An adaptive semi-parametric model for analyzing longitudinal panel count data is presented. Panel data refers here to data collected as the number of events occurring between specific follow-up times over a period of observation of a subject. The counts are assumed to arise from a mixed non-homogeneous Poisson process where frailties account for heterogeneity common to this type of data. The generating intensity of the counting process is assumed to be a smooth function modeled with penalized splines. A main feature is that the penalization used to control the amount of smoothing, usually assumed to be time homogeneous, is allowed to be time dependent so that the spline can more easily adapt to sharp changes in curvature regimes. The finite sample properties of the proposed estimating functions are investigated and comparisons made with a simpler model assuming a time homogeneous penalty.
Group for Research in Decision Analysis