Panel Count Data Research Articles

Saddlepoint p-values for a class of nonparametric tests for the current status and panel count data under generalized permuted block design

<abstract><p>Current status and panel count data appear in many applied fields, including medicine, clinical trials, epidemiology, econometrics, demography, engineering and public health. Therefore, in this article, we use the saddlepoint approximation method to approximate the exact p-value of a number of nonparametric tests for the current status and panel count data under a generalized permuted block design. The saddlepoint approximation is referred to as higher-order approximation and it is more accurate than the methods that lead to approximations that are accurate to the first order, such as the asymptotic normal approximation method. To verify the accuracy and efficiency of the saddlepoint approximation method, a simulation study is conducted. The simulation study results confirm that the saddlepoint approximation method is more powerful than the existing approximation method. Furthermore, number of real current status and panel count data sets are analyzed and displayed as illustrative examples.</p></abstract>

Sieve estimation of semiparametric accelerated mean models with panel count data

A widely adopted semiparametric model for analyzing panel count data is a proportional mean model, which may be deemed inappropriate when the proportionality assumption is violated. Motivated by the popular accelerated failure time model that relaxes such assumption, we investigate accelerated mean models for semiparametric regression analysis of panel count data. For estimation of bundled parameters, we develop a sieve least squares estimation procedure, which is robust in the sense that no distributional assumption is required for the underlying recurrent event process. Overcoming the theoretical challenges from bundled parameters, we establish the consistency and convergence rate of the proposed estimators, and derive the asymptotic normality of both the finite-dimensional estimator and the functionals of the infinite-dimensional estimator. Simulation studies demonstrate promising performances of the proposed approach, and an application to a skin cancer chemoprevention trial yields some new findings.

Regression Analysis of Panel Count Data With Both Time-Dependent Covariates and Time-Varying Effects

Regression Analysis of Panel Count Data With Both Time-Dependent Covariates and Time-Varying Effects

Nonparametric inference for reversed mean models with panel count data

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.

Polynomial spline estimation of panel count data model with an unknown link function

Polynomial spline estimation of panel count data model with an unknown link function

Joint analysis of informatively interval-censored failure time and panel count data.

Interval-censored failure time and panel count data, which frequently arise in medical studies and social sciences, are two types of important incomplete data. Although methods for their joint analysis have been available in the literature, they did not consider the observation process, which may depend on the failure time and/or panel count of interest. This study considers a three-component joint model to analyze interval-censored failure time, panel counts, and the observation process within a unique framework. Gamma and distribution-free frailties are introduced to jointly model the interdependency among the interval-censored data, panel count data, and the observation process. We propose a sieve maximum likelihood approach coupled with Bernstein polynomial approximation to estimate the unknown parameters and baseline hazard function. The asymptotic properties of the resulting estimators are established. An extensive simulation study suggests that the proposed procedure works well for practical situations. An application of the method to a real-life dataset collected from a cardiac allograft vasculopathy study is presented.

Inference of a time-varying coefficient regression model for multivariate panel count data

Panel count data consist of the numbers of event occurrences between two consecutive observation times and are prevalent in many areas. Correspondingly a bulk of literature has been developed for the analysis of panel count data with time-independent or time-dependent covariates but assuming time-invariant covariate effects. However, the time-invariant coefficient assumption is too restrictive in reality and fails to represent the time-dynamic association between the covariates and event occurrence rates. In this paper, we discuss regression analysis of multivariate panel count data where both the covariates and their effects may be time-varying. We propose a marginal estimating equation approach combined with the B-splines that approximate the functional forms of the regression coefficients. The asymptotic properties of the proposed estimators are rigorously established. A simulation study is conducted to assess the performance of the proposed estimation procedure and suggests that it works well for practical situations. The proposed methodology is applied to a real dataset that motivated this study.

Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data

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.

Spatial panel count data: modeling and forecasting of urban crimes

The steadily growing access to high-quality spatio-temporal crime count data with a high level of spatial detail allows to uncover interesting relationships between crime types within and between small regional units. Data coherent forecasting of such counts has to take the integer and non-negative nature of the data into account. Spatial panel data models that meet the criterion of coherency are relatively sparse. This paper proposes a new spatial panel regression framework with fixed effects to overcome these shortcomings. Depending on whether time dynamic effects are included in the model specification, estimation and inference are based either on a pseudo maximum likelihood method or on quasi-differenced generalized methods of moments. The models’ usefulness is demonstrated in a forecasting exercise of monthly crime counts at census tract level from Pittsburgh, Pennsylvania.

