Continuous Longitudinal Responses Research Articles

Joint modeling of mixed skewed longitudinal responses using convolution of normal and log-normal distributions: a Bayesian approach

This paper investigates the joint modeling of mixed ordinal and continuous longitudinal responses using a random effects model and applying a conditional approach. For the ordinal responses, a latent variable model with a logistic distribution is employed. To address skewness in the data, the model incorporates normal and log-normal convolution (NLNC) for both the error term and the random effects in the longitudinal model. Parameter estimation is carried out within a Bayesian framework using Gibbs sampling. The performance of the proposed model is evaluated through simulation studies, comparing it to joint models of mixed ordinal and continuous longitudinal responses assuming skew-normal or normal distributions. The results indicate that joint models using skew-normal or normal distributions can lead to biased parameter estimates, whereas the NLNC joint model performs better overall. Additionally, the proposed method is applied to analyze data from the British Household Panel Survey (BHPS), using life satisfaction and annual income as the correlated ordinal and continuous longitudinal responses, respectively, with annual income showing significant skewness. The results demonstrate that the proposed model provides the best fit for capturing the substantial skewness in the data.

A hidden Markov model for continuous longitudinal data with missing responses and dropout.

We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three 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), and (III) dropout before the end of the period of observation (monotone pattern). The missing-at-random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation-maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.

Joint model for longitudinal mixture of normal and zero-inflated power series correlated responses Abbreviated title:mixture of normal and zero-inflated power series random-effects model

ABSTRACT In this paper, a joint model is presented for analyzing longitudinal continuous and count mixed responses. The frequency distribution of continuous longitudinal response variable for each subject at any time has a skewed and or multi-modal form. Then, a suitable finite mixture of normals is used as its distribution. It seems that the continuous response comes from several distinct sub-populations. The number of zeros of the count response is inflated. Also, a zero-inflated power series (ZIPS) distribution is applied as its distribution in order to model the count response. The correlation of longitudinal responses through time and that of mixed continuous and count responses are modeled by utilizing the random-effects vectors in the finite mixtures of regression (FMR) models. Further, a full likelihood-based approach is used to obtain the maximum likelihood estimates of parameters via the EM algorithm. Then, some simulation studies are performed for assessing the performance of the model. Additionally, an application is illustrated for joint analysis of the number of days during the last month that the individual drank alcohol, as well as the respondents’ weight. Finally, the two first times of the Americans Changing Lives survey are evaluated.

Two-part hidden Markov models for semicontinuous longitudinal data with nonignorable missing covariates.

This study develops a two-part hidden Markov model (HMM) for analyzing semicontinuous longitudinal data in the presence of missing covariates. The proposed model manages a semicontinuous variable by splitting it into two random variables: a binary indicator for determining the occurrence of excess zeros at all occasions and a continuous random variable for examining its actual level. For the continuous longitudinal response, an HMM is proposed to describe the relationship between the observation and unobservable finite-state transition processes. The HMM consists of two major components. The first component is a transition model for investigating how potential covariates influence the probabilities of transitioning from one hidden state to another. The second component is a conditional regression model for examining the state-specific effects of covariates on the response. A shared random effect is introduced to each part of the model to accommodate possible unobservable heterogeneity among observation processes and the nonignorability of missing covariates. A Bayesian adaptive least absolute shrinkage and selection operator (lasso) procedure is developed to conduct simultaneous variable selection and estimation. The proposed methodology is applied to a study on the Alzheimer's Disease Neuroimaging Initiative dataset. New insights into the pathology of Alzheimer's disease and its potential risk factors are obtained.

A Bayesian conditional model for bivariate mixed ordinal and skew continuous longitudinal responses using quantile regression

ABSTRACTIn this paper, we develop a conditional model for analyzing mixed bivariate continuous and ordinal longitudinal responses. We propose a quantile regression model with random effects for analyzing continuous responses. For this purpose, an Asymmetric Laplace Distribution (ALD) is allocated for continuous response given random effects. For modeling ordinal responses, a cumulative logit model is used, via specifying a latent variable model, with considering other random effects. Therefore, the intra-association between continuous and ordinal responses is taken into account using their own exclusive random effects. But, the inter-association between two mixed responses is taken into account by adding a continuous response term in the ordinal model. We use a Bayesian approach via Markov chain Monte Carlo method for analyzing the proposed conditional model and to estimate unknown parameters, a Gibbs sampler algorithm is used. Moreover, we illustrate an application of the proposed model using a part of the British Household Panel Survey data set. The results of data analysis show that gender, age, marital status, educational level and the amount of money spent on leisure have significant effects on annual income. Also, the associated parameter is significant in using the best fitting proposed conditional model, thus it should be employed rather than analyzing separate models.

