Informative prior archetypes allow users to conveniently set
informative priors in `brms.mmrm`

in a robust way, guarding
against common pitfalls such as reference level issues, interpretation
problems, and rank deficiency.

We begin with the FEV dataset from the `mmrm`

package, an
artificial (simulated) dataset of a clinical trial investigating the
effect of an active treatment on FEV1 (forced expired volume in one
second), compared to placebo. FEV1 is a measure of how quickly the lungs
can be emptied and low levels may indicate chronic obstructive pulmonary
disease (COPD).

The dataset is a tibble with 800 rows and 7 variables:

`USUBJID`

(subject ID),`AVISIT`

(visit number),`ARMCD`

(treatment, TRT or PBO),`RACE`

(3-category race),`SEX`

(sex),`FEV1_BL`

(FEV1 at baseline, %),`FEV1`

(FEV1 at study visits),`WEIGHT`

(weighting variable).

We will derive `FEV1_CHG = FEV1 - FEV1_BL`

and analyze
`FEV1_CHG`

as the outcome variable.

```
library(brms.mmrm)
data(fev_data, package = "mmrm")
data <- fev_data |>
brm_data(
outcome = "FEV1",
group = "ARMCD",
time = "AVISIT",
patient = "USUBJID",
reference_time = "VIS1",
reference_group = "PBO",
covariates = c("WEIGHT", "SEX")
) |>
brm_data_chronologize(order = "VISITN")
data
#> # A tibble: 800 × 10
#> USUBJID AVISIT ARMCD RACE SEX FEV1_BL FEV1 WEIGHT VISITN VISITN2
#> <fct> <ord> <fct> <fct> <fct> <dbl> <dbl> <dbl> <int> <dbl>
#> 1 PT2 VIS1 PBO Asian Male 45.0 NA 0.465 1 0.330
#> 2 PT2 VIS2 PBO Asian Male 45.0 31.5 0.233 2 -0.820
#> 3 PT2 VIS3 PBO Asian Male 45.0 36.9 0.360 3 0.487
#> 4 PT2 VIS4 PBO Asian Male 45.0 48.8 0.507 4 0.738
#> 5 PT3 VIS1 PBO Black or African A… Fema… 43.5 NA 0.682 1 0.576
#> 6 PT3 VIS2 PBO Black or African A… Fema… 43.5 36.0 0.892 2 -0.305
#> 7 PT3 VIS3 PBO Black or African A… Fema… 43.5 NA 0.128 3 1.51
#> 8 PT3 VIS4 PBO Black or African A… Fema… 43.5 37.2 0.222 4 0.390
#> 9 PT5 VIS1 PBO Black or African A… Male 43.6 32.3 0.411 1 -0.0162
#> 10 PT5 VIS2 PBO Black or African A… Male 43.6 NA 0.422 2 0.944
#> # ℹ 790 more rows
```

The functions listed at https://openpharma.github.io/brms.mmrm/reference/index.html#informative-prior-archetypes can create different kinds of informative prior archetypes from a dataset like the one above. For example, suppose we want to place informative priors on the successive differences between adjacent time points. This approach is appropriate and desirable in many situations because the structure naturally captures the prior correlations among adjacent visits of a clinical trial. To do this, we create an instance of the “successive cells” archetype.

The instance of the archetype is an ordinary tibble, but it adds new
columns with prefixes `"x_"`

and `"nuisance_"`

.
These new columns constitute a custom model matrix to describe the
desired parameterization.

```
archetype
#> # A tibble: 800 × 20
#> x_PBO_VIS1 x_PBO_VIS2 x_PBO_VIS3 x_PBO_VIS4 x_TRT_VIS1 x_TRT_VIS2 x_TRT_VIS3
#> * <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0 0 0 0 0 0
#> 2 1 1 0 0 0 0 0
#> 3 1 1 1 0 0 0 0
#> 4 1 1 1 1 0 0 0
#> 5 1 0 0 0 0 0 0
#> 6 1 1 0 0 0 0 0
#> 7 1 1 1 0 0 0 0
#> 8 1 1 1 1 0 0 0
#> 9 1 0 0 0 0 0 0
#> 10 1 1 0 0 0 0 0
#> # ℹ 790 more rows
#> # ℹ 13 more variables: x_TRT_VIS4 <dbl>, nuisance_WEIGHT <dbl>,
#> # nuisance_SEX_Male <dbl>, USUBJID <fct>, AVISIT <ord>, ARMCD <fct>, RACE <fct>,
#> # SEX <fct>, FEV1_BL <dbl>, FEV1 <dbl>, WEIGHT <dbl>, VISITN <int>, VISITN2 <dbl>
```

