Using package::function inside formula in R gives different results (specifically survival::strata inside coxph)

I believed the following two formula calls should be equivalent.

install.packages("survival")
library(survival)

Model 1

coxph(Surv(futime, fustat) ~ age + strata(rx), data=ovarian)

Call:
coxph(formula = Surv(futime, fustat) ~ age + strata(rx), data = ovarian)

       coef exp(coef) se(coef)     z       p
age 0.13735   1.14723  0.04741 2.897 0.00376

Likelihood ratio test=12.69  on 1 df, p=0.0003678
n= 26, number of events= 12 

Model 2

coxph(Surv(futime, fustat) ~ age + survival::strata(rx), data=ovarian)

Call:
coxph(formula = Surv(futime, fustat) ~ age + survival::strata(rx), 
    data = ovarian)

                             coef exp(coef) se(coef)      z       p
age                       0.14733   1.15873  0.04615  3.193 0.00141
survival::strata(rx)rx=2 -0.80397   0.44755  0.63205 -1.272 0.20337

Likelihood ratio test=15.89  on 2 df, p=0.0003551
n= 26, number of events= 12 

However they are not. The second model, which references 'strata' specifically using the "::" operator, treats it like a fixed effect variable in the model, rather than fitting the model separately within levels of 'strata'. I do not know if this is:

A) An issue with using 'package::function' type calls within a formula in R, or
B) An issue with the survival package and namespaces/dependencies

I want to use the call to Model 2, as I am building a package and don't want to have to attach the entire survival package (which is large) when loading mine.

Any help on this would be much appreciated.

In coxph(), there are these lines:

special <- c("strata", "tt", "frailty", "ridge", "pspline")
tform$formula <- if (missing(data)) 
  terms(formula, special)
else terms(formula, special, data = data)

Therefore, in the first case, coxph correctly detects the strata but not in the second case. We can see this using your example:

library(survival)

formula1 <- Surv(futime, fustat) ~ age + strata(rx)
formula2 <- Surv(futime, fustat) ~ age + survival::strata(rx)
special <- c("strata", "tt", "frailty", "ridge", "pspline")
data <- ovarian

t1 <- terms(formula1, special, data = data)
t2 <- terms(formula2, special, data = data)

attr(t1, "specials")$strata
#> [1] 3
attr(t2, "specials")$strata
#> NULL

While I don't know the specifics of coxph(), I would say that this difference later leads to the differences in results.

Therefore, you should avoid using the prefix survival:: in the formula. If for some reason, you have to use this prefix, you can use the following trick:

library(survival)

# here
strata <- survival::strata
coxph(Surv(futime, fustat) ~ age + strata(rx), data=ovarian)
#> Call:
#> coxph(formula = Surv(futime, fustat) ~ age + strata(rx), data = ovarian)
#> 
#>        coef exp(coef) se(coef)     z       p
#> age 0.13735   1.14723  0.04741 2.897 0.00376
#> 
#> Likelihood ratio test=12.69  on 1 df, p=0.0003678
#> n= 26, number of events= 12