A Bayesian random effects model for analyzing mixed negative binomial and continuous longitudinal responses

ABSTRACTA general Bayesian random effects model for analyzing longitudinal mixed correlated continuous and negative binomial responses with and without missing data is presented. This Bayesian model, given some random effects, uses a normal distribution for the continuous response and a negative binomial distribution for the count response. A Markov Chain Monte Carlo sampling algorithm is described for estimating the posterior distribution of the parameters. This Bayesian model is illustrated by a simulation study. For sensitivity analysis to investigate the change of parameter estimates with respect to the perturbation from missing at random to not missing at random assumption, the use of posterior curvature is proposed. The model is applied to a medical data, obtained from an observational study on women, where the correlated responses are the negative binomial response of joint damage and continuous response of body mass index. The simultaneous effects of some covariates on both responses are also investigated.

Joint Modeling of Longitudinal and Survival Data

The joint modeling of longitudinal and survival data has received remarkable attention in the methodological literature over the past decade; however, the availability of software to implement the methods lags behind. The most common form of joint model assumes that the association between the survival and the longitudinal processes is underlined by shared random effects. As a result, computationally intensive numerical integration techniques such as adaptive Gauss–Hermite quadrature are required to evaluate the likelihood. We describe a new user-written command, stjm, that allows the user to jointly model a continuous longitudinal response and the time to an event of interest. We assume a linear mixed-effects model for the longitudinal submodel, allowing flexibility through the use of fixed or random fractional polynomials of time. Four choices are available for the survival submodel: the exponential, Weibull or Gompertz proportional hazard models, and the flexible parametric model (stpm2). Flexible parametric models are fit on the log cumulative-hazard scale, which has direct computational benefits because it avoids the use of numerical integration to evaluate the cumulative hazard. We describe the features of stjm through application to a dataset investigating the effect of serum bilirubin level on time to death from any cause in 312 patients with primary biliary cirrhosis.

A strategy for selecting among alternative models for continuous longitudinal data

Linear mixed models (LMMs) can be used to analyze continuous longitudinal response variables of research studies. Specific aims are then addressed through tests of fixed effects comparing means. However, generated fixed effects results can vary according to the choice of the covariance structure, and so strategies for selecting a model should be utilized first to identify an appropriate covariance structure. We describe alternative LMMs for analyzing continuous longitudinal data and discuss a strategy for using model selection criteria to choose among those models. This is accomplished through the analysis of an exemplar data set considering a wide variety of alternative models for the means, variances, and correlations.

A transition model for quality‐of‐life data with non‐ignorable non‐monotone missing data

In this paper, we consider a full likelihood method to analyze continuous longitudinal responses with non-ignorable non-monotone missing data. We consider a transition probability model for the missingness mechanism. A first-order Markov dependence structure is assumed for both the missingness mechanism and observed data. This process fits the natural data structure in the longitudinal framework. Our main interest is in estimating the parameters of the marginal model and evaluating the missing-at-random assumption in the Effects of Public Information Study, a cancer-related study recently conducted at the University of Pennsylvania. We also present a simulation study to assess the performance of the model.

On Classification and Regression Trees for Multiple Responses and Its Application

In many application fields, multivariate approaches that simultaneously consider the correlation between responses are needed. The tree method can be extended to multivariate responses, such as repeated measure and longitudinal data, by modifying the split function so as to accommodate multiple responses. Recently, researchers have constructed some decision trees for multiple continuous longitudinal response and multiple binary responses using Mahalanobis distance and a generalized entropy index. However, these methods have limitations according to the type of response, that is, those that are only continuous or binary. In this paper, we will modify the tree for univariate response procedure and suggest a new tree-based method that can analyze any type of multiple responses by using GEE (generalized estimating equations) techniques. To compare the performance of trees, simulation studies on selection probability of true split variable will be shown. Finally, applications using epileptic seizure data and WWW data are introduced.

Using Generalized Estimating Equation to Learn Decision Tree with Multivariate Responses

Previous decision tree algorithms have used Mahalanobis distance for multiple continuous longitudinal response or generalized entropy index for multiple binary responses. However, these methods are...