non-Gaussian Longitudinal Data Research Articles

A time-heterogeneous D-vine copula model for unbalanced and unequally spaced longitudinal data.

In many longitudinal studies, the number and timing of measurements differ across study subjects. Statistical analysis of such data requires accounting for both the unbalanced study design and the unequal spacing of repeated measurements. This paper proposes a time-heterogeneous D-vine copula model that allows for time adjustment in the dependence structure of unequally spaced and potentially unbalanced longitudinal data. The proposed approach not only offers flexibility over its time-homogeneous counterparts but also allows for parsimonious model specifications at the tree or vine level for a given D-vine structure. It further provides a robust strategy to specify the joint distribution of non-Gaussian longitudinal data. The performance of the time-heterogeneous D-vine copula models are evaluated through simulation studies and by a real data application. Our findings suggest improved predictive performance of the proposed approach over the linear mixed-effects model and time-homogeneous D-vine copulamodel.

Robust functional principal component analysis for non-Gaussian longitudinal data

Functional principal component analysis is essential in functional data analysis, but the inference will become unconvincing when non-Gaussian characteristics occur (e.g., heavy tail and skewness). The focus of this manuscript is to develop a robust functional principal component analysis methodology to deal with non-Gaussian longitudinal data, where sparsity and irregularity along with non-negligible measurement errors must be considered. We introduce a Kendall’s τ function to handle the non-Gaussian issues. Moreover, the estimation algorithm is studied and the asymptotic theory is discussed. Our method is validated by a simulation study and it is applied to analyze a real world dataset.

Competing risks joint models using R-INLA

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.

Competing risks joint models using R-INLA

The methodological advancements made in the field of joint models are numerous. None the less, the case of competing risks joint models has largely been neglected, especially from a practitioner's point of view. In the relevant works on competing risks joint models, the assumptions of a Gaussian linear longitudinal series and proportional cause-specific hazard functions, amongst others, have remained unchallenged. In this article, we provide a framework based on R-INLA to apply competing risks joint models in a unifying way such that non-Gaussian longitudinal data, spatial structures, times-dependent splines and various latent association structures, to mention a few, are all embraced in our approach. Our motivation stems from the SANAD trial which exhibits non-linear longitudinal trajectories and competing risks for failure of treatment. We also present a discrete competing risks joint model for longitudinal count data as well as a spatial competing risks joint model as specific examples.

A Comparative Analysis of Generalized Estimating Equations Methods for Incomplete Longitudinal Ordinal Data with Ignorable Dropouts

In longitudinal studies, measurements are taken repeatedly over time on the same experimental unit. These measurements are thus correlated. Missing data are very common in longitudinal studies. A lot of research has been going on ways to appropriately analyze such data set. Generalized Estimating Equations (GEE) is a popular method for the analysis of non-Gaussian longitudinal data. In the presence of missing data, GEE requires the strong assumption of missing completely at random (MCAR). Multiple Imputation Generalized Estimating Equations (MIGEE), Inverse Probability Weighted Generalized Estimating Equations (IPWGEE) and Double Robust Generalized Estimating Equations (DRGEE) have been proposed as elegant ways to ensure validity of the inference under missing at random (MAR). In this study, the three extensions of GEE are compared under various dropout rates and sample sizes through simulation studies. Under MAR and MCAR mechanism, the simulation results revealed better performance of DRGEE compared to IPWGEE and MIGEE. The optimum method was applied to real data set.

Evaluation of Alzheimer’s disease progression based on clinical dementia rating scale with missing responses and covariates

ABSTRACTIn clinical trials, patient’s disease severity is usually assessed on a Likert-type scale. Patients, however, may miss one or more follow-up visits (non-monotone missing). The statistical analysis of non-Gaussian longitudinal data with non-monotone missingness is difficult to handle, particularly when both response and time-dependent covariates are subject to such missingness. Even when the number of patients with intermittent missing data is small, ignoring those patients from analysis seems to be unsatisfactory. The focus of the current investigation is to study the progression of Alzheimer’s disease by incorporating a non-ignorable missing data mechanism for both response and covariates in a longitudinal setup. Combining the cumulative logit longitudinal model for Alzheimer’s disease progression with the bivariate binary model for the missing pattern, we develop a joint likelihood. The parameters are then estimated using the Monte Carlo Newton Raphson Expectation Maximization (MCNREM) method. This approach is quite easy to handle and the convergence of the estimates is attained in a reasonable amount of time. The study reveals that apolipo-protein plays a significant role in assessing a patient’s disease severity. A detailed simulation has also been carried out for justifying the performance of our approach.

