Guessing What Data Was Observed Based On The Model? Suppose I fit a Survival Cox-PH Regression Model in R and get the following results:
Call:
coxph(formula = Surv(time, status) ~ age + sex + ph.ecog, data = lung)

             coef exp(coef)  se(coef)      z        p
age      0.011067  1.011128  0.009267  1.194 0.232416
sex     -0.552612  0.575445  0.167739 -3.294 0.000986
ph.ecog  0.463728  1.589991  0.113577  4.083 4.45e-05

Likelihood ratio test=30.5  on 3 df, p=1.083e-06
n= 227, number of events= 164 
   (1 observation deleted due to missingness)

Based on these results, I can infer information such as:

*

*The number of observations

*The number of events

*The number of variables

*The estimate for the effect of each variable

My Question: Given this information, is it possible to simulate the covariate and response information for n = 227 such observations - such that if a similar Cox-PH model was fit to these newly simulated 227 observations, the resulting regression coefficients would approximately be equal to the original regression coefficients? Can I try to guess (and recreate)  observations might have been observed based on the regression model coefficients?
For example, I know that if I were to "fix" the covariate information for a group of n = 227 "arbitrary created" patients, I could then simulate their survival times (e.g. https://cran.r-project.org/web/packages/simsurv/index.html) - however, if I were to then fit a Cox-PH model to these observations, the model coefficients would not necessarily be close to the original model coefficients.
In general, is this possible to do? Only given the above model summary, could I try and somehow generate the original dataset that this model was trained on?
Thanks!
Note: I realize there are probably an infante number of n = 227 samples that can be randomly simulated such that a Cox-PH Model produces the same regression coefficient estimates as above.


Given this information, is it possible to simulate the covariate and response information for n = 227 such observations - such that if a similar Cox-PH model was fit to these newly simulated 227 observations, the resulting regression coefficients would approximately be equal to the original regression coefficients?

Yes. Earlier, you asked a question about how to simulate survival times.  Simply use the method described there but specify the effects of covariates to be what you see in output of your summary call.
