# 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?

## 1 Answer

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