I am trying to figure out how time to one event affects time to a subsequent event. For example, how time to treatment affects survival time. In my data, I am focusing on oncology and the time to treatment is measured from the time of diagnosis. I understand that a host of other factors (severity of the disease, comorbidities, age and demographics) will affect both treatment and outcome. I have data on most of those factors. I would like to model how those factors affect time to treatment first and survival time next along with the time to treatment. For other types of analyses, such as choice of treatment and 90-day mortality (where both models are logistic regressions), I have used an instrumental variable method, but I am not sure that will work here.
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