Dear list members,
Recently I was handed a project to formulate a model in order to predict the
time that an individual subject might experience a certain event (say
death).
I have time to death data for a sample of subjects, some of whom have died
and some of whom have not and therefore should be right-censored in any
treatment of this data. Along with this I have other qualitative and
quantitative data for each of the subjects within the sample; I would like
to incorporate these in the model.
Due to the nature of the data the Cox PH model came to mind. The model I am
using is the classic PH model:
h(t, X) = h0(t) . exp[AX]
Where X is a vector of p explanatory variables, A a vector of p parameter
estimates and h0(t) the baseline hazard function.
The model above is modeling the hazard rate h(t, X), but I am interested in
making predictions concerning t. The baseline hazard function is the only
term in the above model dependent upon t. I could theoretically assign a
meaningful value to the hazard rate h(t, X), for a new subject, to find an
estimate of t from the baseline hazard rate. My problem arises in that what
is a meaningful value of the hazard rate for a new subject.
The hazard rate is a limit:
h(t) = lim(dt - 0) P(t <=T< t + dt | T >=t)
/ dt
I would like to relate the hazard rate to the probability of death, this way
a meaningful value for the hazard rate for each new subject could be derived
at the point when the probability of death is 0.9 (say).
If you have any suggestions or references that might be of help with this
problem then I would be very grateful, or if you think this project could be
approached in a simpler fashion then I would welcome any suggestions.
I will post a summary of all responses to the list at a later date.
Mathew Kerswill
********************************************************************
This e-mail is intended only for the addressee named above.
As this e-mail may contain confidential or privileged information,
if you are not the named addressee, you are not authorised to
retain, read, copy or disseminate this message or any part of it.
********************************************************************
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|