We have effects of interest to express successive differences:

```
attr(archetype, "brm_archetype_interest")
#> [1] "x_PBO_VIS1" "x_PBO_VIS2" "x_PBO_VIS3" "x_PBO_VIS4" "x_TRT_VIS1" "x_TRT_VIS2"
#> [7] "x_TRT_VIS3" "x_TRT_VIS4"
```

In addition, we have nuisance variables. Some nuisance variables are
continuous covariates, while others are levels of one-hot-encoded
concomitant factors or interactions of those concomitant factors with
baseline and/or subgroup. All nuisance variables are centered at their
means so the reference level of the model is at the “center” of the data
and not implicitly conditional on a subset of the data.^{1} In addition, some
nuisance variables are automatically dropped in order to ensure the
model matrix is full-rank. This is critically important to preserve the
interpretation of the columns of interest and make sure the informative
priors behave as expected.

The factors of interest linearly map to marginal means. To see the
mapping, call `summary()`

on the archetype. The printed
output helps build intuition on how the archetype is parameterized and
what those parameters are doing.^{2}

```
summary(archetype)
#> # This is the "successive cells" 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS1 + x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_PBO_VIS4
#> # TRT:VIS1 = x_TRT_VIS1
#> # TRT:VIS2 = x_TRT_VIS1 + x_TRT_VIS2
#> # TRT:VIS3 = x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3
#> # TRT:VIS4 = x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3 + x_TRT_VIS4
```

Above, `x_PBO_VIS1`

serves as the intercept, and
`x_TRT_VIS1`

is defined relative to `x_TRT_VIS1`

.
The rest of the parameters keep their original interpretations.

Let’s assume you want to assign informative priors to the fixed
effect parameters of interest declared in the archetype, such as
`x_group_1_time_2`

and `x_group_2_time_3`

. Your
priors may come from expert elicitation, historical data, or some other
method, and you might consider distributional
families recommended by the Stan team. However you construct these
priors, `brms.mmrm`

helps you assign them to the model
without having to guess at the automatically-generated names of model
coefficients in R.

In the printed output from `summary(archetype)`

,
parameters of interest such as `x_group_1_time_2`

and
`x_group_2_time_3`

are always labeled using treatment groups
and time points in the data (and subgroup levels, if applicable). This
labeling mechanism is the same regardless of which archetype you choose,
and it the way `brms.mmrm`

helps you assign priors.

`brm_prior_label()`

is one way to create a labeling
scheme. Each call to `brm_prior_label()`

below assigns a
univariate prior to a fixed effect parameter. Each univariate prior is a
Stan code string. Possible choices are documented in the Stan function
reference at https://mc-stan.org/docs/functions-reference/unbounded_continuous_distributions.html.

```
label <- NULL |>
brm_prior_label(code = "student_t(4, -7.57, 4.96)", group = "PBO", time = "VIS1") |>
brm_prior_label(code = "student_t(4, 3.14, 7.86)", group = "PBO", time = "VIS2") |>
brm_prior_label(code = "student_t(4, 8.78, 8.18)", group = "PBO", time = "VIS3") |>
brm_prior_label(code = "student_t(4, 3.36, 8.10)", group = "PBO", time = "VIS4") |>
brm_prior_label(code = "student_t(4, -2.96, 4.78)", group = "TRT", time = "VIS1") |>
brm_prior_label(code = "student_t(4, 3.13, 7.64)", group = "TRT", time = "VIS2") |>
brm_prior_label(code = "student_t(4, 7.65, 8.24)", group = "TRT", time = "VIS3") |>
brm_prior_label(code = "student_t(4, 4.64, 8.21)", group = "TRT", time = "VIS4")
label
#> # A tibble: 8 × 3
#> code group time
#> <chr> <chr> <chr>
#> 1 student_t(4, -7.57, 4.96) PBO VIS1
#> 2 student_t(4, 3.14, 7.86) PBO VIS2
#> 3 student_t(4, 8.78, 8.18) PBO VIS3
#> 4 student_t(4, 3.36, 8.10) PBO VIS4
#> 5 student_t(4, -2.96, 4.78) TRT VIS1
#> 6 student_t(4, 3.13, 7.64) TRT VIS2
#> 7 student_t(4, 7.65, 8.24) TRT VIS3
#> 8 student_t(4, 4.64, 8.21) TRT VIS4
```

