Hello Therry,
it´s really great to receive some feedback from a "pro". I´m not sure if
I´ve got the point right:
You suppose that the cox-model isn´t good at forecasting an expected
survival time because of the issues with the prediction of the
survival-function at the right tail and one should better use parametric
models like an exponential model? Or what do you mean by "smooth
parametric estimate"?
Anyways I just ordered your book at the library. Hopefully I´ll get some
more insights by the lecture of it.
Maybe I should point out why I even tried to do such forecasts.
Following the article "Quantifying climate-related risks and
uncertainties using Cox regression models" by Maia and Meinke I try to
deduce winter-precipitation from lagged Sea-Surface-Temperatures (SSTs).
So precipitation is my survival-time and and the SST-Observations at
different lags are my covariates.
The sample size is only 55 and I´ve got 11 covariates (Lag=0 months to
Lag=10 months) to choose from.
My first goal is to identify the optimal time-lag(s) between
SST-Anomaly-Observation and Precipitation-Observation.
Expectation was that the lag should be some months.
I thought a cox-model would easily provide such a selection. At first I
used the covariates individually. Coefficients for lags between 0 and 5
months were all quite big and then decreasing from 6 to 10 months. So I
think 5 months could be the lag of the process and high persistence of
the SST accounts for the big coefficients for 0-4 months.
As the next step I used all 11 covariates at once. I hoped to gain
similar results. Instead the sign of the coefficients "randomly" jumps
from plus to minus and the magnitude as well is randomly distributed.
I also tried to using sets of three covariates e.g. with lag 4,5,6. But
even then the sign of the coefficients is varying.
So my thought was that maybe I overfitted the model. But in fact I did
not find any literature if that´s even possible. As far as my limited
knowledge goes, overfitted models should reproduce the training-period
very good but other periods very poor. So I first tried to reproduce the
training-period. But so far with no success - as well with using 11
covariates or just 1.
Regards
Bernhard R.
Terry Therneau wrote:
You are mostly correct.
Because of the censoring issue, there is no good estimate of the mean survival
time. The survival curve either does not go to zero, or gets very noisy near
the right hand tail (large standard error); a smooth parametric estimate is what
is really needed to deal with this.
For this reason the mean survival, though computed (but see the
survfit.print.mean option, help(print.survfit)) is not highly regarded. It is
not an option in predict.coxph.
Terry T.
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Hi,
if I got it right then the survival-time we expect for a subject is the
integral over the specific survival-function of the subject from 0 to t_max.
If I have a trained cox-model and want to make a prediction of the
survival-time for a new subject I could use
survfit(coxmodel, newdata=newSubject) to estimate a new
survival-function which I have to integrate thereafter.
Actually I thought predict(coxmodel, newSubject) would do this for me,
but I?m confused which type I have to declare. If I understand the
little pieces of documentation right then none of the available types is
exactly the predicted survival-time.
I think I have to use the mean survival-time of the baseline-function
times exp(the result of type linear predictor).
Am I right?
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