Treatment effect time-averaged archetype

Create a treatment effect informative prior archetype with a special fixed effect to represent the average across time.

Usage

brm_archetype_average_effects(
  data,
  intercept = FALSE,
  baseline = !is.null(attr(data, "brm_baseline")),
  baseline_subgroup = !is.null(attr(data, "brm_baseline")) && !is.null(attr(data,
    "brm_subgroup")),
  baseline_subgroup_time = !is.null(attr(data, "brm_baseline")) && !is.null(attr(data,
    "brm_subgroup")),
  baseline_time = !is.null(attr(data, "brm_baseline")),
  covariates = TRUE,
  prefix_interest = "x_",
  prefix_nuisance = "nuisance_"
)

Arguments

data: A classed data frame from brm_data(), or an informative prior archetype from a function like brm_archetype_successive_cells().
intercept: Logical of length 1. TRUE (default) to include an intercept, FALSE to omit.
baseline: Logical of length 1. TRUE to include an additive effect for baseline response, FALSE to omit. Default is TRUE if brm_data() previously declared a baseline variable in the dataset. Ignored for informative prior archetypes. For informative prior archetypes, this option should be set in functions like brm_archetype_successive_cells() rather than in brm_formula() in order to make sure columns are appropriately centered and the underlying model matrix has full rank.
baseline_subgroup: Logical of length 1.
baseline_subgroup_time: Logical of length 1. TRUE to include baseline-by-subgroup-by-time interaction, FALSE to omit. Default is TRUE if brm_data() previously declared baseline and subgroup variables in the dataset. Ignored for informative prior archetypes. For informative prior archetypes, this option should be set in functions like brm_archetype_successive_cells() rather than in brm_formula() in order to make sure columns are appropriately centered and the underlying model matrix has full rank.
baseline_time: Logical of length 1. TRUE to include baseline-by-time interaction, FALSE to omit. Default is TRUE if brm_data() previously declared a baseline variable in the dataset. Ignored for informative prior archetypes. For informative prior archetypes, this option should be set in functions like brm_archetype_successive_cells() rather than in brm_formula() in order to make sure columns are appropriately centered and the underlying model matrix has full rank.
covariates: Logical of length 1. TRUE (default) to include any additive covariates declared with the covariates argument of brm_data(), FALSE to omit. For informative prior archetypes, this option is set in functions like brm_archetype_successive_cells() rather than in brm_formula() in order to make sure columns are appropriately centered and the underlying model matrix has full rank.
prefix_interest: Character string to prepend to the new columns of generated fixed effects of interest (relating to group, subgroup, and/or time). In rare cases, you may need to set a non-default prefix to prevent name conflicts with existing columns in the data, or rename the columns in your data. prefix_interest must not be the same value as prefix_nuisance.
prefix_nuisance: Same as prefix_interest, but relating to generated fixed effects NOT of interest (not relating to group, subgroup, or time). Must not be the same value as prefix_interest.

Value

A special classed tibble with data tailored to the treatment effect time-averaged archetype. The dataset is augmented with extra columns with the "archetype_" prefix, as well as special attributes to tell downstream functions like brm_formula() what to do with the object.

Details

This archetype has a special fixed effect for each treatment group to represent the mean response averaged across all the time points, and treatment effects are explicitly parameterized.

To illustrate, suppose the dataset has two treatment groups A (placebo/reference group) and B (active/non-reference group), time points 1, 2, and 3, and no other covariates. Let mu_gt be the marginal mean of the response at group g time t given data and hyperparameters. The model has fixed effect parameters beta_1, beta_2, ..., beta_6 which express the marginal means mu_gt as follows:

`mu_A1 = 3 * beta_1 - beta_2 - beta_3`
`mu_A2 = beta_2`
`mu_A3 = beta_3`

`mu_B1 = 3 * beta_1 - beta_2 - beta_3 + 3 * beta_4 - beta_5 - beta_6`
`mu_B2 = beta_2 + beta_5`
`mu_B3 = beta_3 + beta_6`

For group A, beta_1 is the average response in group A averaged across time points. You can confirm this yourself by expressing the average across time (mu_A1 + mu_A2 + mu_A3) / 3 in terms of the beta_* parameters and confirming that the expression simplifies down to just beta_1. beta_2 represents the mean response in group A at time 2, and beta_3 represents the mean response in group A at time 3. beta_4 is the treatment effect of group B relative to group A, averaged across time points. beta_5 is the treatment effect of B vs A at time 2, and beta_6 is analogous for time 3.

