Robust standard errors?

[jalavery]

Thanks for all of your work on this great package! I am trying to apply a weighted survreg model using flexsurvreg, but am noticing that the naive SE is returned with flexsurvreg as opposed to the robust SE from survreg. Is it possible to obtain the robust standard errors when weights are applied to a flexsurvreg object? Reprex below to demonstrate the comparison of the SE. Thank you!

library(flexsurv)
library(gtsummary)
library(tidyverse)

# use trial dataset as an example
head(trial)

# define manual weights, constant across all observations
trial2 <- trial %>% 
  mutate(trt_numeric = as.numeric(trt == "Drug A"),
         manual_weight5 = 5,
         record_id = 1:n()) %>% 
  drop_na()

# try weight of 5 with survreg: (robust) SE and naive SE returned
survreg(Surv(ttdeath, death) ~ trt + stage,
        dist = "lognormal",
        data = trial2,
        weights = manual_weight5,
        robust = TRUE) %>% summary()

# repeat w/ flexsurvreg: only naive SE returned
flexsurvreg(Surv(ttdeath, death) ~ trt + stage,
            dist = "lognormal",
            data = trial2,
            weights = manual_weight5)

[chjackson]

Thanks for the report. This isn't implemented in the package. I'm not familiar with the method - do you have a reference to how it should be calculated?

[jalavery]

Thanks for taking a look. Here is a reference:
Austin PC. Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis. Stat Med 2016; 35:

https://onlinelibrary.wiley.com/doi/full/10.1002/sim.7084

[chjackson]

I've had a go at implementing this in the development version: 9671242 (see here for installation). The robust SEs will be next to the usual SEs in the printed output and the $res and $res.t components of the model object. However this is only done for the models in the package where the derivatives of the log-likelihood are available as analytic functions of the parameters: i.e. the Weibull, Exponential, Gompertz and proportional hazards spline models. For more general models, I think it would need a new mechanism in the package to obtain numerical derivatives, however that'd be a lot more work and not sure when/if I'd get around to that.

[jalavery]

Fantastic, thank you! This is great. I really appreciate all of your work on it.