Semiparametric Regression Analysis of Mixed Recurrent Event and Panel Count Data with Multiple Causes of Failure

Semiparametric Regression Analysis of Mixed Recurrent Event and Panel Count Data with Multiple Causes of Failure

Quantile estimation of semiparametric model with time-varying coefficients for panel count data.

Panel count data frequently occurs in follow-up studies, such as medical research, social sciences, reliability studies, and tumorigenicity experiences. This type data has been extensively studied by various statistical models with time-invariant regression coefficients. However, the assumption of invariant coefficients may be violated in some reality, and the temporal covariate effects would be of great interest in research studies. This motivates us to consider a more flexible time-varying coefficient model. For statistical inference of the unknown functions, the quantile regression approach based on the B-spline approximation is developed. Asymptotic results on the convergence of the estimators are provided. Some simulation studies are presented to assess the finite-sample performance of the estimators. Finally, two applications of bladder cancer data and US flight delay data are analyzed by the proposed method.

Semiparametric analysis of multivariate panel count data with nonlinear interactions.

Multivariate panel count data frequently arise in follow up studies involving several related types of recurrent events. For univariate panel count data, several varying coefficient models have been developed. However, varying coefficient models for multivariate panel count data remain to be studied. In this paper, we propose a varying coefficient mean model for multivariate panel count data to describe the possible nonlinear interact effects between the covariates and the local logarithm partial likelihood procedure is considered to estimate the unknown covariate effects. Furthermore, a Breslow-type estimator is constructed for the baseline mean functions. The consistency and asymptotic normality of the proposed estimators are established under some mild conditions. The utility of the proposed approach is evaluated by some numerical simulations and an application to a dataset of skin cancer study.

Local logarithm partial likelihood estimation of panel count data model with an unknown link function

Panel count data have been extensively discussed in the literature. In general, the existing approaches in modeling panel count data usually assume an exponential form for the dependence of the conditional mean function on covariate variables. However, this assumption may be violated in practice. A more flexible panel count data model with an unknown link function is proposed, and a local logarithm partial likelihood function is formed for the estimation. A two-step iterative algorithm is employed to estimate the unknown link function and covariate effects. Furthermore, the baseline function is obtained by Breslow estimation. Asymptotic properties are derived under some mild conditions. Some numerical simulations and an application of bladder cancer are carried out to confirm and assess the performance of the proposed model and approach.

Confidence intervals for multiple isotonic regression and other monotone models

We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, Han and Zhang (2020) obtained a pointwise limit distribution theory for the so-called block max–min and min–max estimators (Fokianos, Leucht and Neumann (2020); Deng and Zhang (2020)) in this model, but inference remains a difficult problem due to the nuisance parameter in the limit distribution that involves multiple unknown partial derivatives of the true regression function. In this paper, we show that this difficult nuisance parameter can be effectively eliminated by taking advantage of information beyond point estimates in the block max–min and min–max estimators. Formally, let uˆ(x0) (resp. vˆ(x0)) be the maximizing lower-left (resp. minimizing upper-right) vertex in the block max–min (resp. min–max) estimator, and fˆn be the average of the block max–min and min–max estimators. If all (first-order) partial derivatives of f0 are nonvanishing at x0, then the following pivotal limit distribution theory holds: nuˆ,vˆ(x0)(fˆn(x0)−f0(x0))⇝σ·L1d. Here nuˆ,vˆ(x0) is the number of design points in the block [uˆ(x0),vˆ(x0)], σ is the standard deviation of the errors, and L1d is a universal limit distribution free of nuisance parameters. This immediately yields confidence intervals for f0(x0) with asymptotically exact confidence level and oracle length. Notably, the construction of the confidence intervals, even new in the univariate setting, requires no more efforts than performing an isotonic regression once using the block max–min and min–max estimators, and can be easily adapted to other common monotone models including, for example, (i) monotone density estimation, (ii) interval censoring model with current status data, (iii) counting process model with panel count data, and (iv) generalized linear models. Extensive simulations are carried out to support our theory.

Efficacy of Government Responses to COVID-19 in Mediterranean Countries.

