Timeline for Can Survival Models model the time at which a random variable will first pass a certain point?
Current License: CC BY-SA 4.0
23 events
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| Feb 21 at 21:10 | comment | added | Sextus Empiricus | I believe that I still can improve the example by using a case where the proportional hazards are actually not constant in time. | |
| Feb 21 at 21:06 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Feb 21 at 21:03 | comment | added | Uk rain troll | Is it possible to include First Passage Time Regression in your answer? I really like seeing basic examples which show the advantages/disadvantages of a specific modelling approach. E.g. simulate correlated data, fit a model with no correlation structure (1st model) vs a model with correlation structure (2nd model) and show the 2nd model performs better in terms of closer estimates, smaller confidence intervals, etc Is it possible to create a simulation which shows a situation where First Passage Time Regression models are clearly more suitable compared to classic CoxPH? | |
| Feb 21 at 21:03 | comment | added | Uk rain troll | I hate to bother you so much with my questions ... I still can't seem to figure out what kinds of modelling problems are first passage regression models trying to solve. I had left a comment above: | |
| Feb 21 at 20:58 | comment | added | Uk rain troll | thank you for your kind words! I wonder what makes the red curve (corresponding to the cox-ph) quickly catch up and seemingly merge with the black line? is that to be expected for the tail end behavior of the (empirical) cumulative distribution? | |
| Feb 21 at 20:52 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Feb 21 at 20:45 | comment | added | Sextus Empiricus | @firstpassage I have corrected the answer. Your unpacking was well done. A critical point is the part "Statistical theory tells us that p-values have a uniform distribution". That is only true when the null hypothesis is true, but the data were generated with an effect being present and a deviation from the uniform distribution is expected (and also desired). What we want to see is that small p-values have a large probability of occuring. The exponential model does this better than the Cox model (before the edit this was different, but I used a gamma model instead of an exponential model). | |
| Feb 21 at 20:44 | history | undeleted | Sextus Empiricus | ||
| Feb 21 at 20:43 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Feb 21 at 18:33 | history | deleted | Sextus Empiricus | via Vote | |
| Feb 21 at 18:33 | comment | added | Sextus Empiricus | @firstpassage Your comments made me rethink the graph, and I realize that I have switched the horizontal and vertical labels of the graph. I will have to re-investigate this simulation. Possibly the interpretation is completely reversed. | |
| Feb 21 at 18:28 | comment | added | Uk rain troll | @ Ggjj11 : thank you! what do you mean by pack all this into the answer? | |
| Feb 21 at 18:14 | comment | added | Ggjj11 | Huhh I think it would be great to pack all this into the answer. | |
| Feb 21 at 18:10 | comment | added | Uk rain troll | we can see that the p values for the coxph model (black line) are not "hugging" the dotted diagonal line corresponding to theoretical uniform CDF ..... whereas the GLM model is doing this much better. Thus, from the simulation, we conclude that the Cox PH model has less statistical power compared to the GLM. Is my interpretation of your simulation correct? | |
| Feb 21 at 18:08 | comment | added | Uk rain troll | (statproofbook.github.io/P/pval-h0.html , stats.stackexchange.com/questions/10613/…) | |
| Feb 21 at 18:08 | comment | added | Uk rain troll | Wow, this is a great simulation! I will try to unpack whats going on First you simulate a random covariate and survival times - but the survival times are a function of the covariate (i.e. dependent). Next you fit a CoxPH and a GLM model to this data and record the p-value whether the regression coefficient is zero or non-zero: since you deliberately made the times depend on the covariate, ideally it should be non-zero. you repeat this simulation many times and plot the results. Statistical theory tells us that p-values have a uniform distribution, and the uniform CDF is a diagonal line. | |
| Feb 21 at 17:47 | comment | added | Sextus Empiricus | @firstpassage I just added a demonstration for a simple exponential waiting time model. I guess that it will be much the same for more complicated models, and it is just more mathematics to compute everything. The advantage of cox is that it doesn't require the total hazard in time to follow a specific model, and you only look at relative hazard. This allows an application to models where the total hazard (as function of time) might follow complicated patterns. | |
| Feb 21 at 17:42 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Feb 21 at 17:40 | comment | added | Uk rain troll | If you have time, could you please add some mathematical equations to your answer and mathematically show how First Passage Models answer different questions compared to the 3 classic survival models and what are there advantages? I tried to perform a similar mathematical analysis over here stats.stackexchange.com/questions/639491/… .... but I think I was unsuccessful in this regard | |
| Feb 21 at 17:38 | comment | added | Uk rain troll | What I am confused about is how do First Passage Regression Models offer any advantages over these 3 classic survival models? Fundamentally, do First Passage Regression models answer the exact same questions as an AFT model? | |
| Feb 21 at 17:37 | comment | added | Uk rain troll | thanks sextus ... I am scratching my head trying to understand all of this. I think I understand the 3 standard survival models well enough: Kaplan-Meier (Non Parametric), AFT (Parametric) and CoxPH (Semi-Parametric). I understand that AFT assumes a survival time distribution but that comes with risks ... whereas CoxPH does not require a distribution assumption, but can only model the hazard relative to an unobservable baseline hazard (partial likelihood). As a result, regression coefficients in CoxPH are hazards ratios and are relative. | |
| Feb 21 at 17:03 | history | edited | Sextus Empiricus | CC BY-SA 4.0 |
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| Feb 21 at 16:56 | history | answered | Sextus Empiricus | CC BY-SA 4.0 |