Stepwise covariate modelling for exposure-response TTE models

Iteratively adds (ertte_scm_forward()) or removes (ertte_scm_backward()) covariate terms from an ertte model one at a time, selecting each step's term by a likelihood-ratio p-value, AIC, or BIC, and logging the search in a history object retrievable via ertte_scm_history().

Usage

ertte_scm_forward(
  mod,
  candidates,
  threshold = 0.01,
  criterion = "p-value",
  seed = NULL
)

ertte_scm_backward(
  mod,
  candidates,
  threshold = 0.001,
  criterion = "p-value",
  seed = NULL
)

ertte_scm_history(mod)

Arguments

mod: An ertte model object
candidates: Character vector with list of candidate terms
threshold: Threshold to test against. Used only when criterion = "p-value" (the default); ignored otherwise. Defaults to 0.01 for ertte_scm_forward() and 0.001 for ertte_scm_backward().
criterion: Model selection criterion. One of "p-value" (default), "aic", or "bic".
seed: Optional seed to control the order candidate terms are tested within a step. If NULL (the default), one is chosen automatically (see "Candidate test order and seed" below for when this actually matters).

Value

For ertte_scm_forward() and ertte_scm_backward(), the updated ertte model is returned, with the SCM history log updated internally. For ertte_scm_history(), a data frame is returned containing the SCM history log.

Details

Three model selection criteria are available via the criterion argument:

"p-value" (default): Models are compared with a likelihood-ratio Chi-squared test. A term is added if its likelihood-ratio p-value falls below threshold (forward) or removed if its p-value exceeds threshold (backward). When multiple candidates satisfy the threshold within a step, the one with the most extreme p-value is chosen.
"aic": A term is added (forward) or removed (backward) if doing so strictly decreases AIC relative to the current model. When multiple candidates improve AIC, the one yielding the lowest AIC is chosen.
"bic": Same as "aic", but using BIC as the criterion.

When criterion is "aic" or "bic", the threshold argument has no effect and is ignored, and term_p_value is left NA in the history for every candidate tested that step (the likelihood-ratio test isn't computed, since it plays no role in selection). The model_aic and model_bic columns are always recorded regardless of which criterion drove selection, and the history's criterion column records which one was used for each forward/backward step.

Handling problem candidates

A candidate that can't be fit for a given step (e.g. it's aliased with a term already in the model, references a variable missing from the data, or fails to converge) is skipped for that step with a warning, rather than aborting the whole search or being silently selected.

Candidate test order and `seed`

seed exists as a safety measure against run-to-run variation in the order candidate terms are tested within a step (sample(), shuffled before testing one at a time). Model fitting itself (survival::survreg()) is deterministic given a starting formula, so seed only matters in the (essentially measure-zero) case of an exact p-value tie between competing candidates within a step – see the companion erglm package's equivalent documentation for the full rationale, which applies unchanged here.

Examples

# Forward addition by p-value selection
mod0 <- ertte_aft(Surv(time, event) ~ aucss, ertte_data)
mod1 <- ertte_scm_forward(mod0, candidates = c("sex", "dose"))
ertte_scm_history(mod1)
#> # A tibble: 4 × 12
#>   iteration attempt step       criterion action term_tested model_tested        
#>       <int>   <int> <chr>      <chr>     <chr>  <chr>       <chr>               
#> 1         0       0 base model NA        NA     NA          Surv(time, event) ~…
#> 2         1       1 forward    p-value   add    ~sex        Surv(time, event) ~…
#> 3         1       2 forward    p-value   add    ~dose       Surv(time, event) ~…
#> 4         2       3 forward    p-value   add    ~dose       Surv(time, event) ~…
#> # ℹ 5 more variables: model_converged <lgl>, term_p_value <dbl>,
#> #   model_aic <dbl>, model_bic <dbl>, model_updated <int>

# Backward elimination by p-value selection
mod2 <- ertte_aft(Surv(time, event) ~ aucss + sex + dose, ertte_data)
mod3 <- ertte_scm_backward(mod2, candidates = c("sex", "dose"))
ertte_scm_history(mod3)
#> # A tibble: 4 × 12
#>   iteration attempt step       criterion action term_tested model_tested        
#>       <int>   <int> <chr>      <chr>     <chr>  <chr>       <chr>               
#> 1         0       0 base model NA        NA     NA          Surv(time, event) ~…
#> 2         1       1 backward   p-value   remove ~dose       Surv(time, event) ~…
#> 3         1       2 backward   p-value   remove ~sex        Surv(time, event) ~…
#> 4         2       3 backward   p-value   remove ~sex        Surv(time, event) ~…
#> # ℹ 5 more variables: model_converged <lgl>, term_p_value <dbl>,
#> #   model_aic <dbl>, model_bic <dbl>, model_updated <int>

# AIC-based forward addition/backward elimination instead of p-value
mod4 <- ertte_scm_forward(mod0, candidates = c("sex", "dose"), criterion = "aic")
mod5 <- ertte_scm_backward(mod4, candidates = c("sex", "dose"), criterion = "bic")
ertte_scm_history(mod5)
#> # A tibble: 5 × 12
#>   iteration attempt step       criterion action term_tested model_tested        
#>       <int>   <int> <chr>      <chr>     <chr>  <chr>       <chr>               
#> 1         0       0 base model NA        NA     NA          Surv(time, event) ~…
#> 2         1       1 forward    aic       add    ~dose       Surv(time, event) ~…
#> 3         1       2 forward    aic       add    ~sex        Surv(time, event) ~…
#> 4         2       3 forward    aic       add    ~dose       Surv(time, event) ~…
#> 5         3       4 backward   bic       remove ~sex        Surv(time, event) ~…
#> # ℹ 5 more variables: model_converged <lgl>, term_p_value <dbl>,
#> #   model_aic <dbl>, model_bic <dbl>, model_updated <int>