ObjectiveThis article aims to provide empirical evidence on the effectiveness of the governments’ policy measures in response to the COVID-19 pandemic in the Mediterranean countries.MethodsWe considered five categories of response: lockdowns, social distancing, movement restrictions, public health measures, and governance and socio-economic measures. Our main research question is, How long do these measures take to become effective? Our analysis, by longitudinal regressions and panel count data analyses, focuses on one region—the Mediterranean countries—to avoid differences, such as cultural factors, that may influence the evolution of the viral pandemic. We start by investigating heteroscedasticity, and both serial and contemporaneous correlation of the disturbance term across cross-sectional countries.ResultsOur different estimation methods paint very similar trajectories of the efficacy of governments’ response measures. The benefits of these measures increase exponentially with time. We find that the net effects can be divided into three phases. In the first week, the benefits are not guaranteed unless the total number of contamination cases is less than some threshold values, ie if the spread of the virus is not already advanced. Then, indirect effects are revealed. After three weeks, we observe a reduction in the number of the new confirmed viral cases and, thus, the direct net benefits are observed.ConclusionThe earlier governments act, in relation to the evolution of the epidemic, the lower the total cumulative incidence due to the epidemic wave.

Analysis of Road Traffic Accidents in the Punjab by Using Panel Count Data Models

Each year more than three thousand people die and get serious injuries in traffic accidents. Count data model provide more precise tools for planners and decision makers to conduct proactive road safety planning.We analyzed the exploratory research of Road Traffic Accidents (RTAs) and furthermore explores the factors affecting the RTAs frequency in 36 districts of the Punjab over a time period of three years (July 1, 2013 June 30, 2016) with monthly data using panel count data models. Among the models considered, the random parameters Poisson panel count data model is found to fit the data best. The exploratory analysis shows that highly dense populated districts with large number of registered vehicles causes more accidents as compared to low density populated districts. It is found that, most of the variables used to control the variation in the frequency of RTAs counts play vital role with higher significance levels. The application of regression analysis and modeling of RTAs at district level in Punjab will help to identification of districts with high RTAs rates and this could help more efficient road safety management in the Punjab.

Penalized spline estimation for panel count data model with time-varying coefficients

Penalized spline estimation for panel count data model with time-varying coefficients

A kernel regression model for panel count data with nonparametric covariate functions.

The local kernel pseudo-partial likelihood is employed for estimation in a panel count model with nonparametric covariate functions. An estimator of the derivative of the nonparametric covariate function is derived first, and the nonparametric function estimator is then obtained by integrating the derivative estimator. Uniform consistency rates and pointwise asymptotic normality are obtained for the local derivative estimator under some regularity conditions. Moreover, the baseline function estimator is shown to be uniformly consistent. Demonstration of the asymptotic results strongly relies on the modern empirical theory, which generally does not require the Poisson assumption. Simulation studies also illustrate that the local derivative estimator performs well in a finite-sample regardless of whether the Poisson assumption holds. We also implement the proposed methodology to analyze a clinical study on childhoodwheezing.

Beta-binomial models for meta-analysis with binary outcomes: Variations, extensions, and additional insights from econometrics

Background Meta-analysis of systematically reviewed studies on interventions is the cornerstone of evidence based medicine. In the following, we will introduce the common-beta beta-binomial (BB) model for meta-analysis with binary outcomes and elucidate its equivalence to panel count data models. Methods We present a variation of the standard “common-rho” BB (BBST model) for meta-analysis, namely a “common-beta” BB model. This model has an interesting connection to fixed-effect negative binomial regression models (FE-NegBin) for panel count data. Using this equivalence, it is possible to estimate an extension of the FE-NegBin with an additional multiplicative overdispersion term (RE-NegBin), while preserving a closed form likelihood. An advantage due to the connection to econometric models is, that the models can be easily implemented because “standard” statistical software for panel count data can be used. We illustrate the methods with two real-world example datasets. Furthermore, we show the results of a small-scale simulation study that compares the new models to the BBST. The input parameters of the simulation were informed by actually performed meta-analysis. Results In both example data sets, the NegBin, in particular the RE-NegBin showed a smaller effect and had narrower 95%-confidence intervals. In our simulation study, median bias was negligible for all methods, but the upper quartile for median bias suggested that BBST is most affected by positive bias. Regarding coverage probability, BBST and the RE-NegBin model outperformed the FE-NegBin model. Conclusion For meta-analyses with binary outcomes, the considered common-beta BB models may be valuable extensions to the family of BB models.

Robust Estimation of Semiparametric Transformation Model for Panel Count Data

Panel count data are frequently encountered when study subjects are under discrete observations. However, limited literature has been found on variable selection for panel count data. In this paper, without considering the model assumption of observation process, a more general semiparametric transformation model for panel count data with informative observation process is developed. A penalized estimation procedure based on the quantile regression function is proposed for variable selection and parameter estimation simultaneously. The consistency and oracle properties of the estimators are established under some mild conditions. Some simulations and an application are reported to evaluate the proposed approach.