Modulated renewal process models with functional predictors for neural connectivities - Tan, Hongyu, author; Chapman, Phillip L., advisor; Wang, Haonan, advisor; Meyer, Mary C., committee member; Luo, J. Rockey, committee member (Colorado State University. Libraries, 2015)
Recurrent event data arise in fields such as medicine, business and social sciences. In general, there are two types of recurrent event data. One is from a relatively large number of independent processes exhibiting a relatively small number of recurrent events, and the other is from a relatively small number of processes generating a large number of events. We focus on the second type. Our motivating application is a collection of neuron spike trains from a rat brain, recorded during performance of a task. The goal is to model the intensity of events in the response spike train as a function of a set of predictor spike trains and the spike history of the response itself. We propose a multiplicative modulated renewal processes model that is similar to a Cox proportional hazards model. The model for response intensity includes four components: (1) a baseline intensity, or hazard, function that captures the common pattern of time to next event, (2) a log-linear term that quantifies the impact of the predictor spike histories through coefficient functions, (3) a similar log-linear term for the response history, (4) a log-linear regression-type term for external time dependent variables. The coefficient functions for predictor and response histories are approximated by B-spline basis functions. Model parameters are estimated by partial likelihood. Performance of the proposed methods is demonstrated through simulation. Simulations show that both the coefficient function estimates and the asymptotic standard error function estimates are accurate when the sample size is large. For small samples, simulations show that the smoothly absolute clipped deviation (SCAD) penalty outperforms LASSO penalty and unpenalized partial likelihood approach in identifying functional sparsity under various situations. The proposed methods are illustrated on a real spike train data set, in which substantial non-stationarity is identified.