Robust estimation for panel count data with informative observation times

Panel count data usually occur in longitudinal follow-up studies that concern occurrence rates of certain recurrent events and their analysis involves two processes. One is the underlying recurrent event process of interest and the other is the observation process that controls observation times. In some situations, the two processes may be correlated and, for this, several estimation procedures have recently been developed (He et al.; 2009; Huang et al.; 2006; Sun et al.; 2007b; Zhao and Tong, 2011). These methods, however, rely on some restrictive models or assumptions such as the Poisson assumption. In this work, a more general and robust estimation approach is proposed for regression analysis of panel count data with related observation times. The asymptotic properties of the resulting estimates are established and the numerical studies conducted indicate that the approach works well for practical situations.