Interpretation Competing Risk (Stcrreg) – Comparability of Covariates

[John Philipps]

Dear Stata Users,

I have a question regarding the interpretation and comparability of the hazard ratios in a competing risk model obtained from the stcrreg command (Fine and Gray’s Model). I have two competing exit reasons: Exit 1 and Exit 2. When I obtain hazard ratios for my covariates from Exit =1 it looks like the following:

stcrreg Covariate 1 Covariate 2 Covariate 3, compete(failcode = 2 )

	Cause
	EXIT 1
Covariate 1	1.211
	[1.32]
Covariate 2	0.0560*
	[-1.70]
Covariate 3	0.2***
	[2.70]

I interpret this as: “Covariate 3 lowers my probability of exit cause 1 by 80 %”
When I obtain hazard ratios for my covariates from Exit =2 it looks this:

stcrreg Covariate 1 Covariate 2 Covariate 3, compete(failcode = 1 )

	Cause
	Exit 2
Covariate 1	1.434**
	[2.31]
Covariate 2	0.0409*
	[-1.85]
Covariate 3	0.4***
	[2.31]

I interpret this as: “Covariate 3 lowers my probability of exit cause 1 by 60 %”

My question: Can I compare the results from Model 1 and Model 2 in regard to covariate 3?
Is it right to interpret the difference (of 20 %) for covariate 3 between Exit 1 and Exit 2? So to say that “For individual with a higher covariate 3 the probability is 20 % lower experiencing exit 2 then exit 1?



Thanks a lot and regards,

John

[Clyde Schechter]

No, it's not. First, if you were going to do something like that, the difference between the two would be 20 percentage points, not percent. But taking the difference between two hazard ratios is not meaningful at all. You might want to talk about the ratio of the hazard ratios, but not their difference.

Further terminology: the outputs of the Fine and Gray model are known as subhazard ratios.

Also, a (sub)hazard ratio of 0.8 does not mean that your probability of experiencing that outcome is reduced by 20 percent. It means that at any point in time, your probability of experiencing that outcome is reduced by 20 percent if you haven't already experienced it. The actual overall reduction in probability of experiencing the outcome will, in general, be different from 20%, depends on the length of follow-up, and is difficult to calculate.

[John Philipps]

No, it's not. First, if you were going to do something like that, the difference between the two would be 20 percentage points, not percent. But taking the difference between two hazard ratios is not meaningful at all. You might want to talk about the ratio of the hazard ratios, but not their difference.

Dear Clyde,

As always: Many thanks for your detailed answer! And sorry for my sloppy wording in regard to the terminology.
So if I get you right I have to calculate the ratio of the two sub hazard ratios? I searched a while but found not a satisfy answer and this might be an utterly stupid question but: How do I calculate the ratio of two sub hazard ratios for a 95 % confidence interval?
And (2) is there a way to let STATA do this automatically?

Thanks a lot and regards,

John

[Clyde Schechter]

Well, normally this situation arises in the context of a comparison of the subhazard ratios for a predictor in two complementary subsets of the population. I have never seen anybody do this for two different outcomes of a competing risks model. You might try saving the estimates after both runs and then feeding them to -suest- and using -lincom- to estimate the difference of the coefficients of covariate 3 across the two models. I do not know for sure if -suest- supports -stcrreg-, but I think it does. Then exponentiating the difference of the coefficients and its 95% CI will give you an estimate and 95% CI for the ratio of subhazard ratios.

If -suest- does not work with -stcrreg- outputs, I don't know what else to suggest.

[John Philipps]

Dear Cylde,

thanks a lot for your answer ! I will try my best to use suest and lincom to solve this matter. I will come back if I have a solution for the sake of others.

Regards,

John

[John Philipps]

Dear Stata Users,

I tried to store and test the sub hazard ratios for differences. However stcrreg does not support suest, hence this way it is not possible to test for differences.
Question A: Has anybody another idea/solution to test for differences in the sub-hazard ratios, resulting from my Fine and Gray – Competing Risk model? I found some older, similar threads in this forum, unfortunately with now answers.

Question B: @Clyde: Can you explain me how to test for differences in hazard ratios in a Fine and Gray Competing Risk models for two groups?

Your help is highly appreciated!
Regards,

John

[Clyde Schechter]

In any kind of regression, including -stcrreg-, you can test for group differences in a coefficient (or hazard ratio or odds ratio, etc.) by adding a term for the interaction of the grouping variable and the variable whose coefficient you want to test for group differences. So if your original model looks like:

stcrreg Covariate 1 Covariate 2 Covariate 3, compete(failcode = 1 )

and you have a variable called group that distinguishes two groups (let's say the codes for these two groups are 0 and 1) then you can do this:

// If Covariate1 is continuous
stcrreg i.group##c.Covariate1 Covariate2 Covariate3, compete(failcode = 1)

// If Covariate1 is discrete
stcrreg i.group##i.Covariate1 Covariate2 Covariate3, complete(failcode = 1)

You can then test the equality of the Covariate1 subhazard ratios in the two groups by looking at the 1.group#Covariate1 (continuous) or 1.group#1.Covariate1 row of the -stcrreg- regression table output. You can then get the group specific subhazard ratios as follows. For group = 0, it's just the subhazard ratio for Covariate1. For group = 1 it's

nlcome (exp(_b[Covariate1] + _b[1.group#c.Covariate1]))

[John Philipps]

Dear Clyde, Dear Stata Users,

many thanks for your answer. The nlcom command was very helpful form me!

