Analysis of panel count data with time-dependent covariates and informative observation process

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 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.

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

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

Regression Analysis of Panel Count Data II

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 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.

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.

Survival analysis is often used to compare experimental and conventional treatments. In observational studies, the therapy may change during follow-up and such crossovers can be summarized by time-dependent covariates. Given the ever-increasing donor organ shortage, higher-risk kidneys from expanded criterion donors (ECD) are being transplanted. Transplant candidates can choose whether to accept an ECD organ (experimental therapy), or to remain on dialysis and wait for a possible non-ECD transplant later (conventional therapy). A three-group time-dependent analysis of such data involves estimating parameters corresponding to two time-dependent indicator covariates representing ECD transplant and non-ECD transplant, each compared to remaining on dialysis on the waitlist. However, the ECD hazard ratio estimated by this time-dependent analysis fails to account for the fact that patients who forego an ECD transplant are not destined to remain on dialysis forever, but could subsequently receive a non-ECD transplant. We propose a novel method of estimating the survival benefit of ECD transplantation relative to conventional therapy (waitlist with possible subsequent non-ECD transplant). Compared to the time-dependent analysis, the proposed method more accurately characterizes the data structure and yields a more direct estimate of the relative outcome with an ECD transplant.

In survival analyses that include a time-dependent covariate, the standard partial likelihood approach is often complicated by the fact that the necessary observations of the time-dependent covariate are not always available for the subjects in each risk set. In this article, we consider the situation of a binary time-dependent covariate. We specify a longitudinal model for the binary covariate with missing observations and a proportional hazards model for survival time conditional on fixed covariates and the completed time-dependent covariate history. The joint posterior distribution of the missing covariates and the parameters in the covariate and hazard models is simulated using Gibbs sampling. The joint modeling approach allows the missing covariates to be generated using all of the observed covariates as well as the disease outcome and failure time information. Simulation studies show that this approach often leads to lower bias of relative risk estimates associated with the time-dependent covariate and superior coverage of interval estimates as compared to variations of approaches based on imputing missing covariate values using previous values and then performing partial likelihood analysis. Our research is motivated by a study of survival of lung cancer patients after surgery in which current smoking status is a binary time-dependent covariate. We apply the methods to data from this study and explore the advantages of the joint modeling approach. The application demonstrates that the joint modeling approach can have improved efficiency in estimating the coefficients of both the fixed and the time-dependent covariates. Moreover, it can facilitate analyses using more complicated functions of the time-dependent covariate, such as cumulative smoking, that are difficult or inappropriate to use with the comparison 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.

SummaryThe transitional phase of menopause induces significant hormonal fluctuations, exerting a profound influence on the long-term well-being of women. In an extensive longitudinal investigation of women’s health during mid-life and beyond, known as the Study of Women’s Health Across the Nation (SWAN), hormonal biomarkers are repeatedly assessed, following an asynchronous schedule compared to other error-prone covariates, such as physical and cardiovascular measurements. We conduct a subgroup analysis of the SWAN data employing a semiparametric mixture regression model, which allows us to explore how the relationship between hormonal responses and other time-varying or time-invariant covariates varies across subgroups. To address the challenges posed by asynchronous scheduling and measurement errors, we model the time-varying covariate trajectories as functional data with reduced-rank Karhunen–Loéve expansions, where splines are employed to capture the mean and eigenfunctions. Treating the latent subgroup membership and the functional principal component (FPC) scores as missing data, we propose an Expectation-Maximization algorithm to effectively fit the joint model, combining the mixture regression for the hormonal response and the FPC model for the asynchronous, time-varying covariates. In addition, we explore data-driven methods to determine the optimal number of subgroups within the population. Through our comprehensive analysis of the SWAN data, we unveil a crucial subgroup structure within the aging female population, shedding light on important distinctions and patterns among women undergoing menopause.

In the past two decades, joint models of longitudinal and survival data have received much attention in the literature. These models are often desirable in the following situations: (i) survival models with measurement errors or missing data in time-dependent covariates, (ii) longitudinal models with informative dropouts, and (iii) a survival process and a longitudinal process are associated via latent variables. In these cases, separate inferences based on the longitudinal model and the survival model may lead to biased or inefficient results. In this paper, we provide a brief overview of joint models for longitudinal and survival data and commonly used methods, including the likelihood method and two-stage methods.

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

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.