Cox Proportional Hazard Models and Treatment Effects

A core group of brownbag regulars gathered on July 2 to discuss research methodology. The highlight for me was Toni discussing a new idea for a paper. He talked about the benefits of cox proportional hazard models (cphm) v. logistic regression. My takeaway is that the cphm introduces a time variable to the analysis to “censor” those in the treatment group who left for various reasons. Other benefits are that the cphm produce (a) risk of an event at any given day, and (b) keeps people in the model even if they dropout of care for any reason. I couldn’t help but think about how these hazard models – presumably derived from public health – are similar to the treatment effects literature derived from the Rubin Causal Model. Some of the main concepts in treatment effects are:

  • Population and sample Average Treatment Effect (ATE): average outcome Y for treatment group compared to average outcome Y for comparison group
  • Intent To Treat (ITT): an analysis of ATE for those who finished treatment (compliers) and those who did not finish due to crossover or dropout (noncompliers)
  • Treatment on The Treated (TOT) : the ATE on subpopulation of treated units, i.e., those who were actually exposed to the treatment. And can be calculated by ITT/share of compliers

So, it seems to some extent the cphm is a form of ITT because it includes all of those offered a given treatment (child welfare services in Toni’s example). I am wondering, in what others ways might the censoring function of the cphm relate to the treatment effects literature?

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