fine gray models stcrreg

[laure rouch]

Hi all,

I'm interested in the impact of orthostatic hypotension on incident dementia. I had done a cox model :

Dementia / Time from baseline to dementia date
No dementia / Time from baseline to the last visit we KNEW they were dementia free

I've been told by a reviewer to do a fine gray model to take into account a potential competing risk of mortality

Should I do :

Dementia / Time from baseline to dementia date
No dementia but death / Time from baseline to death
No dementia no death / Time from baseline to the last visit of follow-up

or for the categories "no dementia but death AND no dementia no death", I should use the time from baseline to the last visit we KNEW they were dementia free like in the cox model?

Must I use the same time to event as in the cox model and just have 3 categories for the fine gray model? Or must I use the time from baseline to death for the group "no dementia no death" whereas I know that before death, they were dementia free at a specific visit.
Thanks so much for your help and advice +++
Laure

[Clyde Schechter]

Here's how I think about this. You have three possible termination events: onset (really, recognition) of dementia, death, and final observation (last visit). Your time variable should be the earliest of these in every case. Create a three-level variable, event, coded 1 for dementia, 2 for death, and 3 for last visit that characterizes which of these events the time variable refers to. Then, since you are interested in dementia, and death is a competing "nuisance" variable, when you -stset- your data define a failure as event = 1. In your -stcrreg- command specify the -compete()- option as event = 2.

[laure rouch]

Hi Clyde,

Thank you very much for your response. This is also what I was thinking but the thing is that they had very regular examinations so before they die for example they had several cognitive exams and there is a "last" date of visit I know they were dementia free so I was wondering if it was really making sense to do a fine gray model. It's not like if I knew nothing about their cognitive status until they die. For the cox model I considered for those who did not develop dementia (even if they die after or are lost to follow up), for the time I had considered the time until the last visit I knew they were dementia free. What would you think about that?

I also wanted to ask you because my problem is that I'm studying the impact of orthostatic hypotension (a fall in BP from a lying to a standing position) which is supposed to have a negative impact on incident dementia. I used several thresholds. Normally, the more severe the orthostatic hypotension is, the higher risk of dementia you should have. And it's not the case in my study. I've been told that it's maybe due to a competing risk of mortality (those with the more severe orthostatic hypotension die more).

If my cox models, if I consider a higher level of orthostatic hypotension, the HR for dementia risk is not higher (although still significant). If I do a FG model and I see that if I consider a higher level of orthostatic hypotension, the HR are even lower and not significant, what does it mean exactly? That there was a competing risk of mortality or not?
I mean : I thought that doing a FG model instead of a Cox model would help me to find higher HR for those with more severe orthostatic hypotension (which is theoretically expected) and would "solve" the problem of finding a non dose response relationship (which might be due to a competing risk of mortality). But if it's even worse with a FG model, which conclusion should I do?

Thanks for your help so much Clyde.

[Clyde Schechter]

The Fine-Gray model is used when the failure event of interest (onset of dementia) is in competition with some other cause of failure (death) and the risks for the two are associated: those who are at higher risk of becoming demented are also at higher risk of dying. Those conditions are met here. So I think that a Fine-Gray model is more appropriate than a simple Cox model. I was perhaps less than 100% clear in #2, although nothing I said there was incorrect. The "last visit" that I'm referring to is a final visit in a patient for whom there was never a dementia diagnosis: if the patient had dementia diagnosed, that would, by definition, precede (or be) this last visit, and in that case the date of diagnosis becomes the time variable and event = 1.

If your F-G and Cox models are not showing the association you expected, you have several possibilities to consider. Perhaps your expectations are simply incorrect and the association between orthostatic hypotention and dementia incidence is weaker than you believed, or even perhaps non-existent. But there are other possibilities. How large is your sample? What is the confidence interval around your subhazard ratio? Is it wide or narrow? If narrow, then your estimates are fairly precise and you can rely on them more firmly than if the CIs are wide. And what about data quality? I would imagine that dementia diagnosis dates are very noisy data: it is known that cognitive decline is associated with increased variation in cognitive function, which means that a person who is becoming demented will have more days of better than usual functioning and also more days of worse than usual. So it becomes more of a "crap shoot" how they look when you examine them on a particular date. Also, the onset of dementia (for most causes, at least) is gradual, and diagnosing it by applying some cutoff score to a cognitive function assessment introduces yet more noise into the picture. Moreover, the precision of your time variable as limited to, at best, the interval between assessments--and that limit would be achieved only if you had perfect measurement accuracy. So I would expect that getting a good handle on risk factors for dementia would require extraordinary care in dementia ascertainment, with finely-tuned assessments at very frequent intervals. And even then, you probably need a huge sample to average out the remaining measurement noise.

Are the results of the Cox and F-G models really different? If one is "statistically significant" and the other is not, that does not mean they are meaningfully different from each other. Statistical significance is a rather uninformative concept that is a mashup of noise in the data, model misspecification, actual effect size, and sample size. Moreover, it is, itself, an arbitrary and more or less meaningless cutoff imposed by applying a magic number, 0.05, to a continuous random variable (the p-value) in a vain attempt to make the uncertain appear cut-and-dried. It is also very sensitive to small changes in the data. So look at the hazard ratios from both models along with their confidence intervals. Is the magnitude of the difference (actually ratio) of hazard ratios (Cox vs F-G) meaningfully different? If you know that one were correct and the other not, would you do anything differently depending on which one it was? Secondarily, do the confidence intervals overlap? Is either of the hazard ratios inside the confidence interval of the other? These are better ways of deciding whether you are getting different results from the two models than mulling over "statistical significance."

