Determination of correlations in multivariate count data with informative observation times

We consider there are various types of recurrent events and the total number of occurrences are collected at the random observation times. It has concerned that the observation process may not be independent to the multivariate event processes, hence the total counts and observation times may be correlated and the dependence may exist among different types of the event processes as well. Many methods have developed nonparametric models to accommodate such unknown structures; however, it is difficult to assess and directly quantify their correlation relationships. A multivariate frailty model is proposed to this study, in which the event and observation processes are linked by frailty variables whose joint distribution can be implicitly specified through the multivariate normal distribution with some unknown covariance matrix. The Bayesian inference method is conducted to obtain the estimates of the regression coefficients and correlation parameters. We use a form of trigonometric functions to represent the covariance matrix, so that it meets the positive-definiteness condition efficiently during the estimation schemes. The simulation studies demonstrate the utility of the proposed models. We apply the model to a skin cancer prevention study, and aim to determine the covariate and association effects. We found treatment is significant in determining the duration of examination times; prior-counts, age and gender are significant variables on the occurrence rates of tumor counts. Using the covariance matrix to access the underlying dependent structure, the mutual correlations among them are all positive, and the basal cell counts are more related to the examination times.

Multivariate Count Data Models for Time Series Forecasting

Count data appears in many research fields and exhibits certain features that make modeling difficult. Most popular approaches to modeling count data can be classified into observation and parameter-driven models. In this paper, we review two models from these classes: the log-linear multivariate conditional intensity model (also referred to as an integer-valued generalized autoregressive conditional heteroskedastic model) and the non-linear state-space model for count data. We compare these models in terms of forecasting performance on simulated data and two real datasets. In simulations, we consider the case of model misspecification. We find that both models have advantages in different situations, and we discuss the pros and cons of inference for both models in detail.

Multivariate hierarchical frameworks for modeling delayed reporting in count data

In many fields and applications, count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short‐term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty. We discuss previous approaches to modeling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay mechanism are modeled simultaneously in a flexible way. This framework can also be easily adapted to allow for the presence of underreporting in the final observed count. To illustrate our approach and to compare it with existing frameworks, we present a case study of reported dengue fever cases in Rio de Janeiro. Based on both within‐sample and out‐of‐sample posterior predictive model checking and arguments of interpretability, adaptability, and computational efficiency, we discuss the relative merits of different approaches.