Consider a situation where we have individual patient survival data from a series of clinical trials of patients treated in a similar way. We might have a dataset that looks like this, with n total subjects from k total trials, experiencing events (event = 1) or censored (event = 0) at time t.
Note that there are no covariates (e.g. treatment, age, gender). We are interested in the survival of a group of people, whose information is collected from various trials, like might occur in a meta-analysis for example. Following Glidden DV et al. [Stat Med 2004] terminology, we could have a number of possible models for this data. Using R packages survival and coxme, we could fit them:
1. Marginal model, normal variance
f1 <- coxph(Surv(time, event) ~ 1)
2. Marginal model, robust variance
f2a <- coxph(Surv(time, event) ~ cluster(trial)) f2b <- coxph(Surv(time, event) ~ 1, robust = T)`
3. Conditional model, fixed effects
f3 <- coxph(Surv(time, event) ~ trial)
4. Conditional model, stratified
f4 <- coxph(Surv(time, event) ~ strata(trial))
5. Conditional model, random effects (frailty)
f5a <- coxph(Surv(time, event) ~ frailty(trial)) f5b <- coxme(Surv(time, event) ~ (1 | trial))
I have a few questions about these models.
- In the absence of covariates, are models f2a and f2b really different from f1?
- Why does fitting model f2a result in an error while f2b does not?
- How do I examine the baseline hazards of the various models (e.g. plot them) to see how these models differ in their treatment of the hazards?
I appreciate any insight that can be provided