As an alternative to `brm_prior_label()`

, you can start
with a template and manually fill in the Stan code.

```
template <- brm_prior_template(archetype)
template
#> # A tibble: 8 × 3
#> code group time
#> <chr> <chr> <chr>
#> 1 <NA> PBO VIS1
#> 2 <NA> PBO VIS2
#> 3 <NA> PBO VIS3
#> 4 <NA> PBO VIS4
#> 5 <NA> TRT VIS1
#> 6 <NA> TRT VIS2
#> 7 <NA> TRT VIS3
#> 8 <NA> TRT VIS4
```

```
label <- template |>
mutate(
code = c(
"student_t(4, -7.57, 4.96)",
"student_t(4, 3.14, 7.86)",
"student_t(4, 8.78, 8.18)",
"student_t(4, 3.36, 8.10)",
"student_t(4, -2.96, 4.78)",
"student_t(4, 3.13, 7.64)",
"student_t(4, 7.65, 8.24)",
"student_t(4, 4.64, 8.21)"
)
)
label
#> # A tibble: 8 × 3
#> code group time
#> <chr> <chr> <chr>
#> 1 student_t(4, -7.57, 4.96) PBO VIS1
#> 2 student_t(4, 3.14, 7.86) PBO VIS2
#> 3 student_t(4, 8.78, 8.18) PBO VIS3
#> 4 student_t(4, 3.36, 8.10) PBO VIS4
#> 5 student_t(4, -2.96, 4.78) TRT VIS1
#> 6 student_t(4, 3.13, 7.64) TRT VIS2
#> 7 student_t(4, 7.65, 8.24) TRT VIS3
#> 8 student_t(4, 4.64, 8.21) TRT VIS4
```

After you have a labeling scheme, `brm_prior_archetype()`

can create a `brms`

prior for the important fixed effects.^{3}

```
prior <- brm_prior_archetype(label = label, archetype = archetype)
prior
#> prior class coef group resp dpar nlpar lb ub source
#> student_t(4, -7.57, 4.96) b x_PBO_VIS1 <NA> <NA> user
#> student_t(4, 3.14, 7.86) b x_PBO_VIS2 <NA> <NA> user
#> student_t(4, 8.78, 8.18) b x_PBO_VIS3 <NA> <NA> user
#> student_t(4, 3.36, 8.10) b x_PBO_VIS4 <NA> <NA> user
#> student_t(4, -2.96, 4.78) b x_TRT_VIS1 <NA> <NA> user
#> student_t(4, 3.13, 7.64) b x_TRT_VIS2 <NA> <NA> user
#> student_t(4, 7.65, 8.24) b x_TRT_VIS3 <NA> <NA> user
#> student_t(4, 4.64, 8.21) b x_TRT_VIS4 <NA> <NA> user
```

In less common situations, you may wish to assign priors to nuisance
parameters. For example, our model accounts for interactions between
baseline and discrete time, and it may be reasonable to assign priors to
these slopes based on high-quality historical data. This requires a
thorough understanding of the fixed effect structure of the model, but
it can be done directly through `brms`

. First, check the
formula for the included nuisance parameters. `brm_formula()`

automatically understands archetypes.

```
brm_formula(archetype)
#> FEV1 ~ 0 + x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_PBO_VIS4 + x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3 + x_TRT_VIS4 + nuisance_WEIGHT + nuisance_SEX_Male + unstr(time = AVISIT, gr = USUBJID)
#> sigma ~ 0 + AVISIT
```

The `"nuisance_*"`

terms are the nuisance variables, and
the ones involving baseline are
`nuisance_FEV1_BL.AVISITVIS1`

,
`nuisance_FEV1_BL.AVISITVIS2`

,
`nuisance_FEV1_BL.AVISITVIS3`

, and
`nuisance_FEV1_BL.AVISITVIS4`

. Because there is no overall
slope for baseline, we can interpret each term as the linear rate of
change in the outcome variable per unit increase in baseline for a given
discrete time point. Suppose we use this interpretation to construct
informative priors `student_t(4, -0.83, 1)`

,
`student_t(4, -0.78, 1)`

,
`student_t(4, -0.86, 1)`

, and
`student_t(4, -0.82, 1)`

, respectively. Use
`brms::set_prior()`

and `c()`

to append these
priors to our existing `prior`

object:

The model still has many parameters where we did not set priors, and
`brms`

sets automatic defaults. You can see these defaults
with `brms::get_prior()`

.

https://paul-buerkner.github.io/brms/reference/set_prior.html
documents many of the default priors set by `brms`

. In
particular, `"(flat)"`

denotes an improper uniform prior over
all the real numbers.

