Statistical Analysis of Panel Count Data

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.

Panel count data typically refer to data arising from studies with recurrent events, in which subjects are observed only at discrete time points rather than under continuous observations. We investigate a general situation where a recurrent event process is eventually truncated by an informative terminal event and we are particularly interested in behaviors of the recurrent event process near the terminal event. We propose a reversed mean model for estimating the mean function of the recurrent event process. We develop a two-stage sieve likelihood-based method to estimate the mean function, which overcomes the computational difficulties arising from a nuisance functional parameter involved in the likelihood. The consistency and the convergence rate of the two-stage estimator are established. Allowing for the convergence rate slower than the standard rate, we develop the general weak convergence theory of M-estimators with a nuisance functional parameter, and then apply it to the proposed estimator for deriving the asymptotic normality. Furthermore, a class of two-sample tests is developed. The proposed methods are evaluated with extensive simulation studies and illustrated with panel count data from the Chinese Longitudinal Healthy Longevity Study.

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.

Panel count data and interval-censored data are two types of incomplete data that often occur in event history studies. Almost all existing statistical methods are developed for their separate analysis. In this paper, we investigate a more general situation where a recurrent event process and an interval-censored failure event occur together. To intuitively and clearly explain the relationship between the recurrent current process and failure event, we propose a failure time-dependent mean model through a completely unspecified link function. To overcome the challenges arising from the blending of nonparametric components and parametric regression coefficients, we develop a two-stage conditional expected likelihood-based estimation procedure. We establish the consistency, the convergence rate and the asymptotic normality of the proposed two-stage estimator. Furthermore, we construct a class of two-sample tests for comparison of mean functions from different groups. The proposed methods are evaluated by extensive simulation studies and are illustrated with the skin cancer data that motivated this study.

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.

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

Regression Analysis of Panel Count Data II

Panel-count data arise when each study subject is observed only at discrete time points in a recurrent event study, and only the numbers of the event of interest between observation time points are recorded (Sun and Zhao, 2013). However, sometimes the exact number of events between some observation times is unknown and what we know is only whether the event of interest has occurred. In this article, we will refer this type of data to as mixed panel-count data and propose a likelihood-based semiparametric regression method for their analysis by using the nonhomogeneous Poisson process assumption. However, we establish the asymptotic properties of the resulting estimator by employing the empirical process theory and without using the Poisson assumption. Also, we conduct an extensive simulation study, which suggests that the proposed method works well in practice. Finally, the method is applied to a Childhood Cancer Survivor Study that motivated this study.

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.

In modern biomedical datasets, it is common for recurrent outcomes data to be collected in an incomplete manner. More specifically, information on recurrent events is routinely recorded as a mixture of recurrent event data, panel count data, and panel binary data; we refer to this structure as general mixed recurrent event data. Although the aforementioned data types are individually well-studied, there does not appear to exist an established approach for regression analysis of the three component combination. Often, ad-hoc measures such as imputation or discarding of data are used to homogenize records prior to the analysis, but such measures lead to obvious concerns regarding robustness, loss of efficiency, and other issues. This work proposes a maximum likelihood regression estimation procedure for the combination of general mixed recurrent event data and establishes the asymptotic properties of the proposed estimators. In addition, we generalize the approach to allow for the existence of terminal events, a common complicating feature in recurrent event analysis. Numerical studies and application to the Childhood Cancer Survivor Study suggest that the proposed procedures work well in practical situations.

A nonparametric test for the equality of counting processes with panel count data

The brain is exposed to continuous sensory input from the environment (and the body). How does the brain encode such continuous sensory input and translate it into neural activity, e.g., stimulus-induced activity? Results from cellular recordings show that single neurons and a population of neurons represent the stimulus in a rather sparse way so that many stimuli are represented in one neuron’s (or one population of neurons’) activity. This amounts to a many-to-one relationship between stimuli and neurons entailing sparse coding. As such, sparse coding must be distinguished from other coding strategies like dense and local coding that propose a one-to-many and one-to-one relationship between stimuli and neurons. How is such sparse coding possible? The neurons’ (and population of neurons’) activity seems to encode the statistical frequency distribution of stimuli across their different discrete points in physical time and space; that is, their natural statistics. However, this is possible only when presupposing that differences between the stimuli’s different discrete points in physical space and time are encoded into neural activity. In other words, spatial and temporal differences (between the different discrete points in physical time and space) must be encoded into neural activity in order for sparse coding as a many-to-one relationship between stimuli and neurons to be possible.

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.

The current status and panel count data frequently arise from cancer and tumorigenicity studies when events currently occur. A common and widely used class of two sample tests, for current status and panel count data, is the permutation class. We manipulate the double saddlepoint method to calculate the exact mid-p-values of the underlying permutation distributions of this class of tests. Permutation simulations are replaced by analytical saddlepoint computations which provide extremely accurate mid-p-values that are exact for most practical purposes and almost always more accurate than normal approximations. The method is illustrated using two real tumorigenicity panel count data. To compare the saddlepoint approximation with the normal asymptotic approximation, a simulation study is conducted. The speed and accuracy of the saddlepoint method facilitate the calculation of the confidence interval for the treatment effect. The inversion of the mid-p-values to calculate the confidence interval for the mean rate of development of the recurrent event is discussed.