StepReg with missing imputation

Question

I'm trying to do a stepwise Cox regression imputing missing values.

As a first step I tried a simple stepwise procedure using the StepReg package but I ran into the following issue:

set.seed(123)
library(tidyverse)
lung_na <- survival::lung %>%
  mutate(sex = factor(sex, levels = c(1, 2))) %>% # make sex as factor
  na.omit()

res6 <- StepReg::stepwise(
  formula = survival::Surv(time, status) ~ age + sex + ph.ecog + ph.karno + pat.karno + meal.cal + wt.loss,
  data = lung_na,
  type = "cox",
  strategy = "forward",
  metric = "AICc"
)
#> Error in data.frame(Parameter = c("initial formula", "regression type", : arguments imply differing number of rows: 11, 12
res6
#> Error: object 'res6' not found

^{Created on 2025-01-03 with reprex v2.1.1}

I can't seem to understand why an error occurs using a complete formula and not using survival::Surv(time, status) ~ . as the formula inside the example.

I'm using the complete formula because the following step would be, using the mice package, this:

model_lung_imp <- with(
  data = lung_imp,
  StepReg::stepwise(
    formula = survival::Surv(time, status) ~ age + sex + ph.ecog + ph.karno + pat.karno + meal.cal + wt.loss,
    data = ???,
    type = "cox",
    strategy = "forward",
    metric = "AICc"
  )
)

which doesn't work with dot formulas. In this case it's also not particularly clear how to pass the data argument to the with() formula.

This is an example with a normal Cox regression:

set.seed(123)
library(survival)
library(mice)
#> 
#> Attaching package: 'mice'
#> The following object is masked from 'package:stats':
#> 
#>     filter
#> The following objects are masked from 'package:base':
#> 
#>     cbind, rbind
lung_imp <-
  survival::lung |>
  mice::mice(method = "cart", print = F)
model_lung_imp <- with(
  data = lung_imp,
  survival::coxph(survival::Surv(time, status) ~ age + sex + ph.ecog + ph.karno + pat.karno + meal.cal + wt.loss)
)
summary(mice::pool(model_lung_imp))
#>        term      estimate    std.error   statistic        df      p.value
#> 1       age  1.166524e-02 0.0095162812  1.22581919 154.84482 0.2221277796
#> 2       sex -5.918487e-01 0.1717995858 -3.44499507 155.11338 0.0007347178
#> 3   ph.ecog  5.728645e-01 0.1870627320  3.06241937 145.77603 0.0026153061
#> 4  ph.karno  1.341023e-02 0.0094293986  1.42217219 154.85166 0.1569874005
#> 5 pat.karno -1.269711e-02 0.0070854108 -1.79200694 137.03091 0.0753384836
#> 6  meal.cal -1.991951e-05 0.0002478896 -0.08035637  66.20331 0.9361962526
#> 7   wt.loss -1.003045e-02 0.0066743084 -1.50284529 127.96469 0.1353428021

^{Created on 2025-01-03 with reprex v2.1.1}

Any tips on how to accomplish this?

Thank you.