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The research question revolves around whether a time-varying intervention at a center enhances the transplantation hazard per person. I have patient-level data and I need to account for the center transplant volume. I believe adjusting for the center transplant volume is inappropriate, as it is in the pathway of the event and functions more as a mediator than a confounder. To address transplant volume per center and also, specific practices in each hospital in the analysis, I was planning to conduct the analysis with clustering, as follows:

mod1 = coxph(Surv(tstart, tstop, status)~int.tv, cluster = center_code, data = dat)

But I am not sure if it would be more appropriate to use strata() instead as follows:

mod2 = coxph(Surv(tstart, tstop, status)~int.tv+strata(center_code), data = dat)

What do you think would be the correct approach here? also what would be the difference in the interpretation? there is also a flailty() term that could be considered, but I am not understanding the differences between all these terms.

mod2 = coxph(Surv(tstart, tstop, status)~int.tv+frailty(center_code), data = dat)

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  • $\begingroup$ You might be overthinking the possibilities here. Cluster seems to me to be the most natural. Frailty doesn't seem helpful since it is usually a quality that varies among individuals and only incidentally across centers. $\endgroup$ Jan 6 at 22:09

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Any of those could be reasonable choices, depending on what you want to evaluate.

The strata() choice allows for different baseline hazards among the values of center_code, but doesn't impose any further structure related to center_code or allow comparisons among centers.

The cluster() and frailty() choices are of marginal and conditional (mixed-effect) models, respectively. Section 9.2 of Therneau and Grambsch puts the distinction between them this way, in the context of a study using litters of rats:

The marginal [cluster] model estimates the population averaged relative risk due to treatment; that is, the risk of a random sample of treated rats relative to a random sample of untreated, and the frailty model estimates the relative risk within litters.

The cluster() term provides the same point estimates of coefficients as would the model without it; the standard errors are adjusted to take within-center correlations into account. The frailty() term imposes a particular distribution (gamma, gaussian or t) of random effects among centers. The coxme package allows for more complex Gaussian random effects; it might allow you to evaluate int.tv as a random effect among centers.

If there are only a few values of center_code, you might consider treating it as a fixed effect, and perhaps including an interaction between center_code and int.tv to evaluate differences among centers directly, around a shared baseline hazard.

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