Initial values for Weibull survival model with brms

Interfaces brms
,
1

When trying something out on the colon dataset from the R survival package, I ran into trouble with initialization for a simple Weibull model. A-priori I expect the intercept to be about 7.5 or so (\approx log(5*365.25 days) = log of 5 years median survival for colon cancer has been mentioned in the literature). I think the problem is that initialization is using a N(0,1), which is very far away from 7.5. As a result sampling failed a lot with errors. Is the solution really to use an offset the way I did below? Is there some way to set an initial value for just one parameter (the intercept) and leave all the rest as N(0,1), which should work for everything else?

By the way, if I switched to Cox regression, is there an easy way to make it stratified (to reflect that the things I put into the formula for shape might impact the shape of the survival curve)?

library(tidyverse)
library(survival)
library(tidymodels)
library(brms)

data(cancer) 
# Only model mortality (etype==2)
colon <- colon %>%
    filter(etype==2) %>%
    dplyr::select(-etype) %>%
    mutate(id=as.integer(id))

# I have some pre-processing steps that make sense for various reasons
# (e.g. making continuous predictors approx. N(0,1) helps with interpreting priors)
preprocess_recipe <- recipe(status ~ ., data = colon) %>% 
    update_role(time, new_role = "outcome") %>%
    update_role(id, study, new_role = "ID") %>% 
    step_indicate_na(all_predictors()) %>%
    step_impute_median(all_numeric_predictors()) %>%
    step_impute_mode(all_nominal_predictors()) %>%
    step_sqrt(nodes) %>%
    step_mutate(age = 125 - age) %>%
    step_log(age) %>%
    step_normalize(age, nodes) %>%
    step_zv(all_predictors())

# Train recipe and apply it to all data at once (may do CV later)
myrecipe <- prep(preprocess_recipe, training = colon)
all_data <- bake(myrecipe, new_data = colon, everything())

model_weibull <- bf(time | cens(1-status) ~ 1 + factor(rx) + age + nodes + factor(extent) + surg + offset(7.5), #sex + obstruct + adhere + differ +  
                    shape ~ 1 + rx + nodes,
                    family=weibull(link_shape = "log"))

prior_weibull <- prior(normal(0, 2.5), class=Intercept) +
    prior(normal(0, 1), class=b) +
    prior(normal(0, 1), class=Intercept, dpar=shape) +
    prior(normal(0, 0.25), class=b, dpar=shape)

fit_weibull <- brm(model_weibull,
                   data=all_data,
                   prior=prior_weibull,
                   cores=4, 
                   seed=234235)
  • Operating System: x86_64, linux-gnu
  • R version: R version 4.0.5 (2021-03-31)
  • brms Version: 2.18.0
2

About the intercept thing: Keep in mind that, by default, the intercept you set priors on and initialize is the intercept after centering all predictors around 0. This change is corrected for after model fitting but for priors and inits it matter. If you want the original intercept to be used (without internal centering), use bf(..., center = FALSE). Perhaps that already helps?

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3

@paul.buerkner, is there a difference between the bf(..., center = FALSE) method and the y ~ 0 + Intercept + ... method?

4

they are equivalent.

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