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it took me a while to see how it was right-censored. But once I considered that the goal is to measure *durations*, it became more clear.

Yea, like consider someone in that acquired group. You know that their *duration* is atleast 495 days,(now - jan 2018), and certainly more. Thus we have a lower bound on their duration -> right censoring

thanks so much

Hi everyone, just wondering if anyone can answer this SO question here: https://stackoverflow.com/questions/56126057/predicting-survival-probability-at-current-time

@CamDavidsonPilon I was wondering, in general, what is the effect of censorship on estimation? *durations* and *observed* are basically passed to any *fit* method, but it's not clear from the provided equations how they are used? Even for the simplest KM estimator, where *n* is the number of subjects at risk and *d* is the number of death events (assuming observed death?), so what about censored observations? Thanks!

Hi @bkos, good question. Generally, censorship makes estimation harder, as we loose information. It might be not obvious from the KM equations, but it affects the denominator $n_i$ - the number of subjects at risk. A censored individual may not be present in this count.

For parametric models, check out section 2 of this article: https://cran.r-project.org/web/packages/flexsurv/vignettes/flexsurv.pdf

I am trying to recreate fitting the WeibullAFTFitter in pytorch by writing my own loss function. I am trying to follow the tutorial here in pymc3 but I think that is rather different to the weibull AFT model mentioned in lifelines. Is there some tutorial that I can look to try and implement the lifelines model myself?

If I do manage to use a loss function, it opens up the possibility to use deep learning models instead of linear models, which would be an advantage.

If it helps when I assumed that

`time = beta * x + e`

where e was gumbel distributed, I ended up with this loss function:```
def gumbel_sa_loss(y_pred, targ):
failed = targ[...,:1]
e = y_pred - targ[...,1:]
exp_e = torch.exp(e)
failed_loss = failed * (exp_e - e)
censored_loss = - (1 - failed) * torch.log(1 - torch.exp(-exp_e))
log_lik = failed_loss + censored_loss
return log_lik.mean()
```

Im fairly sure though that weibullAFT models are attempting to do something else to model the time to begin with.

You'll need to implement the likelihood in pytorch, and I think a good summary of parametric survival likelihoods is in section 2 of this article: https://cran.r-project.org/web/packages/flexsurv/vignettes/flexsurv.pdf

For AFT models, note that it's `log(time) = beta * x + e`

(the log is important)

:wave: minor lifelines release, v0.21.2 is available. Changelog: https://github.com/CamDavidsonPilon/lifelines/releases/tag/v0.21.2

Can someone take a look at my question here: https://stackoverflow.com/questions/56214952/upper-limit-on-duration-for-survival-analysis. Sorry for asking so many questions.

@sachinruk, are you able to share the final dataset with me, privately? I'm at cam.davidson.pilon@gmail.com. Datasets that cause problems are a good motivation for internal improvements

Hello All,

I would like to ask for some help getting started to lifelines, there was simple tasks I could not found an direct way of doing, I am particularly interested on Cox models.

1) I was not able to find a way to retrieve the hazards at time t and the survival at time t, for a Cox PH model, I only get the information about the baselines and the coefficients (which are for some reason called "hazards_"). Of course I could generate the hazards and the survival, with this information but it would be nice to do it directly. If it is not my fault of not being able to find this direct way, I would gladly contribute to lifelines.

2) How does one generate the adjusted (considering the covariates) survival curves for PH Cox model, for the data used to fit the model, before I do any prediction, apparently now there is only support for plotting the baseline survival function.