The downstream methods in `brms.mmrm`

automatically
understand how to work with informative prior archetypes. Notably, the
formula uses custom interest and nuisance variables instead of the
original variables in the data.

```
formula <- brm_formula(archetype)
formula
#> FEV1 ~ 0 + x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_PBO_VIS4 + x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3 + x_TRT_VIS4 + nuisance_WEIGHT + nuisance_SEX_Male + unstr(time = AVISIT, gr = USUBJID)
#> sigma ~ 0 + AVISIT
```

The model can accept the archetype, formula, and prior. Usage is the same as in non-archetype workflows.

```
model <- brm_model(
data = archetype,
formula = formula,
prior = prior,
refresh = 0
)
#> Compiling Stan program...
#> Start sampling
brms::prior_summary(model)
#> prior class coef group resp dpar nlpar lb ub
#> (flat) b
#> (flat) b nuisance_SEX_Male
#> (flat) b nuisance_WEIGHT
#> student_t(4, -7.57, 4.96) b x_PBO_VIS1
#> student_t(4, 3.14, 7.86) b x_PBO_VIS2
#> student_t(4, 8.78, 8.18) b x_PBO_VIS3
#> student_t(4, 3.36, 8.10) b x_PBO_VIS4
#> student_t(4, -2.96, 4.78) b x_TRT_VIS1
#> student_t(4, 3.13, 7.64) b x_TRT_VIS2
#> student_t(4, 7.65, 8.24) b x_TRT_VIS3
#> student_t(4, 4.64, 8.21) b x_TRT_VIS4
#> (flat) b sigma
#> (flat) b AVISITVIS1 sigma
#> (flat) b AVISITVIS2 sigma
#> (flat) b AVISITVIS3 sigma
#> (flat) b AVISITVIS4 sigma
#> lkj_corr_cholesky(1) Lcortime
#> source
#> default
#> (vectorized)
#> (vectorized)
#> user
#> user
#> user
#> user
#> user
#> user
#> user
#> user
#> default
#> (vectorized)
#> (vectorized)
#> (vectorized)
#> (vectorized)
#> default
```

Marginal mean estimation, post-processing, and visualization automatically understand the archetype without any user intervention.

```
draws <- brm_marginal_draws(
data = archetype,
formula = formula,
model = model
)
summaries_model <- brm_marginal_summaries(draws)
summaries_data <- brm_marginal_data(archetype)
brm_plot_compare(model = summaries_model, data = summaries_data)
```

`brms.mmrm`

supports a variety of informative prior
archetypes with different kinds of fixed effects. For example,
`brms.mmrm`

supports simple cell mean and treatment effect
parameterizations.

```
summary(brm_archetype_cells(data, intercept = FALSE))
#> # This is the "cells" 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS4
#> # TRT:VIS1 = x_TRT_VIS1
#> # TRT:VIS2 = x_TRT_VIS2
#> # TRT:VIS3 = x_TRT_VIS3
#> # TRT:VIS4 = x_TRT_VIS4
```

```
summary(brm_archetype_effects(data, intercept = FALSE))
#> # This is the "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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS4
#> # TRT:VIS1 = x_PBO_VIS1 + x_TRT_VIS1
#> # TRT:VIS2 = x_PBO_VIS2 + x_TRT_VIS2
#> # TRT:VIS3 = x_PBO_VIS3 + x_TRT_VIS3
#> # TRT:VIS4 = x_PBO_VIS4 + x_TRT_VIS4
```

There are archetypes to parameterize the average across all time
points in the data. Below, `x_group_1_time_2`

is the average
across time points for group 1 because it is the algebraic result of
simplifying
`(group_1:time_2 + group_1:time_3 + group_1:time_3) / 3`

.

```
summary(brm_archetype_average_cells(data, intercept = FALSE))
#> # This is the "average cells" 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).
#> #
#> # PBO:VIS1 = 4*x_PBO_VIS1 - x_PBO_VIS2 - x_PBO_VIS3 - x_PBO_VIS4
#> # PBO:VIS2 = x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS4
#> # TRT:VIS1 = 4*x_TRT_VIS1 - x_TRT_VIS2 - x_TRT_VIS3 - x_TRT_VIS4
#> # TRT:VIS2 = x_TRT_VIS2
#> # TRT:VIS3 = x_TRT_VIS3
#> # TRT:VIS4 = x_TRT_VIS4
```

