Interpretation of the Hazard Ratio in a Cox regression model with time varying covariate(s)



Let’s consider an exposure and an outcome that is repeatedly assessed at each unit of time (days) after surgery. The association between the current status of exposure is used to predict the occurrence of the event during the next unit of time. The value of the independent variable is update at each unit of time.

Is the HR in this example thus represent the “instantaneous relative risk” conferred by the exposure? (Considering that the proportionality assumption is true)

In this setting, is the HR and the Likelihood Ratio (LR) become one and the same?