Prior labeling for `brm_archetype_average_effects()`

Within each treatment group, the initial time point represents the average, and each successive time point represents the response within that actual time. To illustrate, consider the example in the Details section. In the labeling scheme for brm_archetype_average_effects(), you can label the prior on beta_1 using brm_prior_label(code = "normal(1.2, 5)", group = "A", time = "1"). Similarly, you cal label the prior on beta_5 with brm_prior_label(code = "normal(1.3, 7)", group = "B", time = "2"). To confirm that you set the prior correctly, compare the brms prior with the output of summary(your_archetype). See the examples for details.

Nuisance variables

In the presence of covariate adjustment, functions like brm_archetype_successive_cells() convert nuisance factors into binary dummy variables, then center all those dummy variables and any continuous nuisance variables at their means in the data. This ensures that the main model coefficients of interest are not implicitly conditional on a subset of the data. In other words, preprocessing nuisance variables this way preserves the interpretations of the fixed effects of interest, and it ensures informative priors can be specified correctly.

Prior labeling

Informative prior archetypes use a labeling scheme to assign priors to fixed effects. How it works:

1. First, assign the prior of each parameter a collection
  of labels from the data. This can be done manually or with
  successive calls to [brm_prior_label()].
2. Supply the labeling scheme to [brm_prior_archetype()].
  [brm_prior_archetype()] uses attributes of the archetype
  to map labeled priors to their rightful parameters in the model.

For informative prior archetypes, this process is much more convenient and robust than manually calling brms::set_prior(). However, it requires an understanding of how the labels of the priors map to parameters in the model. This mapping varies from archetype to archetype, and it is documented in the help pages of archetype-specific functions such as brm_archetype_successive_cells().

