Treatment-effect-like successive differences archetype

Create an informative prior archetype where the fixed effects are successive differences between adjacent time points and terms in non-reference groups are treatment effects.

Usage

brm_archetype_successive_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,
  clda = FALSE,
  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.

clda

TRUE to opt into constrained longitudinal data analysis (cLDA), FALSE otherwise. To use cLDA, reference_time must have been non-NULL in the call to brm_data() used to construct the data.

Some archetypes cannot support cLDA (e.g. brm_archetype_average_cells() and brm_archetype_average_effects()).

In cLDA, the fixed effects parameterization is restricted such that all treatment groups are pooled at baseline. (If you supplied a subgroup variable in brm_data(), then this constraint is applied separately within each subgroup variable.) cLDA may result in more precise estimates when the time variable has a baseline level and the baseline outcomes are recorded before randomization in a clinical trial.

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 successive differences 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

Within the reference treatment group (e.g. placebo), each fixed effect is either an intercept on the first time point or the difference between two adjacent time points. In each non-reference treatment group, each model parameter is defined as an effect relative to the reference group.

To illustrate, suppose the dataset has two treatment groups A and B, time points 1, 2, and 3, and no other covariates. Say group A is the reference group (e.g. placebo). 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 = beta_1`
  `mu_A2 = beta_1 + beta_2`
  `mu_A3 = beta_1 + beta_2 + beta_3`

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

For group A, beta_1 is the time 1 intercept, beta_2 represents time 2 minus time 1, and beta_3 represents time 3 minus time 2. beta_4 is the treatment effect of group B relative to group A at time 1. beta_5 is the treatment effect of the difference between times 2 and 1, relative to treatment group A. Similarly, beta_6 is the treatment effect of the difference between times 3 and 2, relative to treatment group A.

Prior labeling for `brm_archetype_successive_effects()`

Within each treatment group, each intercept is labeled by the earliest time point, and each successive difference term gets the successive time point as the label. To illustrate, consider the example in the Details section. In the labeling scheme for brm_archetype_successive_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_successive_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
#>  *            <dbl>            <dbl>            <dbl>            <dbl>
#>  1                1                0                0                0
#>  2                1                1                0                0
#>  3                1                1                1                0
#>  4                1                0                0                0
#>  5                1                1                0                0
#>  6                1                1                1                0
#>  7                1                0                0                0
#>  8                1                1                0                0
#>  9                1                1                1                0
#> 10                1                0                0                0
#> # ℹ 590 more rows
#> # ℹ 19 more variables: x_group_2_time_3 <dbl>, x_group_2_time_4 <dbl>,
#> #   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 "successive 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 = x_group_1_time_2
#> #   group_1:time_3 = x_group_1_time_2 + x_group_1_time_3
#> #   group_1:time_4 = x_group_1_time_2 + x_group_1_time_3 + x_group_1_time_4
#> #   group_2:time_2 = x_group_1_time_2 + x_group_2_time_2
#> #   group_2:time_3 = x_group_1_time_2 + x_group_1_time_3 + x_group_2_time_2 + x_group_2_time_3
#> #   group_2:time_4 = 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
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)
}