Two related questions to that:

Question A:
Is it possible to test whether the sub hazard ratios for Covariate1 for group=1 in competing event 1 is different from those for Covariate1 for group 1 in competing event 2?
E.g.

 stcrreg i.group##c.Covariate1 Covariate2 Covariate3, compete(failcode = 1)

Vs.

 stcrreg i.group##c.Covariate1 Covariate2 Covariate3, compete(failcode = 2)

I tried to save the coefficients after each regression with estimates store and access it with nlcom but you need suest for that – and suest as I wrote before does not work with stcrreg (… was estimated with cluster(id) error, might be the same issues as here: https://www.statalist.org/forums/for...crreg-or-stcox

Question B:
Is it possible to test the difference for group 1 and group 0 as “standalone”, so to treat it like a covariate:

 stcrreg i.group Covariate1 Covariate2 Covariate3, compete(failcode = 1)

Saying that the sub hazard ratio for group 1 is X controlling for Covariate1, Covariate2 and Covariate3 ?

Ideally I like to combine both solutions to question A and B.

Thanks a lot !

Regards,

John

[Dennis Lund Hansen]

Dear John

Your opening question :

My question: Can I compare the results from Model 1 and Model 2 in regard to covariate 3?
Is it right to interpret the difference (of 20 %) for covariate 3 between Exit 1 and Exit 2? So to say that “For individual with a higher covariate 3 the probability is 20 % lower experiencing exit 2 then exit 1?

Makes me suspect that you are interpretation the subdistribution hazard ratios as just an ordinary hazard ratio for exit with respect to a given cause?
The risk set retains everybody who had exited due to competing risk, therefore is the subdistribution hazard ration / Fine-Gray-subHR expressing the relative change in the instantaneous rate of the occurrence of the event in those subjects who are event‐free or who have experienced a competing event. [Austin, 2017]
The subdistribution hazard function is related to the cumulative incidence function, and the subdistribution hazard ratio / Fine-Gray-subHR is expressing the effect of the covariat on the subdistribution hazard function and indirectly the effect on the cumulative incidens. An increas in subdistribution hazard function will lead to an increase in cumulative incidence, but the magnitude is hard or impossible to predict. A common recommendation is to only interpret the direction of the subHR - if the ratio is above 1 then the covariat increases the cumulative incidence, and below one it decreased the cumulative incidence.

Some suggested literature if you are not already familiar with it:

Austin, P. C. and J. P. Fine (2017). "Practical recommendations for reporting Fine-Gray model analyses for competing risk data." Stat Med 36(27): 4391-4400.

Andersen, P. K., et al. (2012). "Competing risks in epidemiology: possibilities and pitfalls." Int J Epidemiol 41(3): 861-870.

Lau, B., et al. (2009). "Competing risk regression models for epidemiologic data." Am J Epidemiol 170(2): 244-256.

[Clyde Schechter]

Dennis Lund Hansen makes an excellent point in #9.

Concerning question B, yes you can run that model. But do not interpret the result as showing you that there is a difference in the effect of Covariate1 (or anything else) by group. All it does is say that the baseline subhazard rate (when other covariates are all 0) differs by group. The effects of the other Covariates are independent of group in this model: but those effects operate on a different baseline.

[John Philipps]

Dear Clyde, Dear Dennis,

thank you very much for your explanations and for the papers, this was extremely helpful for me !
This also explains why most of my "peer papers" do not interpret differences in sub-hazard ratios. The problem is that both of my hazard ratios for both causes are below 1, which is very strange in the field my study is in. I also used time-variant covariates (tvc option) which did not change the result.

Very last question: I have seen that some authors use a competing risk model which is not the Fine and Gray approach. Is there a different command in STATA for competing risks I'm not aware of? Stcompadj, as far as I know is also using CIFs, which would cause the same problem as above...

Thanks and regards,

John

[Dennis Lund Hansen]

Dear John

You can use stcompet (https://www.stata-journal.com/articl...article=st0059) to draw the non-parametric cumulative incidence, and then compare it to the to the semiparametric version which you can obtain using -stcurve- (generic Stata command) after running -stcrreg-.
Please note: there is a newer version of stcompet on ssc, than the one from stata journal.

Do you only have two causes of exit or is it only those two interested in? I mean do you have at third cause with an elevated subHR? It could be, that the subjects are exiting so fast due to the competing cause, that they are not availible to exit due to the two other causes?

