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.

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.

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.