Interpretation of tvcs in -stcox- using propensity scores

[Manette Dinnessen]

Hi all,

I am examining the comparative effectiveness of different treatment groups on event-free survival, for which I used a Cox ph model. I used inverse probability weigting (a propensity score method) to minimize the effects of measured confounding on outcomes. However, I am not sure whether I should add time-varying covariates to the model and how I should interpret these estimates.

This is an example of an analysis that I performed:

Aim: to assess the comparative effectiveness of R-CVP (n=289) versus R-CVP followed by rituximab-maintanance (n=444) on event-free survival for the treatment of patients with follicular lymphoma (an indolent non-hodgkin lymphoma).

The following pre-defined set of potential confounders, measured at the start of therapy, were included in the propensity score:
• Sex (male and female)
• Age in years as a continuous variable
• Disease stage (I, II, III, IV)
• Grade (1-2, 3, and unknown)
• WHO performance score (0, 1, ≥2, and unknown)
• Presence of B-symptoms (no or unknown and yes)
• Hemoglobin <12 g/dl (no or unknown and yes)
• Number of nodal areas >4 (no or unknown and yes)
• Geographical region of the treatment hospital
• Teaching hospital (no and yes)

I examined the proportional hazards assumption for treatment and all confounders. For categorical variables, the PH assumption was tested by plotting the log of the − log survival function {log[− log(S(t)]} against the log of the survival time [log(t)] using the following code:

stset fu_jaren, failure(event_dummy==1)
stcox i.treatment i.sex age i.hemoglobin i.nodal i.stage i.who i.ldhuln i.bsymptoms i.region i.teachinghospital, schoenfeld(sch*) scaledsch(sca*)
Stphtest, detail
stphplot, by(treatment) title(Plot of -log(-log(Survival(follow-up))))

Stphtest yields a p-value of 0.0000 for treatment. Stphplot yields the following plot:

I also examined the effect of adding treatment as a tvc to the model. The first output underneath shows the output for a model in which I did not add a tvc for treatment (just the main effect and propensity score). In the second output, I added a tvc for treatment to the model. In the third output, I also added a tvc for treatment to the model, but this time, I did not include treatment as a main effect.

stcox i.behandeling propensity

Output 1 Cox regression with Breslow method for ties
No. of subjects = 1,331		Number of obs = 679
No. of failures = 638		Wald chi2(2) = 33.93
Time at risk = 4,654.5371		Prob > chi2 = 0.0000
Log pseudolikelihood = -4271.6143
_t	Haz. ratio	Robust std. err.	z	P>z	[95% conf. interval]
rcvp + r-maintenance	0.4396135	0.0730853	-4.94	0	0.3173654	0.6089511
propensity	1.83689	0.6268052	1.78	0.075	0.9410792	3.585421

stcox i.behandeling propensity, tvc(i.behandeling)

Output 2 Cox regression with Breslow method for ties
No. of subjects = 1,331		Number of obs = 679
No. of failures = 638		Wald chi2(3) = 50.80
Time at risk = 4,654.5371		Prob > chi2 = 0.0000
Log pseudolikelihood = -4247.3564
_t	Haz. ratio	Robust std. err.	z	P>z	[95% conf. interval]
main
rcvp + r-maintenance	0.2075507	0.0555933	-5.87	0	0.1227796	0.3508505
propensity	1.830812	0.6133204	1.81	0.071	0.9494931	3.530169
tvc
rcvp + r-maintenance	1.450145	0.165103	3.26	0.001	1.160112	1.812688
Note: Variables in tvc equation interacted with _t.

stcox propensity, tvc(behandeling)

Output 3 Cox regression with Breslow method for ties
No. of subjects = 1,331		Number of obs = 679
No. of failures = 638		Wald chi2(3) = 50.80
Time at risk = 4,654.5371		Prob > chi2 = 0.0000
Log pseudolikelihood = -4247.3564
_t	Haz. ratio	Robust std. err.	z	P>z	[95% conf. interval]
main
propensity	1.620532	0.5161944	1.52	0.13	0.8680024	3.025479
tvc
treatment	0.8889526	0.0547947	-1.91	0.056	0.7877907	1.003105
Note: Variables in tvc equation interacted with _t.

These are my questions:

1. Is the ph assumption violated? The plot in itself does not worry me too much, but in combination with the p-value <0.05 for the tvc effect in the Cox model, I would think that the ph assumption is violated.

2. If the ph assumption for treatment is violated, can I add a tvc for treatment to account for this? An alternative may be to stratify by follow-up time, but I prefer to add a tvc since I do not have many observations for other treatment groups for which I am going to examine the comparative effectiveness.

3. Should I keep treatment as a main effect (output 2), or should I only include it as a tvc (output 3)?

4. How should I interpret the hazard ratios for treatment? It seems that the effect of treatment is stronger when including the time-varying covariate, which makes sense as the ‘original’ hazard ratio is based on an effect that is diluted over time (see the stphplot) and I corrected for that. However, it feels counterintuitive to say that the HR for 5-year event-free survival is much stronger after correcting for the time effect, as the effect is smaller after five years (see stphplot).


I really appreciate any help.


Best regards,
Manette Dinnessen