# how to interpret the output of parametric survival regression in python?

I am trying to fit a parametric survival regression for a dataset that I have, I wanted to understand the interpretation of the output of the lifeline package for the lognormal AFT model I have built. I have dummified the features and have fit the model like below:

lnf = LogNormalAFTFitter().fit(data_train, 'durations', event_col='events')


The results are as below. I'm trying to understand 1. What are the important features, How much each feature increases or decreases the survival time, 2. How can I calculate cumulative hazard for each row in my table

I am confused as to whether the coefficients determine the survival time or hazard ratio?

Since you've chosen an AFT model, the interpretation is based on the survival. The AFT model looks like:

$$S(t | x) = S_0\left( \frac{t}{\lambda(x)} \right)$$

where $$\lambda(x) = \exp(\beta_0 + \beta_1x_1 + ...)$$. The interpretation is that $$\lambda$$ decreasing "speeds up" (accelerates) a subject "down the survival curve".

So, with that in mind, let's focus on the variable file_hour_6.0. Its exponentiated coefficient value is 0.54, so if that variable is 1.0 (vs 0.0), it will "slow" time by 0.54 units (i.e. ~double the time, since 1/0.54 is approx. 2), relative to the baseline hour. Subjects with file_hour_6.0 will "fall down the survival curve" faster.

Some other points:

• The hazard ratio isn't part of this AFT model, so there's no interpretation there.
• the important variables: well, you may beed some variable selection procedure for that, like using the l1_ratio and penalizer to create a sparse solution (see docs)
• "How can I calculate cumulative hazard for each row in my table" - I'm not sure what you mean by this.
• Hi, I had loaded the wrong table earlier, I have edited my results. My follow up question is what I thought is my baseline is file_hour_0, and the exponential value for file_hour_6 is 0.54, which implies events that have file_hour_6 as 1 will have survival time 0.46 times slower than file_hour_0, is this assumption wrong? Apr 15 '20 at 16:19
• I've updated my answer and adding more interpretation Apr 15 '20 at 17:29