If you look in the paper by Lau et al. then you can see, their suggested algorthem for interpret subhazard ratios and cause-specifik hazard ratios (table 2).
If you follow the recommendation from Latouche et al. then you can report cause-specifik hazard ratios and subhazard ratios together and perhaps find an explanation in that.

As an example, we have just made at study of risk of cardiovascular death in patients with a specifik subtype of blood disorders. We expected to find a high risk of thrombosis - based on findings in alike diseases. Due to time varying coefficients we also had to time split / time interact the dataset. But (surprisingly) we found that with in the first year the subhazard ratios was one, but the cause specifik hazard ratio was close to 1.5 and the non-parametric cumulative incidence was elevated compared to the comparisons, but the elevation was generated with in the first few weeks. Our interpretation ended up being something like (a bit truncated) :
those who are alive with the disease do at any point in time have an increased death rate from thrombosis, but the cumulative incidens is nearly unaffected, as the risk of dying of competing causes is (extremly) high (cause specifik and subhazard ratios above 100 for some causes of death).


I do not have an experience with stcompadj or other competing risk methods, in my small area Fine-Gray is pretty much the one and only acknowledge method.

Some extra litteratur on subhazard rations and cause-specifik hazard ratios:

Latouche, A., et al. (2013). "A competing risks analysis should report results on all cause-specific hazards and cumulative incidence functions." J Clin Epidemiol 66(6): 648-65

[Ches Zin]

Dear Statalists,
I just would like to ask some clarifications about the result of competing risk regression(crr). Whether the result of the crr is expected to be different from the result produced by logistic regression using the same outcome and covariates. The failure of my study is overdose and the competing event is death among 4 different groups. My covariates are various types of drugs. Using the logistic regression (overdose: yes/no), the results of all covariates do make sense i.e having for example drug such as bzd increases the odd ratio (>1) of having overdose. However, in the crr, the results of covariates are different in which, it showed that the subhazard ratio (<1) when using bzd. Is this mean that using bzd is associated with less risk of overdose or less time to get overdose i.e faster rate to experience overdose?. Appreciate any help in my confusion. Below is the example of the output:


stset time2_od, failure(od3==1)
stcrreg ib1.egfr_group4 bzd gabapre nsaids, compete (od3== 2)

(od3==1 is overdose and od3==2 is death)
The output from crr

egfr_group4	SHR	std.err	z	p	LCI	ULI
2	1.421334	.2067297	2.42	0.016	1.068786	1.890172
3	.8429133	.1851923	-0.78	0.437	.5479862	1.296571
4	.4356478	.2268408	-1.60	0.111	.1570062	1.208799
bzd	.6779164	.0802209	-3.29	0.001	.5375881	.8548751
gabapre	1.083918	.1356086	0.64	0.520	.848209	1.385128
nsaids	1.820016	.2578678	4.23	0.000	1.378711	2.402576

The output from logistic regression

egfr_group4	OR	std.err	z	p	LCI	UCI
2	1.480941	.2052498	2.83	0.005	1.128668	1.943163
3	1.495196	.3427427	1.75	0.079	.9540646	2.343249
4	1.322554	.6875359	0.54	0.591	.4774327	3.663655
bzd	1.545758	.1948304	3.46	0.001	1.207409	1.978922
gabapre	1.3798	.1634841	2.72	0.007	1.093862	1.740483
nsaids	.8698313	.1256196	-0.97	0.334	.6553992	1.154421

Thanks in advance for any help.

[Clyde Schechter]

Is this mean that using bzd is associated with less risk of overdose or less time to get overdose i.e faster rate to experience overdose?.

A (sub)hazard ratio < 1 means that the risk at any instant of the failure event (overdose, in your case) is lower when the regressor (bzd, in your case) takes on a higher value. (It isn't clear whether bzd is a discrete yes-no 0/1 variable or is a continuous variable, such as a dose or cumulative exposure measure, but the same principle applies either way.) This lower instantaneous risk implies that the time to failure event is longer in cases where the regressor takes on a higher value. So this seems to contradict your logistic regression result.

But that is only apparent, not real. It is possible that the ultimate probability of overdose is higher with more bzd, but it occurs later, after more exposure. Perhaps it is a drug to which tolerance develops rapidly. Another thing to consider is that with competing-risks regression, the impact of the competing outcome, death, is folded into the result. In other words, even though we witness more overdose with higher bzd, that might happen if bzd exposure is associated with lower mortality from other causes, thereby leaving people at risk of overdose for a longer period of time, even though the actual risk over that longer period of time is lower with more bzd.

Yes, it's complicated and a little hard to grasp. That's in the nature of competing risk models: there is a direct effect that is estimated by the SHR, and it may differ from the overall observed effect because of change in the exposure that results from change in the occurrence of the competing event(s).

[Ches Zin]

Thanks so much Clyde. It helps me to understand better.. Best