Fitting the Fractional Polynomial Model to Non-Gaussian Longitudinal Data.

As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet growth modeling with non-Gaussian data is somewhat limited when considering the transformed expectation of the response via a linear predictor as a functional form of explanatory variables. In this study, we introduce a fractional polynomial model (FPM) that can be applied to model non-linear growth with non-Gaussian longitudinal data and demonstrate its use by fitting two empirical binary and count data models. The results clearly show the efficiency and flexibility of the FPM for such applications.

Testing for misspecification in generalized linear mixed models

Generalized linear mixed models have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research shows that the results obtained from these models are not always robust against departures from the assumptions on which they are based. Therefore, diagnostic tools for the detection of model misspecifications are of the utmost importance. In this paper, we propose 2 diagnostic tests that are based on 2 equivalent representations of the model information matrix. We evaluate the power of both tests using theoretical considerations as well as via simulation. In the simulations, the performance of the new tools is evaluated in many settings of practical relevance, focusing on misspecification of the random-effects structure. In all the scenarios, the results were encouraging, however, the tests also exhibited inflated Type I error rates when the sample size was small or moderate. Importantly, a parametric bootstrap version of the tests seems to overcome this problem, although more research in this direction may be needed. Finally, both tests were also applied to analyze a real case study in psychiatry.

A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models

Estimation in generalized linear mixed models for non-Gaussian longitudinal data is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. It is known that the results obtained from these models are not always robust against misspecification of the random-effects structure. Therefore, diagnostic tools for the detection of this misspecification are of the utmost importance. Three diagnostic tests, based on the eigenvalues of the variance-covariance matrices for the fixed-effects parameters estimates, are proposed in the present work. The power and type I error rate of these tests are studied via simulations. A very acceptable performance was observed in many cases, especially for those misspecifications that can have a big impact on the maximum likelihood estimators.

Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

Generalized linear mixed models (GLMMs) have become a frequently used tool for the analysis of non-Gaussian longitudinal data. Estimation is based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. Recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based. In the present work we have used simulations with a logistic random-intercept model to study the impact of misspecifying the random-effects distribution on the type I and II errors of the tests for the mean structure in GLMMs. We found that the misspecification can either increase or decrease the power of the tests, depending on the shape of the underlying random-effects distribution, and it can considerably inflate the type I error rate. Additionally, we have found a theoretical result which states that whenever a subset of fixed-effects parameters, not included in the random-effects structure equals zero, the corresponding maximum likelihood estimator will consistently estimate zero. This implies that under certain conditions a significant effect could be considered as a reliable result, even if the random-effects distribution is misspecified.

Analyzing Incomplete Discrete Longitudinal Clinical Trial Data

Commonly used methods to analyze incomplete longitudi- nal clinical trial data include complete case analysis (CC) and last observation carried forward (LOCF). However, such methods rest on strong assumptions, including missing completely at random (MCAR) for CC and unchanging profile after dropout for LOCF. Such assump- tions are too strong to generally hold. Over the last decades, a number of full longitudinal data analysis methods have become available, such as the linear mixed model for Gaussian outcomes, that are valid un- der the much weaker missing at random (MAR) assumption. Such a method is useful, even if the scientific question is in terms of a sin- gle time point, for example, the last planned measurement occasion, and it is generally consistent with the intention-to-treat principle. The validity of such a method rests on the use of maximum likelihood, un- der which the missing data mechanism is ignorable as soon as it is MAR. In this paper, we will focus on non-Gaussian outcomes, such as binary, categorical or count data. This setting is less straightforward since there is no unambiguous counterpart to the linear mixed model. We first provide an overview of the various modeling frameworks for non-Gaussian longitudinal data, and subsequently focus on generalized linear mixed-effects models, on the one hand, of which the parameters can be estimated using full likelihood, and on generalized estimating equations, on the other hand, which is a nonlikelihood method and hence requires a modification to be valid under MAR. We briefly com- ment on the position of models that assume missingness not at random and argue they are most useful to perform sensitivity analysis. Our developments are underscored using data from two studies. While the case studies feature binary outcomes, the methodology applies equally well to other discrete-data settings, hence the qualifier discrete in the title.