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)
?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.
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
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
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
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?
times
parameter. If this were possible, I think it might allow me to add seasonality to a competing risk model that captures the cumulative hazard of the outcome-of-interest. So I guess my question is two-fold. a) Is that possible with lifelines, b) Does that make sense for modeling competing risk.
class SeasonalHazardFitter(ParametericUnivariateFitter):
"""
The idea of this class would be to fit custom seasonality to an
exponential-like hazard model.
"""
_fitted_parameter_names = ['a_q1_', 'a_q2_', 'a_q3_', 'a_q4_' 'dates']
def _cumulative_hazard(self, params, times):
# Pull out fiscal quarters and dates corresponding to times.
# Each element of the dates array corresponds an element of the
# times array.
a_q1_, a_q2_, a_q3_, a_q4_, dates = params
# Call a function that associates fiscal quarter with date
quarters = get_fiscal_quarters(dates)
# Get the hazard for each time
q_lookup = {1: a_q1_, 2: a_q2_, 3: a_q3_, 4:a_q4}
hazards = np.array([q_lookup[quarter] for quarter in quarters])
# Return the cumulative hazard
# You'd have to be more careful to actually do the
# integration properly, but you get the idea.
return np.cumsum(hazards)
dates
are not an unknown. They are known constants. It makes sense that everything that goes into params should be unknown. Not sure what I was thinking there. Putting it in a global/class/instance variable makes sense. I just want to be sure I understand how _cumulative_hazard()
is called.params
: get tweaked by the optimizationtimes
: the times passed into the fitter as "durations"return
: The cumulative hazard encountered over the duration represented by each timedate
. So the cumulative hazard for each time would be the integral of the hazard from the "start_date" to the "end_date". (where these can be derived from an element of time
and its corresponding date.) What I really care about is the cumulative incidence function (CIF) for each kind of event. If the idea of getting dates
into the _cumulative_hazard
function works, then I was hoping to use this technique to model the CIF for one of the competing event types.
Your explanation of _cumulative_hazard
is correct. But you can also see it as simply the cumulative hazard you wish to implement (i.e., not necessary to think about "durations" or "unknowns")
I was thinking about your seasonal model, and actually tried to code something up, but there is a problem I think. The _cumulative_hazard
is invoked for both the censored and uncensored data, so your code needs to handle that (and you won't know which until you see the shapes of the input data)
Clock-dependent hazards I think are actually pretty common
Agree, but I feel like the common strategy is to use a regression model or fit N univariate models (i.e. partition the data)
I think a seasonal model is a great idea, so I want this to work.