Analyzing Panel Count Data with Informative Observation Times

In this paper, we study panel count data with informative observation times. We assume nonparametric and semiparametric proportional rate models for the underlying recurrent event process, where the form of the baseline rate function is left unspecified and a subject-specific frailty variable inflates or deflates the rate function multiplicatively. The proposed models allow the recurrent event processes and observation times to be correlated through their connections with the unobserved frailty; moreover, the distributions of both the frailty variable and observation times are considered as nuisance parameters. The baseline rate function and the regression parameters are estimated by maximizing a conditional likelihood function of observed event counts and solving estimation equations. Large sample properties of the proposed estimators are studied. Numerical studies demonstrate that the proposed estimation procedures perform well for moderate sample sizes. An application to a bladder tumor study is presented to illustrate the use of the proposed methods.

Modelling zero-inflated count data when exposure varies: with an application to tumor counts)

This paper is concerned with the analysis of zero-inflated count data when time of exposure varies. It proposes a modified zero-inflated count data model where the probability of an extra zero is derived from an underlying duration model with Weibull hazard rate. The new model is compared to the standard Poisson model with logit zero inflation in an application to the effect of treatment with thiotepa on the number of new bladder tumors.

Count data of germinated Gonyostomum semen cells and subsequent cell divisions

Colonization of new habitats through dispersal of phytoplankton cysts might be limited, if resident populations outcompete invaders during germination. We reciprocally transferred Gonyostomum semen (Raphidophyceae) cysts from three lakes into native and foreign waters originating from the respective habitats. Germination rate and germling growth were impacted by water origin, but there was no preference for native water. Gonyostomum semen's ability to germinate in different conditions might explain its expansion in northern Europe.