cox regression time-varying effects (variable exposure as a continous variable) Is it possible to do Cox survival analysis with time-dependent covariates, but include the exposure variable as a continuous variable?
I have an exposure measured at two different times, and my outcome is death, so I wanted to run a Cox analysis with a time-dependent variable, but for this type of analysis I have only seen exposure variables that are dichotomous (binary) variables.
 A: This might be possible, but it requires extreme care in setting up and interpreting the model.
A Cox model is based on comparisons between the case having an event at a given time and all of the cases still at risk at that time. It only evaluates predictor values known to be in place at each event time.
Say that you know the exposure for an individual at time = 0 is A and at some later time $T$ you find that it is now B. The model will assume that the value for that individual is A for all times before $T$, and is B for all times after $T$. If this is an observational study about exposure, that has big risks of mis-identifying the actual exposure.
Even if you are setting the exposure values experimentally instead of just observing them, the model won't necessarily incorporate information about the prior exposure unless you construct a corresponding predictor variable. You would have to apply your understanding of the subject matter to decide whether and how to account for prior exposure values.
