Question about non decrasing cumulative hazard function

[MWIESNERVOLVO]

Hey!
I have seen that for the starting values init, it is ensured that the cumulative hazard function is non-decreasing. I couldn`t figure out if this is also ensured in the likelihood optimization process.

Thanks in advance!

[chjackson]

If the cumulative hazard decreases from one observed data point to the next, then the likelihood will be zero and the parameters will be rejected during optimisation, but no further theoretical check is done for non-decreasingness over all times.

The M-spline survival model in the survextrap package (and paper) deals with this problem in a much nicer way!

[MWIESNERVOLVO]

Thanks for your response! I assume you defined the likelihood to be 0 in your code somewhere in this case (I can not find that, sorry). I compared your package with the rstpm2 package and it seems as if flexsurvreg manages to always get a non decreasing C.H compared to the rstpm2 package. I just wanted to verify how you achieve that. I think the approach with quadratic modelling very nice to obtain the starting values as this is not mentioned in the book "Flexible Parametric survival analysis by Royston and Lambert". In fact I am writing my thesis about Royston and Parmar PH models where I also derive how to compute the median numerically and confidenceintervals with the delta method. I am using the Leibnitz rule here. Does that sound right to you? I am not sure if you implemented that yet. Would you maybe to willing to have a look at a few pages.

Best
Mathis

[MWIESNERVOLVO]

[chjackson]

See

flexsurv/R/spline.R

Line 189 in 1ed1b9a

ret[ind][ret[ind]<=0] <- 0

- the PDF at a time where the log cumulative hazard is negative is defined to be zero. So if any such times appear in the data, the likelihood function for the corresponding parameters will be zero.

flexsurv doesn't use the delta method for confidence intervals, just random sampling from the multivariate normal distribution of the MLEs.

Though yes, it does use numerical root-finding to get quantiles of the survival distribution for spline modesl (and any model where the quantiles are not analytic)

[MWIESNERVOLVO]

Thanks a lot. If you don`t mind I have one more question. Is it possible to fit a parametric PWP model with varying hazard ratios for every event. I tried to fit something like: flexsurvreg(Surv(tstart,tstop,status) ~ var1strata(event)+....+varkstrata(event)). I run into problems here. Do you have any idea how to do this? My idea was to fit a PWP-GT model by just fitting k different flexsurvspline models?

Thanks in advance.

[MWIESNERVOLVO]

flexsurvreg(Surv(tstart,tstop,status) ~ var1strata(event)+....+varkstrata(event))^^

[chjackson]

The Prentice, Williams & Peterson and related models for recurrent events data? I have never done any modelling of recurrent events data or considered how flexsurv might be used for that. Are these set up using a survival model with time-dependent covariates? flexsurv doesn't properly support time-dependent covariates - see the explanation in the user guide section 3.1. The start-stop-status syntax can be used, but the appropriate likelihood won't be calculated, because it cannot tell which observations are from the same individual.

[MWIESNERVOLVO]

Yes exactly, I mean the Prentice, Williams & Peterson model. Yes, the covariates are usually time dependent since they change most of the time after each event. It is basically a cox model with a different baseline for every event and time dependent covariates. Sometimes even the hazard ratios (betas) are allowed to differ with every event. Since the flexsurv model basically models the baseline, it should be at least possible for time independent covariates by fitting model separately for every event. Or what do you think? I am only worried about the risk set as it only includes subjects that already experienced j-1 events.

[chjackson]

I am not familiar with this model, so I don't think I can advise beyond this. Have you looked for literature on fully parametric modelling of recurrent events data - I'd be surprised if nobody has done anything like that before.