R: Cell-means-like successive differences archetype

brm_archetype_successive_cells {brms.mmrm}

R Documentation

Cell-means-like successive differences archetype

Description

Create an informative prior archetype where the fixed effects are successive differences between adjacent time points.

Usage

brm_archetype_successive_cells(
  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`	`TRUE` to make one of the parameters an intercept, `FALSE` otherwise. If `TRUE`, then the interpretation of the parameters in the "Details" section will change, and you are responsible for manually calling `summary()` on the archetype and interpreting the parameters according to the output. In addition, you are responsible for setting an appropriate prior on the intercept. In normal usage, `brms` looks for a model parameter called `"Intercept"` and uses the data to set the prior to help the MCMC runs smoothly. If `intercept = TRUE` for informative prior archetypes, the intercept will be called something else, and `brms` cannot auto-generate a sensible default prior.
`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`.

Details

In this archetype, each fixed effect is either an intercept on the first time point or the difference between two adjacent time points, and each treatment group has its own set of fixed effects independent of the other treatment groups.

To illustrate, suppose the dataset has two treatment groups A and B, 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 = beta_1`
  `mu_A2 = beta_1 + beta_2`
  `mu_A3 = beta_1 + beta_2 + beta_3`

  `mu_B1 = beta_4`
  `mu_B2 = beta_4 + beta_5`
  `mu_B3 = 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, beta_5, and beta_6 behave analogously for group B.

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.

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 for `brm_archetype_successive_cells()`

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_cells(), 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.

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")
)
archetype <- brm_archetype_successive_cells(data)
archetype
summary(archetype)
formula <- brm_formula(archetype)
formula
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
class(prior)
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)
}

[Package brms.mmrm version 1.1.0 Index]