Hazard function when variables(s) are not observed Say I have a hazard function that is related to some survival time(under right independent censoring) with a number of covariates. How do I find the hazard function if some of/all covariates are not observed? Is there a standard procedure for this?
 A: The Kaplan Meier curve is the non-parametric maximum likelihood estimate of the survivor function under missing data. As such the KM curve is a much better descriptive statistic for survival than an estimate of the raw "hazard", and presents much of the same information. For instance, the Y axis on a survivor plot is interpreted as a percentage of participants surviving past a certain point, whereas a hazard plot has Y axis interpreted as an "instantaneous rate of failure" which is not intuitive, even though they present related information.
If you fit a parametric survival model (Weibull, Exponential, Gamma, etc), you can produce an estimate of the hazard function from the model parameters. However, if the parametric assumption fails, there may be unexpected behavior in your estimates. For instance, bathtub shaped hazards will not reveal their bathtub shape when fitting exponential or weibull models.
Lastly, you can use an inefficient (and probably biased?) non-parametric hazard estimate using a kernal density estimate for the Schoenfeld residuals of the partial likelihood estimated with a Cox model having no model terms to get a flexible estimate of the baseline hazard function.
