Continuous-Time Proportional Hazards Regression for Ecological Monitoring Data

We consider a continuous-time proportional hazards model for the analysis of ecological monitoring data where subjects are monitored at discrete times and fixed sites across space. Since the exact time of event occurrence is not directly observed, we rely on dichotomous event indicators observed at monitoring times to make inference about the model parameters. We use autoregression on the response at neighboring sites from a previous time point to take into account spatial dependence. The interesting fact is utilized that the probability of observing an event at a monitoring time when the underlying hazards is proportional falls under the class of generalized linear models with binary responses and complementary log-log link functions. Thus, a maximum likelihood approach can be taken for inference and the computation can be carried out using standard statistical software packages. This approach has significant computational advantages over some of the existing methods that rely on Monte Carlo simulations. Simulation experiments are conducted and demonstrate that our method has sound finite-sample properties. A real dataset from an ecological study that monitored bark beetle colonization of red pines in Wisconsin is analyzed using the proposed models and inference. Supplementary materials that contain technical details are available online.