.e., Gauss-Hermite quadrature in the case of Gaussian random effects and nonparametric maximum likelihood estimation for an unspecified random effect distribution. An approximation of the expected Fisher information matrix is derived from an expansion of the EM estimating equations. This allows for inferential arguments based on EM estimates, as demonstrated by an example and simulations.
32 citations
"Inferences for joint modelling of r..." refers methods in this paper
...Note that in order to have stabilized values of the standard errors (SEs) of the estimates, we consider here a MC-based sandwich technique (see [6])....
[...]