There is also a treatment effect version where
`x_group_2_time_2`

becomes the time-averaged treatment effect
of group 2 relative to group 1.

```
summary(brm_archetype_average_effects(data, intercept = FALSE))
#> # 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).
#> #
#> # PBO:VIS1 = 4*x_PBO_VIS1 - x_PBO_VIS2 - x_PBO_VIS3 - x_PBO_VIS4
#> # PBO:VIS2 = x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS4
#> # TRT:VIS1 = 4*x_PBO_VIS1 - x_PBO_VIS2 - x_PBO_VIS3 - x_PBO_VIS4 + 4*x_TRT_VIS1 - x_TRT_VIS2 - x_TRT_VIS3 - x_TRT_VIS4
#> # TRT:VIS2 = x_PBO_VIS2 + x_TRT_VIS2
#> # TRT:VIS3 = x_PBO_VIS3 + x_TRT_VIS3
#> # TRT:VIS4 = x_PBO_VIS4 + x_TRT_VIS4
```

The example in this vignette uses the “successive cells” archetype, where fixed effects represent successive differences between adjacent time points.

```
summary(brm_archetype_successive_cells(data, intercept = FALSE))
#> # This is the "successive cells" 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS1 + x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_PBO_VIS4
#> # TRT:VIS1 = x_TRT_VIS1
#> # TRT:VIS2 = x_TRT_VIS1 + x_TRT_VIS2
#> # TRT:VIS3 = x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3
#> # TRT:VIS4 = x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3 + x_TRT_VIS4
```

There is also a treatment effect version of the successive differences archetype:

```
summary(brm_archetype_successive_effects(data, intercept = FALSE))
#> # 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS1 + x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_PBO_VIS4
#> # TRT:VIS1 = x_PBO_VIS1 + x_TRT_VIS1
#> # TRT:VIS2 = x_PBO_VIS1 + x_PBO_VIS2 + x_TRT_VIS1 + x_TRT_VIS2
#> # TRT:VIS3 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3
#> # TRT:VIS4 = x_PBO_VIS1 + x_PBO_VIS2 + x_PBO_VIS3 + x_PBO_VIS4 + x_TRT_VIS1 + x_TRT_VIS2 + x_TRT_VIS3 + x_TRT_VIS4
```

Archetypes can be customized. As an example, consider the simple cell means archetype.

```
summary(brm_archetype_cells(data))
#> # This is the "cells" 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS4
#> # TRT:VIS1 = x_TRT_VIS1
#> # TRT:VIS2 = x_TRT_VIS2
#> # TRT:VIS3 = x_TRT_VIS3
#> # TRT:VIS4 = x_TRT_VIS4
```

To include an intercept term which all the marginal means share, set
`intercept = TRUE`

.

```
summary(brm_archetype_cells(data, intercept = TRUE))
#> # This is the "cells" 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS1 + x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS1 + x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS1 + x_PBO_VIS4
#> # TRT:VIS1 = x_PBO_VIS1 + x_TRT_VIS1
#> # TRT:VIS2 = x_PBO_VIS1 + x_TRT_VIS2
#> # TRT:VIS3 = x_PBO_VIS1 + x_TRT_VIS3
#> # TRT:VIS4 = x_PBO_VIS1 + x_TRT_VIS4
```

To set up constrained longitudinal data analysis (cLDA), set
`clda = TRUE`

. This constraint pools all treatment groups at
baseline, and it can help model clinical trials where a baseline
measurement is observed before randomization. Some archetypes cannot
support cLDA (e.g. `brm_archetype_average_cells()`

and
`brm_archetype_average_effects()`

).

```
summary(brm_archetype_cells(data, clda = TRUE))
#> # This is the "cells" 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).
#> #
#> # PBO:VIS1 = x_PBO_VIS1
#> # PBO:VIS2 = x_PBO_VIS2
#> # PBO:VIS3 = x_PBO_VIS3
#> # PBO:VIS4 = x_PBO_VIS4
#> # TRT:VIS1 = x_PBO_VIS1
#> # TRT:VIS2 = x_TRT_VIS2
#> # TRT:VIS3 = x_TRT_VIS3
#> # TRT:VIS4 = x_TRT_VIS4
```

`brm_recenter_nuisance()`

can retroactively recenter a nuisance column to a fixed value other than its mean.↩︎`summary()`

also invisibly returns a simple character vector with the equations below.↩︎`brms`

priors are documented in https://paul-buerkner.github.io/brms/reference/set_prior.html.↩︎