[Jonas Kristensen]

Okay Thank you. So firstly, i have read something more in regards to stratified cox-regression and your answer in #50:
"In stratified cox regression there are seperate reference-rates for each category of the factor that defines strata. The seperate reference-rates does not have to be proportionate. Stratification is therefore an alternative correction method that can be used for correction of categorical variables, and a method that does not prerequisite proportionality"
To me this sounds like the approach that would suit this problem of non-proportinate hazards. Can you help me understand why this is not the way to go?

by convergence you mean; "similarity of hazards/rates" or "proportionality"? I am probably misunderstanding, but isn't the puporse of doing time varying cox, to not have to "worry" about convergence/proportionality?

And for my own understanding, could you say that using the below commands, would be like making an adjusted analysis of
first, the association between stroke severity and fractures, adjusted for civil status sex age ami diabetes and alcohol intake,
and then second, civil status and fractures, adjusted for stroke severity sex age ami diabetes and alcohol intake WITHOUT having to consider the effect (modification) of time?
So the hazard ratios that i get from that output are in fact the final results?

stcox stroke_severity civil_status sex age ami diabetes alcohol_intake , tvc(i.stroke_severity) texp(_t)
stcox civil_status stroke_severity sex age ami diabetes alcohol_intake , tvc(i.civil_status) texp(_t)

Lastly, because of this issue, i am thinking of adjusting for less variables to make it less complicated. Maybe only sex age and diabetes, which are the most heavily related factors to fractures in the elderly population.

[Clyde Schechter]

You have too many commas in there. Only the comma before the -tvc()- option should be there. And no "and" either.

In any modeling situation, more variables makes the likelihood more complicated and increases the chance of non-convergence. Nevertheless, I would go with the model that makes sense from an epidemiologic point of view. If you can't get it to converge, you can start over from simple and try to build up to it as closely as possible later. But you don't have that much to lose by trying the full model first.

[Jonas Kristensen]

Yes, the hazards are sadly not proportionate either when using stratified cox.

How would the cox with time varying covariates command look for the analysis of stroke severity and civil status, adjusted for sex, age, ami, diabetes and alcohol intake,

stcox stroke_severity civil_status sex age ami, diabetes and alcohol_intake , tvc(i.stroke_severity) texp(_t)
stcox stroke_severity civil_status sex age ami, diabetes and alcohol_intake , tvc(i.stroke_severity) texp(ln(_t))

Would it be something like the above, specifically for stroke severity?
And would it be unwise to adjust for so many variables when doing using time varying covariates?

[Clyde Schechter]

Those commands are correct syntax for stratified Cox models. Whether stratifying the Cox models will solve your PH problem remains to be seen--that is not what it is typically used for, though it sometimes has that effect. The more direct approach to resolving the PH problem is to use time-varying covariates. That is, however, a more complicated undertaking.

[Jonas Kristensen]

Okay. I am also thinking that i will have to explore other options than the cox proportional hazards model. I have tried removing offending vaiables, but the PH-assumption isn't even met for the univariate analysis of the associations for both stroke severity and civil status.

I am either thinking of using a cox model with time varying parameters, splitting the 15 year follow up into 3-5 year intervals or using stratified cox, but i am not sure which one is the most rational choice.

If i then theoretically, after having concluded that the PH-assumption wasn't met, decide to use for example the stratified cox model. Would the command then just look like the following (if i am still interested in the risk factors; stroke severity and civil status, adjusted for sex, age, AMI, diabetes and alcohol intake)

stcox i.stroke_severity , strata(civil_status sex age ami diabetes alcohol)
stcox i.civil_status , strata(stroke_severity sex age ami diabetes alcohol)

[Clyde Schechter]

With the caveat that I am always reluctant, at best, to decide on model structure based on any kind of significance test, the null hypothesis of the test carried out by -estat phtest- is that the hazards are proportional, so a low p-value is more consistent with the hazards not being proportional.

There are several alternative approaches that can be used when the PH assumption is violated.

1. Consider other models that don't rely on PH. Some of the parametric survival regressions, for example. Of course, they involve additional assumptions of their own.

2. Use time varying covariates in your Cox model.

3. Omit the offending variable(s) from your modeling.

[Jonas Kristensen]

Thank you for your advice. Hmm i am a bit unsure of what to do when the PH-assumption does not seem to be met?
In regards to the PH-assumption test, does the test being significant (p=0,0000) indicate that there is not proportionality then?

