Studies of memory trajectories using longitudinal data often result in highly non-representative samples due to selective study enrollment and attrition. An additional bias comes from practice effects that result in improved or maintained performance due to familiarity with test content or context. These challenges may bias study findings and severely distort the ability to generalize to the target population. In this study we propose an approach for estimating the finite population mean of a longitudinal outcome conditioning on being alive at a specific time point. We develop a flexible Bayesian semi-parametric predictive estimator for population inference when longitudinal auxiliary information is known for the target population. We evaluate sensitivity of the results to untestable assumptions and further compare our approach to other methods used for population inference in a simulation study. The proposed approach is motivated by 15-year longitudinal data from the Betula longitudinal cohort study. We apply our approach to estimate lifespan trajectories in episodic memory, with the aim to generalize findings to a target population.
Dyadic data are common in the social and behavioral sciences, in which members of dyads are correlated due to the interdependence structure within dyads. The analysis of longitudinal dyadic data becomes complex when nonignorable dropouts occur. We propose a fully Bayesian selection-model-based approach to analyze longitudinal dyadic data with nonignorable dropouts. We model repeated measures on subjects by a transition model and account for within-dyad correlations by random effects. In the model, we allow subject's outcome to depend on his/her own characteristics and measure history, as well …
In longitudinal studies, subjects may be lost to follow-up, or miss some of the planned visits, leading to incomplete response sequences. When the probability of non-response, conditional on the available covariates and the observed responses, still depends on unobserved outcomes, the dropout mechanism is said to be non ignorable. A common objective is to build a reliable association structure to account for dependence between the longitudinal and the dropout processes. Starting from the existing literature, we introduce a random coefficient based dropout model where the association between ou…
Joint multivariate longitudinal and time-to-event data are gaining increasing attention in the biomedical sciences where subjects are followed over time to monitor the progress of a disease or medical condition. In the insurance context, claims outcomes may be related to a policyholder's dropout or decision to lapse a policy. This paper introduces a generalized method of moments technique to estimate dependence parameters where associations are represented using copulas. A simulation study demonstrates the viability of the approach. The paper describes how the joint model provides new informat…
We propose an inferential approach for maximum likelihood estimation of the hidden Markov models for continuous responses. We extend to the case of longitudinal observations the finite mixture model of multivariate Gaussian distributions with Missing At Random (MAR) outcomes, also accounting for possible dropout. The resulting hidden Markov model accounts for different types of missing pattern: (i) partially missing outcomes at a given time occasion; (ii) completely missing outcomes at a given time occasion (intermittent pattern); (iii) dropout before the end of the period of observation (mono…
Adressing Separation: A Firth-corrected Joint Model for Longitudinal and Time-to-event Data with an Application on Dropout from Vocational Training
Georg-August University Göttingen（哥廷根乔治-奥古斯特大学）；Chair of Spatial Data Science and Statistical Learning（空间数据科学与统计学习教席）；Campus Institute Data Science (CIDAS)（校园数据科学研究所（CIDAS））
We illustrate a class of conditional models for the analysis of longitudinal data suffering attrition in random effects models framework, where the subject-specific random effects are assumed to be discrete and to follow a time-dependent latent process. The latent process accounts for unobserved heterogeneity and correlation between individuals in a dynamic fashion, and for dependence between the observed process and the missing data mechanism. Of particular interest is the case where the missing mechanism is non-ignorable. To deal with the topic we introduce a conditional to dropout model. A …
Longitudinal data are common in clinical trials and observational studies, where missing outcomes due to dropouts are always encountered. Under such context with the assumption of missing at random, the weighted generalized estimating equations (WGEE) approach is widely adopted for marginal analysis. Model selection on marginal mean regression is a crucial aspect of data analysis, and identifying an appropriate correlation structure for model fitting may also be of interest and importance. However, the existing information criteria for model selection in WGEE have limitations, such as separate…
In this work, blood pressure eleven years ahead is modeled using data from a longitudinal population-based health survey, the Trondelag Health (HUNT) Study, while accounting for missing data due to dropout between consecutive surveys (20-50 %). We propose and validate a shared parameter model (SPM) in the Bayesian framework with age, sex, body mass index, and initial blood pressure as explanatory variables. Further, we propose a novel evaluation scheme to assess data missing not at random (MNAR) by comparing the predictive performance of the fitted SPM with and without conditioning on the miss…
On a penalised likelihood approach for joint modelling of longitudinal covariates and partly interval-censored data -- an application to the Anti-PD1 brain collaboration trial
In health cohort studies, repeated measures of markers are often used to describe the natural history of a disease. Joint models allow to study their evolution by taking into account the possible informative dropout usually due to clinical events. However, joint modeling developments mostly focused on continuous Gaussian markers while, in an increasing number of studies, the actual quantity of interest is non-directly measurable; it constitutes a latent variable evaluated by a set of observed indicators from questionnaires or measurement scales. Classical examples include anxiety, fatigue, cog…
