Neurological disease is often associated with changes in firing activity in specific brain areas. Accurate statistical models of neural spiking can provide insight into the mechanisms by which the disease develops and clinical symptoms manifest. Point process theory provides a powerful framework for constructing, fitting, and evaluating the quality of neural spiking models. We illustrate an application of point process modeling to the problem of characterizing abnormal oscillatory firing patterns of neurons in the subthalamic nucleus (STN) of patients with Parkinson's disease (PD). We characterize the firing properties of these neurons by constructing conditional intensity models using spline basis functions that relate the spiking of each neuron to movement variables and the neuron's past firing history, both at short and long time scales. By calculating maximum likelihood estimators for all of the parameters and their significance levels, we are able to describe the relative propensity of aberrant STN spiking in terms of factors associated with voluntary movements, with intrinsic properties of the neurons, and factors that may be related to dysregulated network dynamics.