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. ----begin included message -------------- 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?
survival::predict.coxph
2 messages · Terry Therneau, Bernhard Reinhardt
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. ----begin included message -------------- 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?