Examples

set.seed(0L)
data <- brm_simulate_outline(
  n_group = 2,
  n_patient = 100,
  n_time = 4,
  rate_dropout = 0,
  rate_lapse = 0
) |>
  dplyr::mutate(response = rnorm(n = dplyr::n())) |>
  brm_data_change() |>
  brm_simulate_continuous(names = c("biomarker1", "biomarker2")) |>
  brm_simulate_categorical(
    names = c("status1", "status2"),
    levels = c("present", "absent")
  )
dplyr::select(
  data,
  group,
  time,
  patient,
  starts_with("biomarker"),
  starts_with("status")
)
#> # A tibble: 600 × 7
#>    group   time   patient     biomarker1 biomarker2 status1 status2
#>    <chr>   <chr>  <chr>            <dbl>      <dbl> <chr>   <chr>  
#>  1 group_1 time_2 patient_001     -1.42      -0.287 absent  present
#>  2 group_1 time_3 patient_001     -1.42      -0.287 absent  present
#>  3 group_1 time_4 patient_001     -1.42      -0.287 absent  present
#>  4 group_1 time_2 patient_002     -1.67       1.84  absent  present
#>  5 group_1 time_3 patient_002     -1.67       1.84  absent  present
#>  6 group_1 time_4 patient_002     -1.67       1.84  absent  present
#>  7 group_1 time_2 patient_003      1.38      -0.157 absent  absent 
#>  8 group_1 time_3 patient_003      1.38      -0.157 absent  absent 
#>  9 group_1 time_4 patient_003      1.38      -0.157 absent  absent 
#> 10 group_1 time_2 patient_004     -0.920     -1.39  present present
#> # ℹ 590 more rows
archetype <- brm_archetype_average_effects(data)
archetype
#> # A tibble: 600 × 23
#>    x_group_1_time_2 x_group_1_time_3 x_group_1_time_4 x_group_2_time_2
#>  *            <int>            <int>            <int>            <int>
#>  1                3               -1               -1                0
#>  2                0                1                0                0
#>  3                0                0                1                0
#>  4                3               -1               -1                0
#>  5                0                1                0                0
#>  6                0                0                1                0
#>  7                3               -1               -1                0
#>  8                0                1                0                0
#>  9                0                0                1                0
#> 10                3               -1               -1                0
#> # ℹ 590 more rows
#> # ℹ 19 more variables: x_group_2_time_3 <int>, x_group_2_time_4 <int>,
#> #   nuisance_biomarker1 <dbl>, nuisance_biomarker2 <dbl>,
#> #   nuisance_status1_absent <dbl>, nuisance_status2_present <dbl>,
#> #   nuisance_baseline <dbl>, nuisance_baseline.timetime_2 <dbl>,
#> #   nuisance_baseline.timetime_3 <dbl>, patient <chr>, time <chr>, group <chr>,
#> #   missing <lgl>, change <dbl>, baseline <dbl>, biomarker1 <dbl>, …
summary(archetype)
#> # This is the "average effects" informative prior archetype in brms.mmrm.
#> # The following equations show the relationships between the
#> # marginal means (left-hand side) and fixed effect parameters
#> # (right-hand side).
#> # 
#> #   group_1:time_2 = 3*x_group_1_time_2 - x_group_1_time_3 - x_group_1_time_4
#> #   group_1:time_3 = x_group_1_time_3
#> #   group_1:time_4 = x_group_1_time_4
#> #   group_2:time_2 = 3*x_group_1_time_2 - x_group_1_time_3 - x_group_1_time_4 + 3*x_group_2_time_2 - x_group_2_time_3 - x_group_2_time_4
#> #   group_2:time_3 = x_group_1_time_3 + x_group_2_time_3
#> #   group_2:time_4 = x_group_1_time_4 + x_group_2_time_4
formula <- brm_formula(archetype)
formula
#> change ~ 0 + x_group_1_time_2 + x_group_1_time_3 + x_group_1_time_4 + x_group_2_time_2 + x_group_2_time_3 + x_group_2_time_4 + nuisance_biomarker1 + nuisance_biomarker2 + nuisance_status1_absent + nuisance_status2_present + nuisance_baseline + nuisance_baseline.timetime_2 + nuisance_baseline.timetime_3 + unstr(time = time, gr = patient) 
#> sigma ~ 0 + time
prior <- brm_prior_label(
  code = "normal(1, 2.2)",
  group = "group_1",
  time = "time_2"
) |>
  brm_prior_label("normal(1, 3.3)", group = "group_1", time = "time_3") |>
  brm_prior_label("normal(1, 4.4)", group = "group_1", time = "time_4") |>
  brm_prior_label("normal(2, 2.2)", group = "group_2", time = "time_2") |>
  brm_prior_label("normal(2, 3.3)", group = "group_2", time = "time_3") |>
  brm_prior_label("normal(2, 4.4)", group = "group_2", time = "time_4") |>
  brm_prior_archetype(archetype)
prior
#>           prior class             coef group resp dpar nlpar   lb   ub source
#>  normal(1, 2.2)     b x_group_1_time_2                       <NA> <NA>   user
#>  normal(1, 3.3)     b x_group_1_time_3                       <NA> <NA>   user
#>  normal(1, 4.4)     b x_group_1_time_4                       <NA> <NA>   user
#>  normal(2, 2.2)     b x_group_2_time_2                       <NA> <NA>   user
#>  normal(2, 3.3)     b x_group_2_time_3                       <NA> <NA>   user
#>  normal(2, 4.4)     b x_group_2_time_4                       <NA> <NA>   user
class(prior)
#> [1] "brmsprior"  "data.frame"
if (identical(Sys.getenv("BRM_EXAMPLES", unset = ""), "true")) {
tmp <- utils::capture.output(
  suppressMessages(
    suppressWarnings(
      model <- brm_model(
        data = archetype,
        formula = formula,
        prior = prior,
        chains = 1,
        iter = 100,
        refresh = 0
      )
    )
  )
)
suppressWarnings(print(model))
brms::prior_summary(model)
draws <- brm_marginal_draws(
  data = archetype,
  formula = formula,
  model = model
)
summaries_model <- brm_marginal_summaries(draws)
summaries_data <- brm_marginal_data(data)
brm_plot_compare(model = summaries_model, data = summaries_data)
}