```
from math import exp
def hazard( phdata, coef, baseline, i, t ):
cov = phdata.iloc[i].drop(labels=['censored?, 'eventdate'])
base = baseline.at[float(t),'baseline hazard']
haz= base*exp(cov.dot(coef))
return haz
```

this is what I meant by the hazard at t, for instance. I could not find where it was implemented, is this equivalent to the `predict_partial_hazard(X)`

?Thanks

You can view how to terms "parital", "log-partial", etc. relate using this formula: https://lifelines.readthedocs.io/en/latest/Survival%20Regression.html#cox-s-proportional-hazard-model

It looks like you want the hazard per subject over time (not the cumulative hazard). The most appropriate way is to do something like `cph.predict_cumulative_hazard(phdata).diff()`

as the cumulative hazard and the hazard are related in that manner. Using `predict_cumulative_hazard`

is helpful since it takes care of any strata arguments, and de-meaning necessary.

You mentioned to me privately about why I subtract the mean of the covariates in the prediction methods. The reason is that the algorithm is computed using demeaned data, and hence the baseline hazard "accounts" for the demeaned data and grows or shrinks appropriately (I can't think of a better way to say this without a whiteboard/latex). From the POV of the *hazard* then, the values are the same. However, the log-partial hazard and the partial hazard will be different. This is okay, as there is no interpretation of the (log-)partial hazard *without* the baseline hazard (another way to think about this: it's unit-less). The only use of the (log-)partial hazard is determining rankings. That is, the multiplying by the baseline hazard is necessary to recover the hazards.

All this to say: the Cox model can be confusing, and ((log-)partial) hazards are not intuitive. I am more and more of a fan of AFT models now: https://lifelines.readthedocs.io/en/latest/Survival%20Regression.html#accelerated-failure-time-models

@CamDavidsonPilon , I believe there *is* an interpretation of the "(log-)partial hazard without the baseline", namely, when you are computing the hazard ratio (the baselines are crossed out, because, essentially, you divide the hazard of one individual by the hazard of another).

How do you compute the log likelihood, to estimate the beta coefficients if not by the hazard ratio?

How do you compute the log likelihood, to estimate the beta coefficients if not by the hazard ratio?

@CamDavidsonPilon Love your work! I have encountered a problem when fitting a CoxPHfitter and trying to test the proportional hazards assumption. I make a call to check_assumptions() with show_plots=True but my program hangs and never shows the plots (or the full advice either I'm pretty sure). Do you have an idea on whats going on?

Hi all, I'm having issues with convergence for the CoxPHFitter in lifelines that I'm not seeing in R. It gives me this message

"ConvergenceError: Convergence halted due to matrix inversion problems. Suspicion is high collinearity. Please see the following tips in the lifelines documentation:

https://lifelines.readthedocs.io/en/latest/Examples.html#problems-with-convergence-in-the-cox-proportional-hazard-model

Matrix is singular."

Even when I reduce the dataset to just the time at observation, whether or not event happened, and a single covariate. Graphically I have verified that there is not a perfect decision boundary - I have also modeled this in R and it has worked perfectly. When looking at the algorithm step output, it does look like that Newton algorithm is diverging:

Iteration 1: norm_delta = 2.29694, step_size = 0.9500, ll = -27814.17290, newton_decrement = 3481.08865, seconds_since_start = 0.0

Iteration 2: norm_delta = 5.84762, step_size = 0.9500, ll = -36925.79270, newton_decrement = 37483.21855, seconds_since_start = 0.0

Iteration 3: norm_delta = 108.73423, step_size = 0.7125, ll = -40227.22948, newton_decrement = 210617.17243, seconds_since_start = 0.1

Iteration 4: norm_delta = 14575.06691, step_size = 0.2095, ll = -1076963.03641, newton_decrement = 106456100.74164, seconds_since_start = 0.1

Any thoughts on what is happening here?

Hi @CamDavidsonPilon I have a question about the Efron calculations in CoxPHFitter. Mainly I'm interested if the quantity numer is the numerator and denom the denominator of the likelihood equation used in efron ties (taken from slide 7 from http://myweb.uiowa.edu/pbreheny/7210/f18/notes/11-01.pdf)? Thanks in advance and thank you so much for lifelines!

@WillTarte, yes, that's because the bootstrapping + lowess plotting is very slow per variable, so if you have many variables, it can hang for a while. I suggest trying without show_plots and seeing if you can fix the presented problems (actually, this gives me the idea of being able to select what variables to check). CamDavidsonPilon/lifelines#730

@jennyatClover, try decreasing the step size (default 0.95) in

`fit`

. For example, `cph.fit( ..., step_size=0.30)`

(or decrease more if necessary). I would appreciate if you could share the dataset with me as well (privately, at cam.davidson.pilon@gmail.com), as datasets that fail convergence as useful to try new methods against.
@MattB27 the equation on page 7 of the pdf is not what is implemented. Recall, the MLE, I take the log, then differentiate. `numer`

and `denom`

in the code refer to the numerator and denominator in the fraction here:

which is the resulting equation after logging + differentiating the eq on page 7

Ok, I can see that now. And if I’m following the logic right then when there are no shared event times or when the event is shared with censored times than the normal MLE is used which gives the different Numer and Denom in the else statement. I’m trying to implement a Breslow tie method (I understand Efron should be preferred) but Breslow might be nice to match with other software that may still have it as default.

:wave: a minor version of lifelines was released, with some quality-of-life improvements. https://github.com/CamDavidsonPilon/lifelines/releases/tag/v0.21.3

What's the best way to save a lifelines model? (or is this not possible)? I'd like to automate the model to make predictions daily, but retrain only weekly. The model in question is a lognormal AFT.

I tried to use joblib, but it threw a PicklingError: `PicklingError: Can't pickle <function unary_to_nary.<locals>.nary_operator.<locals>.nary_f at 0x1a378e9f28>: it's not found as autograd.wrap_util.unary_to_nary.<locals>.nary_operator.<locals>.nary_f`

For 1., hm, so strange. I am surprised that even reducing it to a single covariate still makes it fail. Is there a constant column in the dataframe?

If you have an individual, who has the 'death' event, but then becomes alive again, and then has a 'death' event again. How do you treat this? should you use a time based model, and record the death event something like this [t0 - t1, death] [t2 - t3, death], or do you not record the death event but still you a time based model, recording a gap in between the 'observations' [t0 - t1, t2-t3, death]

OR could you use a standard(non-temportal) model and treat them as separate individuals? What would the mathematical ramifications be to use a standard model like this?

@veggiet_gitlab this is called recurrent event analysis, and is a harder problem than survival analysis (obviously). You can still use some survival analysis tools though, but with some caution. One approach is to use coxph model with the "cluster" argument: https://lifelines.readthedocs.io/en/latest/Examples.html#correlations-between-subjects-in-a-cox-model

I'd like to introduce some interaction terms between ordinal variables into the lognormal AFT model, but after adding the interaction column, the algorithm now fails to converge. Is there a way to introduce interactions for categorical/ordinal variables without creating convergence issues?

@blissfulchar_twitter it sounds like the convergence issues might be due to sparse data. You could check the counts for each category to verify. If interaction terms are important, you could consider collapsing some of the ordinal categories together. For example, if you have 5 categories, you could make it 3 instead

@pzivich Thanks Paul! Looking into your sparsity suggestion I realized the DF with the interaction terms was not merging correctly with the main DF (it was dropping about 80% of the data). I fixed this issue and the model fits correctly now. Oops. Thanks for pointing me in the right direction :)