In longitudinal data a response variable is measured over time, or under different conditions, for a cohort of individuals. In many situations all intended measurements are not available which results in missing values. If the missing value is never followed by an observed measurement, this leads to dropout pattern. The missing values could be in the response variable, the covariates or in both. The missingness mechanism is termed non-random when the probability of missingness depends on the missing value and may be on the observed values. In this case the missing values should be considered i…
In clinical trials, mixed effects models for repeated measures (MMRM) and pattern mixture models (PMM) are often used to analyze longitudinal continuous outcomes. We describe a simple missing data imputation algorithm for the MMRM that can be easily implemented in standard statistical software packages such as SAS PROC MI. We explore the relationship of the missing data distribution in the control-based and delta-adjusted PMMs with that in the MMRM, and suggest an efficient imputation algorithm for these PMMs. The unobserved values in PMMs can be imputed by subtracting the mean difference in t…
An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models including the linear, binary logistic, multinomial logistic, proportional odds, Poisson, negative binomial, skew-normal, skew-t regressions or a mixture of these models. The MDA algorithm is applied to the sensitivity analyses of longitudinal trials with nonignorable dropout using the controlled pattern imputations that assume the treatment effect reduces or di…
Dropout represents a typical issue to be addressed when dealing with longitudinal studies. If the mechanism leading to missing information is non-ignorable, inference based on the observed data only may be severely biased. A frequent strategy to obtain reliable parameter estimates is based on the use of individual-specific random coefficients that help capture sources of unobserved heterogeneity and, at the same time, define a reasonable structure of dependence between the longitudinal and the missing data process. We refer to elements in this class as random coefficient based dropout models (…
Diverse analysis approaches have been proposed to distinguish data missing due to death from nonresponse, and to summarize trajectories of longitudinal data truncated by death. We demonstrate how these analysis approaches arise from factorizations of the distribution of longitudinal data and survival information. Models are illustrated using cognitive functioning data for older adults. For unconditional models, deaths do not occur, deaths are independent of the longitudinal response, or the unconditional longitudinal response is averaged over the survival distribution. Unconditional models, su…
The mixed effects model for repeated measures (MMRM) has been widely used for the analysis of longitudinal clinical data collected at a number of fixed time points. We propose a robust extension of the MMRM for skewed and heavy-tailed data on basis of the multivariate skew-t distribution, and it includes the multivariate normal, t, and skew-normal distributions as special cases. An efficient Markov chain Monte Carlo algorithm is developed using the monotone data augmentation and parameter expansion techniques. We employ the algorithm to perform controlled pattern imputations for sensitivity an…
In randomized trials with continuous-valued outcomes the goal is often to estimate the difference in average outcomes between two treatment groups. However, the outcome in some trials is longitudinal, meaning that multiple measurements of the same outcome are taken over time for each subject. The target of inference in this case is often still the difference in averages at a given timepoint. One way to analyze these data is to ignore the measurements at intermediate timepoints and proceed with a standard covariate-adjusted analysis (e.g. ANCOVA) with the complete cases. However, it is generall…
The rich longitudinal individual level data available from electronic health records (EHRs) can be used to examine treatment effect heterogeneity. However, estimating treatment effects using EHR data poses several challenges, including time-varying confounding, repeated and temporally non-aligned measurements of covariates, treatment assignments and outcomes, and loss-to-follow-up due to dropout. Here, we develop the Subgroup Discovery for Longitudinal Data (SDLD) algorithm, a tree-based algorithm for discovering subgroups with heterogeneous treatment effects using longitudinal data by combini…
When Method Choice Changes Statistical Inference: A Comparison of a Baseline Two-Stage Approach and Bayesian Joint Modeling for Longitudinal and Survival Data in an HIV Clinical Trial
Joint modeling technique is a recent advancement in effectively analyzing the longitudinal history of patients with the occurrence of an event of interest attached to it. This procedure is successfully implemented in biomarker studies to examine parents with the occurrence of tumor. One of the typical problem that influences the necessary inference is the presence of missing values in the longitudinal responses as well as in covariates. The occurrence of missingness is very common due to the dropout of patients from the study. This article presents an effective and detailed way to handle the m…
In various data situations joint models are an efficient tool to analyze relationships between time dependent covariates and event times or to correct for event-dependent dropout occurring in regression analysis. Joint modeling connects a longitudinal and a survival submodel within a single joint likelihood which then can be maximized by standard optimization methods. Main burdens of these conventional methods are that the computational effort increases rapidly in higher dimensions and they do not offer special tools for proper variable selection. Gradient boosting techniques are well known am…