[Clyde Schechter]

First, I am looking at the plots in the left panel of each graph. These are the ones that should appear parallel.

For indtotal_grp, it appears to me that the curve for the mild group intersects the other curves--it is not parallel to the others. The others appear to be parallel overall. It's a bit hard to say because the others are also fairly close to each other, so it is difficult to discern the difference between non-parallelism and noise simply resulting in intersections and divergences in what are really almost the same curve. Similarly the curve for civil = other looks to me like it is not parallel to the others, and again some of the remaining curves are very close to each other so it is difficult to discern.

If, in the end, you are going to report a survival model that is adjusted for covariates, it is best to examine the proportional hazards assumption with the same adjustments.

[Jonas Kristensen]

I am happy to see you write that, because that is also what i ended up doing. I used log-log plots as well as a PH-assumption test. From the below plots and PH-test, i have concluded that there is proportionality. Would you agree with this?
And if i am adjusting for age, AMI, diabetes and alcohol intake, is it crucial that these are adjusted for when i check for propotionality in log-log plots and should i confirm proportionality for both unadjusted and adjusted plots then?

Tabel ?. PH-assumption test

Estat phtest	Chi2	Prob> Chi2
Stroke severity	211,14	0,0000
Civil status	104,61	0,0000

[Clyde Schechter]

If you want to use significance tests to do this, then your code would be the way to do that.

Personally, I don't like using significance tests for this (or for much else). My preference is to look at plots of log-log survival, which you can get with the -stphplot- command and then make judgments about whether the curves look reasonably parallel.

[Jonas Kristensen]

Okay, thank you.
So would it be sufficient to do the following to estimate proportionality:

stcox i.stroke_severity
estat phtest

stcox i.civil
estat phtest

And if the p-value is above 0,05 in the PH-test, then conclude that there are proportionality (including assessing kaplan meier)?

[Clyde Schechter]

For the purposes of examining the proportional hazards assumption, an ordinal variable should be thought of as a categorical variable--its ordinal properties are not relevant here.

[Jonas Kristensen]

Hello again
Thank you for your last reply and support Mr. Schechter. A new question has arisen in regards to checking the proportional hazards assumption when having ordinal variables (Stroke severity=mild/moderate/severe/very severe/unknown) and (civil status= living with someone/living alone/Other/unknown)

This is usually this is done by assessing proportionality from a kaplan meier plot, by using the command "estat" and i have also seen i done by using "stcox … tvc(var) texp(_t-50)". But all of the examples i have ever seen, are with dichotomous variables and not with ordinal variables.

I have attached grafs of the smooth hazard etimates for stroke severity and civil status (with and without 95%CI)
Should the others categories be proportional to the reference-category? The reference group is very severe (blue line) for stroke severity and living with someone (blue line) for civil status.

All the best, Jonas

[Clyde Schechter]

Well, my bias is to almost always do more analyses and present them all.

Unfortunately, journals face costs associated with increasing the length of articles, so they impose limits on length. This inevitably leads authors to leave out important information, because the length limits are usually unreasonably severe and leave inadequate room for good scientific presentation. The good news is that most journals now allow authors to write a supplement to their paper which they will then host on their website. So you can present what you think are the most important analyses in the paper itself, and then refer the reader to additional anayses in the supplement. For my part, I take advantage of this, and in my recent publications my supplements are typically substantially longer than the articles themselves, but provided a much fuller picture of what was done and what the results imply.

[Jonas Kristensen]

Thank you for the advice!
In the litterature, the scientists in general do not describe how they handle (censure or exclusion) patients who aquire a second stroke in the follow-up period, even though they only investigate patients with first ever stroke, so it is hard to make a decision based on prior research.

As mentioned i am leaning towards simply censuring patients with second stroke, both in the analysis of stroke severity, civil status and incidence rate of fractures. The information on stroke severity and civil status is collected when the patient is admitted with stroke.

My last question in regards to this is, do you think it would make sense to do a seperate analysis for stroke severity were patients with second stroke are censured, but not doing this for the other analysis. It just seems overkill, when other articles hardly describe what they do with patients with multiple strokes in terms of exclusion and censuring?