[R] Is there an equivalent to predict(..., type="linear") of a Proportional hazard model for a Cox model instead?

[Terry Therneau]

1. survreg() does NOT fit a proportional hazards model, a mistake
repeated multiple times in your post

2. The coxph function operates on the risk scale: large values of Xbeta
= large death rates = bad
   The survreg operates on the time scale: large values of xbeta =
longer liftetime = good.

3. predict(fit, type='risk') = exp(predict(fit, type='linear')) in a Cox
model returns an estimate of the relative risk for each subject.  That
is, his/her predicted death rate as compared to the others in the
sample.  It has no units of "years" or "days" or anything else.  The
predicted survival TIME for a subject is something else entirely.

  predict(fit, type='response') in a survreg model does give predicted
survvival times.  

  If you really want to understand the interrelationships of these
things more deeply I think you need some textbook time.  Read the book
by Kalbfleisch and Prentice for accelerated failure time models, or even
better Escobar and Meeker which comes from the industrial reliability
view.  For predicted survival from a Cox model see Chapter 10 of
Therneau and Grambsch.  The answers to your specific questions would be
a document rather than an email.

Terry Therneau