A Semi-Parametric Model for Longitudinal Count Data

Asthma is an important chronic disease of childhood. An intervention programme for managing asthma was designed on principles of self-regulation and was evaluated by a randomized longitudinal study.The study focused on several outcomes, and, typically, missing data remained a pervasive problem. We develop a pattern-mixture model to evaluate the outcome of intervention on the number of hospitalizations with non-ignorable dropouts. Pattern-mixture models are not generally identifiable as no data may be available to estimate a number of model parameters. Sensitivity analyses are performed by imposing structures on the unidentified parameters.We propose a parameterization which permits sensitivity analyses on clustered longitudinal count data that have missing values due to non-ignorable missing data mechanisms. This parameterization is expressed as ratios between event rates across missing data patterns and the observed data pattern and thus measures departures from an ignorable missing data mechanism. Sensitivity analyses are performed within a Bayesian framework by averaging over different prior distributions on the event ratios. This model has the advantage of providing an intuitive and flexible framework for incorporating the uncertainty of the missing data mechanism in the final analysis.

Paradigms for substance abuse cue-reactivity research involve pharmacological or stressful stimulation designed to elicit stress and craving responses in cocaine-dependent subjects. It is unclear as to whether stress induced from participation in such studies increases drug-seeking behavior. We propose a 2-state Hidden Markov model to model the number of cocaine abuses per week before and after participation in a stress-and cue-reactivity study. The hypothesized latent state corresponds to 'high' or 'low' use. To account for a preponderance of zeros, we assume a zero-inflated Poisson model for the count data. Transition probabilities depend on the prior week's state, fixed demographic variables, and time-varying covariates. We adopt a Bayesian approach to model fitting, and use the conditional predictive ordinate statistic to demonstrate that the zero-inflated Poisson hidden Markov model outperforms other models for longitudinal count data.

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.

Longitudinal designs for biomarker traits are very appealing for a number of reasons. First, the collection of repeated biomarker measurements over time allows investigators to characterize both the overall and individual trajectories in these measurements. This helps investigators to understand overall effects as well as how individuals vary around these average effects. Distinguishing individual heterogeneity from average trend is impossible without longitudinal data. This distinction is important for understanding individual between-subject in its own right, as well as in developing predictors of disease outcome from longitudinal marker data. There are many statistical issues that are unique to longitudinal data analysis ranging from correctly specifying realistic models which characterize average changes over time and individual variation, accounting for observations that are taken at unequally spaced observation times which may differ between individuals, to accounting for missing data due to occasionally missed measurements or loss to follow-up. When the reason for missing data is not related to the underlying observation process, most longitudinal data analysis methods can be routinely applied. However, complex modelling is necessary when the reason for missing an observation or dropout is directly related to the underlying outcome process [1–2]. Statistical techniques that appropriately analyze continuous and discrete longitudinal data have been discussed by many authors. Diggle, et al. [3] provides a good summary of these techniques for the practitioner, while Fitzmaurice et al. [4] discusses recent advances from a more technical perspective. The three papers in this section present innovative approaches for solving important methodological problems in biomarker studies. Most standard longitudinal data analysis techniques assume that the measurement process is independent of the outcome process. However, when the outcome is related to the underlying observation process, failure to properly account for the observation process can result in bias [5]. Schildcrout et al.[6] proposed an approach for regression modelling for longitudinal binary data where the outcome is measured with probabilities determined by an auxiliary variable that is related, but not identical to the binary outcome. Modelling multivariate longitudinal biomarker data is an increasingly common issue with the advent of an increasing number of important biomarker techniques (e.g., multiple cytokines in a multiplex assay or multiple reproductive hormones that describe complex biological phenomenon). Although various authors have proposed techniques for analyzing multivariate longitudinal data [7–8 and others], little work has focused on estimating multivariate linear mixed models under known constraints in the relationship between the multivariate outcomes. Roy et al [9] proposes such an approach for analyzing multivariate reproductive hormones over the menstrual cycle, where established relationships have solid biological justification. Finally, the collection of longitudinal biomarker data as disease predictors is becoming an increasingly important design in diagnostic medicine. Pfeiffer et al. [10] proposes flexible non-parametric methodology for combining biomarkers that exploits the longitudinal structure in formulating a score that is used for predicting a binary outcome.

We describe a mixed-effect hurdle model for zero-inflated longitudinal count data, where a baseline variable is included in the model specification. Association between the count data process and the endogenous baseline variable is modeled through a latent structure, assumed to be dependent across equations. We show how model parameters can be estimated in a finite mixture context, allowing for overdispersion, multivariate association and endogeneity of the baseline variable. The model behavior is investigated through a large-scale simulation experiment. An empirical example on health care utilization data is provided.

Several methods have been proposed in the literature for computing unbiased and efficient estimates of the parameters of generalized linear models when the covariates are measured with error. However, to our knowledge, no documented research on computational techniques for parameter estimation currently exist in the literature when the data is a longitudinal count data influenced by an unobservable latent variable and observable covariates that are measured with error. In this paper, we propose a nonstationary conditionally Poisson mixed model for such data and develop unbiased estimating equations with iterative methods for computing estimates of the effect of the covariates, variance of the latent variable, and the correlation index parameter. The performance of the iterative methods is examined through extensive simulation studies. The results show that the methods performed well when the magnitude of the measurement error is not so large as to dominate or mask the effect of the true covariates. Using observed longitudinal count data on the number of patents awarded to 168 firms in the United States from 1974 to 1979 along with associated covariate information on the type of firm, log of the book value of capital in 1972 and research and development (R & D) expenditures we have demonstrated how the methods proposed in this paper can be applied to a real data. In addition, we derive the influence function of the estimator of the covariate effect and discuss the asymptotic properties of the estimator. Journal of Statistical Research 2024, Vol. 58, No. 1, pp. 151-180.

