# How to interpret CoxPH survival regression

I have a time to event data. Where 20% of the events are observed, so, 80% of the events are censored. Using this data I developed a CoxPH model using python lifelines. For this data I got model summary like below

Iteration 1: norm_delta = 0.71969, step_size = 0.95000, ll = -11597.41595, newton_decrement = 487.49971, seconds_since_start = 0.2
Iteration 2: norm_delta = 0.41603, step_size = 0.95000, ll = -11042.74025, newton_decrement = 74.48468, seconds_since_start = 0.5
Iteration 3: norm_delta = 0.19189, step_size = 0.95000, ll = -10958.25644, newton_decrement = 8.61687, seconds_since_start = 0.8
Iteration 4: norm_delta = 0.03981, step_size = 0.95000, ll = -10949.05062, newton_decrement = 0.28285, seconds_since_start = 1.0
Iteration 5: norm_delta = 0.00311, step_size = 0.95000, ll = -10948.76412, newton_decrement = 0.00164, seconds_since_start = 1.2
Iteration 6: norm_delta = 0.00016, step_size = 0.95000, ll = -10948.76249, newton_decrement = 0.00000, seconds_since_start = 1.5
Convergence completed after 6 iterations.
<lifelines.CoxPHFitter: fitted with 7350 observations, 5998 censored>
duration col = T
event col = label
number of subjects = 7350
number of events = 1352
log-likelihood = -10948.762
time fit was run = 2018-12-17 10:48:35 UTC

---
coef  exp(coef)  se(coef)        z      p  lower 0.95  upper 0.95
AGE   -0.0001     0.9999    0.0000 -10.6696 0.0000     -0.0001     -0.0001  ***
GRADE -1.0068     0.3654    0.0450 -22.3973 0.0000     -1.0949     -0.9187  ***
---
Signif. codes: 0 '***' 0.0001 '**' 0.001 '*' 0.01 '.' 0.05 ' ' 1

Concordance = 0.797
Likelihood ratio test = 1297.307 on 2 df, p=0.00000


My objective is using this model I want to predict When the event/action is going to happen for a new sample?

I used this method predict_expectation()

As this docs described,

Compute the expected lifetime, E[T], using covarites X.

using the above method I'm getting larger lifetime than expected, for most of the cases. For Example, instead of ~180 days it gives ~1200.

I don't understand Why I'm getting this huge values, even though my concordance value is quite descent.

Am I going into the right direction? Can I predict When the event/action is going to happen for a new sample using coxPH?

• Have you tried centering your age values? It happened to me in stata once, but not sure in R. Just throwing it out there! Dec 17, 2018 at 13:00
• @HuyPham- thanks for the comment, I'm new to survival analysis, can you tell me what is centring age value??? Can you provide detail or link related to this? Dec 17, 2018 at 13:18
• sorry i just mean mean centering it, so subtracting the average value of the age variable and using that to fit your model and prediction (that probably isn't the problem but who knows) Dec 17, 2018 at 13:23
• @HuyPham - I have a age variable ranging from 1 to 10000. Do you want me to do instead of X put as X-XBar ? Dec 17, 2018 at 13:27
• yeah give it a shot, can't hurt. Dec 17, 2018 at 13:28