Epidemic models and statistical tools are developed to study the underlying mechanisms of the spread of an infectious disease. This development is motivated by the invasive Methicillin-resistant Staphylococcus Aureus (MRSA) infections in Children's Hospital intensive care units study, in which one of the aims is to find out whether or not hospital staff may become carriers in the transmission of infectious diseases. We propose a new approach for data arising from such a situation when there is a large number of independent small groups of correlated event times, and previous event occurrence may become part of risk factors for subsequent event occurrence. The latter makes the usual marginal models and frailty models not applicable.

A dynamic hazard function is built to model the risk of susceptible individuals contracting a disease based on a data-driven approach. The regression parameters in this model consist of two parts, one relates how the hazard varies in response to the individuals explanatory variables in a multiplicate scale and the other one is the relative risk of being exposed to failures within its own cluster. Under this set-up, the estimation of covariate effects and standard errors are carried out using a martingale approach. Related hypothesis testing on the contact effect is also developed, extensive simulation studies are conducted to access the performance of the proposed methods. Particular attention is paid to potential bias, which may be caused by discretized of failure times. The data set from Columbia University Children's Hospital is analyzed for MRSA which is caused by bacterial infection. And a summary report and conclusions are provided.