Tweedie Compound Poisson Models with Covariate-Dependent Random Effects for Multilevel Semicontinuous Data.

Multilevel semicontinuous data occur frequently in medical, environmental, insurance and financial studies. Such data are often measured with covariates at different levels; however, these data have traditionally been modelled with covariate-independent random effects. Ignoring dependence of cluster-specific random effects and cluster-specific covariates in these traditional approaches may lead to ecological fallacy and result in misleading results. In this paper, we propose Tweedie compound Poisson model with covariate-dependent random effects to analyze multilevel semicontinuous data where covariates at different levels are incorporated at relevant levels. The estimation of our models has been developed based on the orthodox best linear unbiased predictor of random effect. Explicit expressions of random effects predictors facilitate computation and interpretation of our models. Our approach is illustrated through the analysis of the basic symptoms inventory study data where 409 adolescents from 269 families were observed at varying number of times from 1 to 17 times. The performance of the proposed methodology was also examined through the simulation studies.

Tweedie family of generalized linear models with distribution-free random effects for skewed longitudinal data.

Generalized linear mixed models have played an important role in the analysis of longitudinal data; however, traditional approaches have limited flexibility in accommodating skewness and complex correlation structures. In addition, the existing estimation approaches generally rely heavily on the specifications of random effects distributions; therefore, the corresponding inferences are sometimes sensitive to the choice of random effect distributions under certain circumstance. In this paper, we incorporate serially dependent distribution-free random effects into Tweedie generalized linear models to accommodate a wide range of skewness and covariance structures for discrete and continuous longitudinal data. An optimal estimation of our model has been developed using the orthodox best linear unbiased predictors of random effects. Our approach unifies population-averaged and subject-specific inferences. Our method is illustrated through the analyses of patient-controlled analgesia data and Framingham cholesterol data.

Regressive Class Modelling for Predicting Trajectories of COVID-19 Fatalities Using Statistical and Machine Learning Models.

The COVID-19 (SARS-CoV-2 virus) pandemic has led to a substantial loss of human life worldwide by providing an unparalleled challenge to the public health system. The economic, psychological, and social disarray generated by the COVID-19 pandemic is devastating. Public health experts and epidemiologists worldwide are struggling to formulate policies on how to control this pandemic as there is no effective vaccine or treatment available which provide long-term immunity against different variants of COVID-19 and to eradicate this virus completely. As the new cases and fatalities are recorded daily or weekly, the responses are likely to be repeated or longitudinally correlated. Thus, studying the impact of available covariates and new cases on deaths from COVID-19 repeatedly would provide significant insights into this pandemic's dynamics. For a better understanding of the dynamics of spread, in this paper, we study the impact of various risk factors on the new cases and deaths over time. To do that, we propose a marginal-conditional based joint modelling approach to predict trajectories, which is crucial to the health policy planners for taking necessary measures. The conditional model is a natural choice to study the underlying property of dependence in consecutive new cases and deaths. Using this model, one can examine the relationship between outcomes and predictors, and it is possible to calculate risks of the sequence of events repeatedly. The advantage of repeated measures is that one can see how individual responses change over time. The predictive accuracy of the proposed model is also compared with various machine learning techniques. The machine learning algorithms used in this paper are extended to accommodate repeated responses. The performance of the proposed model is illustrated using COVID-19 data collected from the Texas Health and Human Services.

Linking dynamic patterns of COVID-19 spreads in Italy with regional characteristics: a two level longitudinal modelling approach.

The current statistical modeling of coronavirus (COVID-19) spread has mainly focused on spreading patterns and forecasting of COVID-19 development; these patterns have been found to vary among locations. As the survival time of coronaviruses on surfaces depends on temperature, some researchers have explored the association of daily confirmed cases with environmental factors. Furthermore, some researchers have studied the link between daily fatality rates with regional factors such as health resources, but found no significant factors. As the spreading patterns of COVID-19 development vary a lot among locations, fitting regression models of daily confirmed cases or fatality rates directly with regional factors might not reveal important relationships. In this study, we investigate the link between regional spreading patterns of COVID-19 development in Italy and regional factors in two steps. First, we characterize regional spreading patterns of COVID-19 daily confirmed cases by a special patterned Poisson regression model for longitudinal count; the varying growth and declining patterns as well as turning points among regions in Italy have been well captured by regional regression parameters. We then associate these regional regression parameters with regional factors. The effects of regional factors on spreading patterns of COVID-19 daily confirmed cases have been effectively evaluated.

Analyzing the effect of duration on the daily new cases of COVID-19 infections and deaths using bivariate Poisson regression: a marginal conditional approach.

The whole world is devastated by the impact of the COVID-19 pandemic. The socioeconomic and other effects of COVID-19 on people are visible in all echelons of society. The main goal of countries is to stop the spreading of this pandemic by reducing the COVID-19 related new cases and deaths. In this paper, we analyzed the correlated count outcomes, daily new cases, and fatalities, and assessed the impact of some covariates by adopting a generalized bivariate Poisson model. There are different effects of duration on new cases and deaths in different countries. Also, the regional variation found to be different, and population density has a significant impact on outcomes.

Modelling heterogeneity in clustered count data with extra zeros using compound Poisson random effect.

In medical and health studies, heterogeneities in clustered count data have been traditionally modeled by positive random effects in Poisson mixed models; however, excessive zeros often occur in clustered medical and health count data. In this paper, we consider a three-level random effects zero-inflated Poisson model for health-care utilization data where data are clustered by both subjects and families. To accommodate zero and positive components in the count response compatibly, we model the subject level random effects by a compound Poisson distribution. Our model displays a variance components decomposition which clearly reflects the hierarchical structure of clustered data. A quasi-likelihood approach has been developed in the estimation of our model. We illustrate the method with analysis of the health-care utilization data. The performance of our method is also evaluated through simulation studies.

Pattern-mixture zero-inflated mixed models for longitudinal unbalanced count data with excessive zeros.

Analysis of longitudinal data with excessive zeros has gained increasing attention in recent years; however, current approaches to the analysis of longitudinal data with excessive zeros have primarily focused on balanced data. Dropouts are common in longitudinal studies; therefore, the analysis of the resulting unbalanced data is complicated by the missing mechanism. Our study is motivated by the analysis of longitudinal skin cancer count data presented by Greenberg, Baron, Stukel, Stevens, Mandel, Spencer, Elias, Lowe, Nierenberg, Bayrd, Vance, Freeman, Clendenning, Kwan, and the Skin Cancer Prevention Study Group[New England Journal of Medicine 323, 789-795]. The data consist of a large number of zero responses (83% of the observations) as well as a substantial amount of dropout (about 52% of the observations). To account for both excessive zeros and dropout patterns, we propose a pattern-mixture zero-inflated model with compound Poisson random effects for the unbalanced longitudinal skin cancer data. We also incorporate an autoregressive of order 1 correlation structure in the model to capture longitudinal correlation of the count responses. A quasi-likelihood approach has been developed in the estimation of our model. We illustrated the method with analysis of the longitudinal skin cancer data.