In analysis of longitudinal data, it is not uncommon that observation times of repeated measurements are subject-specific and correlated with underlying longitudinal outcomes. Taking account of the dependence between observation times and longitudinal outcomes is critical under these situations to assure the validity of statistical inference. In this article, we propose a flexible joint model for longitudinal data analysis in the presence of informative observation times. In particular, the new procedure considers the shared random-effect model and assumes a time-varying coefficient for the latent variable, allowing a flexible way of modeling longitudinal outcomes while adjusting their association with observation times. Estimating equations are developed for parameter estimation. We show that the resulting estimators are consistent and asymptotically normal, with variance-covariance matrix that has a closed form and can be consistently estimated by the usual plug-in method. One additional advantage of the procedure is that it provides a unified framework to test whether the effect of the latent variable is zero, constant, or time-varying. Simulation studies show that the proposed approach is appropriate for practical use. An application to a bladder cancer data is also given to illustrate the methodology.

Motivated by the analysis of quality of life data from a clinical trial on early breast cancer, we propose in this paper a generalized partially linear mean-covariance regression model for longitudinal proportional data, which are bounded in a closed interval. Cholesky decomposition of the covariance matrix for within-subject responses and generalized estimation equations are used to estimate unknown parameters and the nonlinear function in the model. Simulation studies are performed to evaluate the performance of the proposed estimation procedures. Our new model is also applied to analyze the data from the cancer clinical trial that motivated this research. In comparison with available models in the literature, the proposed model does not require specific parametric assumptions on the density function of the longitudinal responses and the probability function of the boundary values and can capture dynamic changes of time or other interested variables on both mean and covariance of the correlated proportional responses. Copyright © 2017 John Wiley & Sons, Ltd.

This article investigates a generalized semiparametric varying-coefficient model for longitudinal data that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects. Different link functions can be selected to provide a rich family of models for longitudinal data. The model assumes that the time-varying effects are unspecified functions of time and the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. The estimation procedure is developed using local linear smoothing and profile weighted least squares estimation techniques. Hypothesis testing procedures are developed to test the parametric functions of the covariate-varying effects. The asymptotic distributions of the proposed estimators are established. A working formula for bandwidth selection is discussed and examined through simulations. Our simulation study shows that the proposed methods have satisfactory finite sample performance. The proposed methods are applied to the ACTG 244 clinical trial of HIV infected patients being treated with Zidovudine to examine the effects of antiretroviral treatment switching before and after HIV develops the T215Y/F drug resistance mutation. Our analysis shows benefits of treatment switching to the combination therapies as compared to continuing with ZDV monotherapy before and after developing the 215-mutation.

BackgroundLongitudinal ordinal data are commonly analyzed using a marginal proportional odds model for relating ordinal outcomes to covariates in the biomedical and health sciences. The generalized estimating equation (GEE) consistently estimates the regression parameters of marginal models even if the working covariance structure is misspecified. For small-sample longitudinal binary data, recent studies have shown that the bias of regression parameters may result from the GEE and have addressed the issue by applying Firth’s adjustment for the likelihood score equation to the GEE as if generalized estimating functions were likelihood score functions. In this manuscript, for the proportional odds model for longitudinal ordinal data, the small-sample properties of the GEE were investigated, and a bias-reduced GEE (BR-GEE) was derived.MethodsBy applying the adjusted function originally derived for the likelihood score function of the proportional odds model to the GEE, we produced the BR-GEE. We investigated the small-sample properties of both GEE and BR-GEE through simulation and applied them to a clinical study dataset.ResultsIn simulation studies, the BR-GEE had a bias closer to zero, smaller root mean square error than the GEE with coverage probability of confidence interval near or above the nominal level. The simulation also showed that BR-GEE maintained a type I error rate near or below the nominal level.ConclusionsFor the analysis of longitudinal ordinal data involving a small number of subjects, the BR-GEE is advantageous for obtaining estimates of the regression parameters of marginal proportional odds models.

The initial conditions problem in longitudinal count process: A simulation study

Modelling overdispersion in longitudinal count data in clinical trials with application to epileptic data

ABSTRACTIn this paper, we develop a semiparametric regression model for longitudinal skewed data. In the new model, we allow the transformation function and the baseline function to be unknown. The proposed model can provide a much broader class of models than the existing additive and multiplicative models. Our estimators for regression parameters, transformation function and baseline function are asymptotically normal. Particularly, the estimator for the transformation function converges to its true value at the rate n − 1 ∕ 2, the convergence rate that one could expect for a parametric model. In simulation studies, we demonstrate that the proposed semiparametric method is robust with little loss of efficiency. Finally, we apply the new method to a study on longitudinal health care costs.

In this paper, we present an extension of the Poisson Zero-Modified model with Normal and Generalized Log-Gamma random effects. The random effect induces correlation and accommodate the intrinsic variability of each individual. The Generalized Log-Gamma effect is a generalized Normal effect and can be used in atypical situations where the Normal effect is not appropriate. In particular, the mixed Zero-Modified Poisson model allows us to deal with longitudinal count data, without requiring any previous knowledge about data characteristics, mainly to the number of zero observations (zero-inflated or zero-deflated). We consider the maximum likelihood approach to estimate the model parameters. A simulation study is presented to evaluate the estimators' performance. A real data set referring to the number of notification of infant deaths in the municipalities of the state of Bahia/Brazil is analyzed. The results revealed the Generalized Log-Gamma effect seems to be more appropriate to model this longitudinal data set.

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