Clarification on time-varying Cox formula

[CamDavidsonPilon]

@daphnezht writes:

Quick question, what does the Xi bar denote in this formula? Is that the individual average across all time? Does that influence the estimating result (coefficients)? https://lifelines.readthedocs.io/en/latest/Time%20varying%20survival%20regression.html

Also wondering does anyone know the difference (if any) between the implementation of R package coxph(Surv(tstart, tstop, event) and CoxTimeVaryingFitter in the lifeline package.

[CamDavidsonPilon]

Xi bar is the mean of the matrix X - wait - there should not be a subscript i on it! I'll fix that.

w.r.t. the differences between lifelines and survival in R: computationally they are the same (i.e. some likelihood, and will produce near-identical coefficients), however survival has more time-varying support and is more feature rich. There's no comprehensive lists of differences, however.

[daphnezht]

Got it. The use case we have (and please let me know if we are using this correctly) is we are using this package/ survival analysis framework to build multi-touch attribution model. The user could convert multiple times.
We set X as the count of marketing channel engagement the users had within the past X days as of the stop_col. We set the event_col as the number conversions they have on the stop_col date.
Therefore, we interpret the hazard function as the intensity of users' potential conversion. That's why we are interested in plotting the graph and visualize users' marketing channel engagement and 'conversion potential' over time.

[CamDavidsonPilon]

Maybe - I don't think I'm familiar enough with the domain to help. But the time-varying hazard would just be the exponential of (coefficients (ctv.params_) times the demeaned covariate matrix, X). Even simpler is to forget about the exponential part, and just focus on the log hazard, which has the same information.

[MarkPundurs]

Should there also not be a subscript on Xi bar at https://lifelines.readthedocs.io/en/latest/Survival%20Regression.html#cox-s-proportional-hazard-model ?

[CamDavidsonPilon]

yes! Thanks for pointing that out, too

[Cryptojoyz]

I have a question, why should we subtract the mean value in the Cox time varying formula?

For example, in this example, the actual mean value of var1 should be 0.3, because var1 is a variable that does not change over time, the sample with ID1 actually has only one var1 value, even though the sample with ID 1 has three var1 values. But when calculating the matrix mean this value becomes 0.2. What is the actual meaning of the matrix mean?