Semiparametric Regression Analysis of Panel Count Data with Multiple Modes of Recurrence

Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.

In this article, we extend the joint frailty models proposed by Zhao and Tong (2011) to panel count data with the time-dependent covariates and informative observation and censoring times. A novel estimating equation approach that does not depend on the distribution of frailty variables and the link function is proposed for estimation of parameters, and the asymptotic properties of the proposed estimators are established. Simulation studies demonstrate that the proposed inference procedure performs well. The analysis of a bladder tumor data is presented to illustrate the method.

Regression Analysis of Panel Count Data II

Panel count data occur in studies that concern recurrent events, or event history studies, when study subjects are observed only at discrete time points. By recurrent events, we mean the event that ca

We study a semiparametric model for robust analysis of panel count data with an informative terminal event. To explore the explicit effect of the terminal event on recurrent events of interest, we propose a conditional mean model for a reversed counting process anchoring at the terminal event. Treating the distribution function of the terminal event as a nuisance functional parameter, we develop a predicted least squares-based two-stage estimation procedure with the spline-based sieve estimation technique, and derive the convergence rate of the proposed estimator. Furthermore, overcoming the difficulties caused by the convergence rate slower than , we establish the asymptotic normality for the estimator of the finite-dimensional parameter and a functional of the estimator of the infinite-dimensional parameter. The proposed method is evaluated through extensive simulation studies and illustrated with an application to the Longitudinal Healthy Longevity Survey study on elder people in China.

The Poisson regression model is widely used for count data. This model assumes equidispersion. In practice, equidispersion is seldom reflected in data. However, in real-life data, the variance usually exceeds the mean. This situation is known as overdispersion. Negative binomial distribution and other Poisson mix models are often used to model overdispersion count data. Another extension of the negative binomial distribution in another model for count data is the univariate generalized Waring. In addition, the model developed by Famoye can be used in the analysis of count data. When the count data contains a large number of zeros, it is necessary to use zero-inflated models. In this study, different generalized regression models are emphasized for the analysis of excessive zeros count data. For this purpose, a real data set was analysed with the generalized Poisson model, generalized negative binomial model, generalized negative binomial Famoye, generalized Waring model, and the foregoing zero-inflated models. Log-likelihood, Akaike information criterion, Bayes information criterion, Vuong statistics were used for model comparisons.

Panel count data often occur in a long-term recurrent event study, where the exact occurrence time of the recurrent events is unknown, but only the occurrence count between any two adjacent observation time points is recorded. Most traditional methods only handle panel count data for a single type of event. In this paper, we propose a Bayesian semiparameteric approach to analyze panel count data for multiple types of events. For each type of recurrent event, the proportional mean model is adopted to model the mean count of the event, where its baseline mean function is approximated by monotone I-splines. The correlation between multiple types of events is modeled by common frailty terms and scale parameters. Unlike many frequentist estimating equation methods, our approach is based on the observed likelihood and makes no assumption on the relationship between the recurrent process and the observation process. Under the Poisson counting process assumption, we develop an efficient Gibbs sampler based on novel data augmentation for the Markov chain Monte Carlo sampling. Simulation studies show good estimation performance of the baseline mean functions and the regression coefficients; meanwhile, the importance of including the scale parameter to flexibly accommodate the correlation between events is also demonstrated. Finally, a skin cancer data example is fully analyzed to illustrate the proposed methods.

Different conventional and causal approaches have been proposed for mediation analysis to better understand the mechanism of a treatment. Count and zero-inflated count data occur in biomedicine, economics, and social sciences. This paper considers mediation analysis for count and zero-inflated count data under the potential outcome framework with nonlinear models. When there are post-treatment confounders which are independent of, or affected by, the treatment, we first define the direct, indirect, and total effects of our interest and then discuss various conditions under which the effects of interest can be identified. Proofs are provided for the sensitivity analysis proposed in the paper. Simulation studies show that the methods work well. We apply the methods to the Detroit Dental Health Project's Motivational Interviewing DVD trial for the direct and indirect effects of motivational interviewing on count and zero-inflated count dental caries outcomes.

This paper considers regression analysis of multivariate panel count data with the focus on variable selection and estimation of significant covariate effects. For the problem, we adopt the penalized estimating equation approach with a focus on the use of the seamless‐$L_0$ penalty. The proposed approach selects variables and estimates regression coefficients simultaneously and the asymptotic properties of the resulting estimates are established. The procedure can be easily carried out with the Newton–Raphson algorithm and is evaluated by simulation studies. Also it is applied to a motivating data set arising from a skin cancer study. The Canadian Journal of Statistics 41: 368–385; 2013 © 2013 Statistical Society of Canada