Finally, in the category of unsolicited advice in an area where my expertise is limited (but not non-existent), part of the problem you face is the great difficulty of looking at dementia as a dichotomous outcome when it is, in fact, difficult to ascertain with precision. I would even venture my personal opinion that the whole idea of dementia is a category error: that it is a term that is applied, with little precision, to people with severely decreased cognitive functioning--cognitive functioning being difficult to quantify precisely in the first place, and the cutoff point between "dementia" and "non-dementia" being either vague or, if made precise, arbitrary. I venture the opinion that it may be more fruitful to analyze the time-trajectories of the cognitive function measures themselves for associations with risk factors of greater or faster decline. Added: Interestingly, this is better understood in non-medical applications of statistics. In political science analyses, they do not model wins and losses of elections: they model the fraction of vote received, or the margin of victory (loss). This is true even though the 50% cutoff is, in this context, not entirely arbitrary! Similarly, sports statisticians generally do not model wins and losses--they model point spreads. Others have caught on to the perils of dichotomizing continuous variables--it is long past time for medicine and epidemiology to catch up.

[laure rouch]

Thank you Clyde so much for your valuable help and extremely relevant comments, as always. I will look at the differential results between the 2 models in more detail taking into account your comments. However, I just wanted to clarify a detail. I’m a bit confused with your sentence that I want to be sure to understand properly: “When you say “The "last visit" that I'm referring to is a final visit in a patient for whom there was never a dementia diagnosis: if the patient had dementia diagnosed, that would, by definition, precede (or be) this last visit, and in that case the date of diagnosis becomes the time variable and event = 1”
This is basically my problem because between the visit the patient “die” or “is lost to follow-up” is not the last visit I know about their dementia status. Sometimes they die or are lost to follow-up 5 years for example after the last visit they had a dementia assessment and I’m sure they are not demented. In those cases, should I consider for the last visit the visit they are reported to be dead or lost to follow-up or the last visit I’m sure they are not demented. Just to clarify this point with you. Thank so much in advance for your help. Again.
Best,
Laure

[Clyde Schechter]

Oh, thanks for clarifying this. It must be the last time at which you know them to be still alive and not demented.

[laure rouch]

Thank you very much Clyde for your answer. May I ask you a little question again?

In my study, with my cox models I found a negative impact of orthostatic hypotension (threshold 10/5 mmHg) on incident dementia but not with a threshold of 15/7 mmHg. Normally the more orthostatic hypotension is severe the more they should develop dementia. It's a bit surprising.
I decided to do FG models to test if a competing risk of mortality could explain those findings. FG models report essentially the same results. So my conclusion was that the potential competing risk of mortality could not explain the fact that I don't find a dose response relationship with different cut offs to define orthostatic hypotension.

However, I thought to consider death and dementia as joint outcomes as a sensitivity analyses. And to consider patients who died as having all developed dementia. And it that case, I find a significant negative effect of orthostatic hypotension with a threshold 15/7 mmHg.

To me, those 2 results (FG and this sensitivity analyses) are not really in accordance. Because with the sensitivity analyses (joint outcome), I was about saying there is a competing risk of mortality. This is the reason why we don't see the negative impact of orthostatic hypotension with this threshold because they die more...

What do you think about that?

It's not a STATA question so I can totally understand that you don't have the time answer my question!

Best,
Laure

[Clyde Schechter]

Well, you don't show the outputs of your analyses, which makes it a bit hard to comment.

Bear in mind that your combined outcome of death or dementia is going to be more frequent than either death or dementia alone. So any analysis based on it is going to have more power and precision. In the competing risk model, you have only the amount of power and precision afforded you by the less frequent of the two outcomes.

In addition, you may be being blindsided here by relying on statistical significance as a way of interpreting your results. In the Cox model of dementia using the 15/7 threshold was the hazard ratio really different from the one you got using 10/5 as the threshold? They may well have been the same, or nearly so, but one was "statistically" significant and the other "not" because there will be fewer people who qualify for the 15/7 threshold, so you lose power and precision again. One of the lessons I always emphasize with my students is that you have to first judge these things by looking at the regression coefficients, or odds ratios, or hazard ratios, etc., themselves, and only look at the p-values later if you have nothing better to do. And never decide anything based just on statistical significance. Statistical significance is full of traps.

Finally, just as I noted earlier that looking at trajectories of cognitive score decline would probably be better than looking at incidence of a dichotomized dementia variable, I am quite sure that treating the orthostatic fall in BP as a continuous variable would be more effective than looking at various thresholds. I should also add that from a statistical perspective, the more extreme the threshold (distance from the population mean) the less reliable the corresponding dichtomous variable becomes.

[laure rouch]

Thank you very much Clyde. You're right. I think I will also try to look at cognitive trajectories over time in addition to dementia which is of course important from a clinical point of view. But I agree with you. I also considered orthostatic fall as a continuous variable. I have interesting results. Clinicians are often interested in clinical definitions of orthostatic hypotension but I totally agree with you. And I will remember your advice. Not focus too much on the arbitrary cut off of 0.05...I understand what you mean. Thank you again for your valuable comments and for taking the time to answer me.
Best,
Laure