Panel count data occur in many fields including clinical, demographical and industrial studies and an extensive literature has been established for their regression analysis. However, most of the existing methods apply only to the situations where both covariates and their effects are constant or one of them may be time-dependent. In the first part of this dissertation, we consider a situation where both covariates and their effects may be time-dependent and an estimating equation-based approach is developed for estimating those time-varying effects. In the method, B-spline functions are employed to approximate time-dependent coefficients and the asymptotic properties of the proposed estimators are established. To assess the performance of the proposed approach, an extensive simulation study is conducted and suggests that it works well in practical situations. An application to the China Health and Nutrition Survey (CHNS) study is provided. In practice, there could exist more than one type of event of interest, such as two types of tumor recurrence, leading to multivariate panel count data. The second part of this dissertation considers marginal mean model for multivariate panel count data with time-dependent coefficient and covariate effects, which has limited previous research. Based on the conditional estimating equation method developed for time-dependent covariates, we approximate the coefficients by B-splines, hence allow both coefficients and covariates to be time-dependent. Simulation studies show that the proposed estimation procedures work well for practical situations. The methodology is again applied to the China Health and Nutrition Survey (CHNS) study. When we consider time-varying covariates and coefficients effects, most of the previous study focused on the proportional mean model because the likelihood function under the rate model involves intractable integration. However, the rate model is more realistic and efficient. Hence, in the third part of this dissertation, we propose a semi-parametric MLE method under the rate model for panel count data with time-dependent covariates and time-varying effects. B-spline functions are employed again to approximate time-dependent coefficients and an efficient Expectation-Maximization-type algorithm is developed to overcome the computational difficulty. The resulting estimators are shown to be consistent and asymptotically efficient. Monte Carlo simulation studies demonstrate that the proposed method enjoys desirable finite-sample properties. An application to The Young Women's Project (YWP) is provided.

McDonald, Erickson, and McDonald (2000) and Murtaugh (2000) have presented two interesting views of analysis and interpretation of data from before-after control-impact (BACI) studies. In my opinion, the general message they convey to the reader is that analysis of data from a BACI design, in combination with professional expertise, can add useful evidence as long as one is prudent about the resulting interpretations. Whether scientists who analyze BACI data will indeed use caution in interpretation, particularly in making statements regarding cause and effect, remains to be seen. McDonald et al.'s (2000) study is application specific, taking the reader through an analysis of bird count data from the Exxon Valdez oil spill (EVOS). The authors prudently phrase their interpretation in terms of a weight of evidence argument rather than the much more difficult one of causation. I see the primary usefulness of this paper as that of encouraging scientists to use more complex models to realistically describe count data through time. (Using these models in data analysis has been considerably enhanced by the increasing availability of various types of computer software.) Particularly with biological data, a conventional first step is to try an additive model on untransformed data or an additive model on log-transformed data with the hope that the log transform restores the assumptions of variance homogeneity and normally distributed error terms. The presence of data recorded on the same units through time necessitates that the Huynh-Feldt condition (also known as sphericity) holds in order to use a conventional repeated measures approach. In case this sphericity condition does not hold, there are references to make conservative adjustments to the usual F-tests. (I do wonder just how many people would take the trouble to test these assumptions and do the proper corrections if such corrections were not already built into the

Molecular ecology regularly requires the analysis of count data that reflect the relative abundance of features of a composition (e.g., taxa in a community, gene transcripts in a tissue). The sampling process that generates these data can be modelled using the multinomial distribution. Replicate multinomial samples inform the relative abundances of features in an underlying Dirichlet distribution. These distributions together form a hierarchical model for relative abundances among replicates and sampling groups. This type of Dirichlet-multinomial modelling (DMM) has been described previously, but its benefits and limitations are largely untested. With simulated data, we quantified the ability of DMM to detect differences in proportions between treatment and control groups, and compared the efficacy of three computational methods to implement DMM-Hamiltonian Monte Carlo (HMC), variational inference (VI), and Gibbs Markov chain Monte Carlo. We report that DMM was better able to detect shifts in relative abundances than analogous analytical tools, while identifying an acceptably low number of false positives. Among methods for implementing DMM, HMC provided the most accurate estimates of relative abundances, and VI was the most computationally efficient. The sensitivity of DMM was exemplified through analysis of previously published data describing lung microbiomes. We report that DMM identified several potentially pathogenic, bacterial taxa as more abundant in the lungs of children who aspirated foreign material during swallowing; these differences went undetected with different statistical approaches. Our results suggest that DMM has strong potential as a statistical method to guide inference in molecular ecology.

In this paper is presented the zero-modified poisson difference and present possible applications of them in the analysis of paired count data. The estimation and inferences of the model parameters were made considering a Bayesian approach using the algorithm of Hamiltonian Markov chain Monte Carlo methods to simulate samples of the joint posterior distribution of interest. Two applications were made for the analysis of paired count data.

Transmuted geometric distribution (TGD) was recently introduced and investigated by Chakraborty and Bhati [Stat. Oper. Res. Trans. 40 (2016), 153–176]. This is a flexible extension of geometric distribution having an additional parameter that determines its zero inflation as well as the tail length. In the present article we further study this distribution for some of its reliability, stochastic ordering and parameter estimation properties. In parameter estimation among others we discuss an EM algorithm and the performance of estimators is evaluated through extensive simulation. For assessing the statistical significance of additional parameter (α), Likelihood ratio test, the Rao’s score tests and the Wald’s test are developed and its empirical power via simulation are compared. We have demonstrate two applications of (TGD) in modeling real life count data.

In this paper we examine estimation in a mixture model under various assumptions for the underlying distribution. We suggest that statistical inference should be carried out using the conditional distribution given the appropriate ancillary statistics. The conditional likelihood approach used here can be justified by Cox's (1958) criterion about ancillarity in the presence of a nuisance parameter, and in the spirit of Godambe's (1976) conditional likelihood optimum estimating equation. The analysis is known to be easier and more stable than the unconditional likelihood function approach. The probability distributions in the analysis of count data discussed here include Poisson, binomial, geometric and negative binomial distributions. The information loss incurred by using the conditional approach is discussed