# 5-arm cluster randomized design

#1

Reposting hidden post by Macartan.

We are interested in a 5 arm trial with clusters. The 5 arm trial admits 5*4/2 comparisons of arms (10!). Plus one might be interested in various estimands that group arms together in different ways.

# Using the design library to get going

To get going lets look at standard code for a 5 arm trial from the multiarm designer:

``````get_design_code(multi_arm_designer(m_arms = 5))
``````

# New design

Now lets base a design off that, but add in clusters. Note that there is an individual level shock and a cluster shock: the ICC is determined by the relative size of these. These are kept at the top as arguments to make them easier to modify though they will get saved into the design object.

``````N  <-  30
outcome_means  <-  c(0, 0, .2, .5, 1)
sd_i  <-  1
sd_cluster <- 0
outcome_sds  <-  c(0, 0, 0, 0, 0)
N_clusters <- 20
N_i_in_clusters <- 10

population <- declare_population(
clusters = add_level(N = N_clusters, u_c = rnorm(N)*sd_cluster),
u_1 = rnorm(N, 0, outcome_sds[1L]),
u_2 = rnorm(N, 0, outcome_sds[2L]), u_3 = rnorm(N, 0, outcome_sds[3L]),
u_4 = rnorm(N, 0, outcome_sds[4L]), u_5 = rnorm(N, 0, outcome_sds[5L]),
u = rnorm(N) * sd_i))

potential_outcomes <- declare_potential_outcomes(formula = Y ~ (outcome_means[1] +
u_1) * (Z == "1") + (outcome_means[2] + u_2) * (Z == "2") +
(outcome_means[3] + u_3) * (Z == "3") + (outcome_means[4] +
u_4) * (Z == "4") + (outcome_means[5] + u_5) * (Z == "5") +
+ u_c + u, conditions = c("1", "2", "3", "4", "5"), assignment_variables = Z)

estimand <- declare_estimands(ate_Y_2_1 = mean(Y_Z_2 - Y_Z_1), ate_Y_3_1 = mean(Y_Z_3 -
Y_Z_1), ate_Y_4_1 = mean(Y_Z_4 - Y_Z_1), ate_Y_5_1 = mean(Y_Z_5 -
Y_Z_1), ate_Y_3_2 = mean(Y_Z_3 - Y_Z_2), ate_Y_4_2 = mean(Y_Z_4 -
Y_Z_2), ate_Y_5_2 = mean(Y_Z_5 - Y_Z_2), ate_Y_4_3 = mean(Y_Z_4 -
Y_Z_3), ate_Y_5_3 = mean(Y_Z_5 - Y_Z_3), ate_Y_5_4 = mean(Y_Z_5 -
Y_Z_4))

assignment <- declare_assignment(num_arms = 5, conditions = c("1", "2", "3",
"4", "5"), clusters = clusters, assignment_variable = Z)

reveal_Y <- declare_reveal(assignment_variables = Z)

estimator <- declare_estimator(handler = function(data) {
estimates <- rbind.data.frame(
ate_Y_2_1 = difference_in_means(formula = Y ~ Z, data = data, clusters = clusters,
condition1 = "1", condition2 = "2"),
ate_Y_3_1 = difference_in_means(formula = Y ~ Z, data = data, clusters = clusters,
condition1 = "1", condition2 = "3"),
ate_Y_4_1 = difference_in_means(formula = Y ~
Z, data = data, clusters = clusters, condition1 = "1", condition2 = "4"),
ate_Y_5_1 = difference_in_means(formula = Y ~ Z, data = data, clusters = clusters,
condition1 = "1", condition2 = "5"),
ate_Y_3_2 = difference_in_means(formula = Y ~
Z, data = data, clusters = clusters, condition1 = "2", condition2 = "3"),
ate_Y_4_2 = difference_in_means(formula = Y ~ Z, data = data, clusters = clusters,
condition1 = "2", condition2 = "4"),
ate_Y_5_2 = difference_in_means(formula = Y ~
Z, data = data, clusters = clusters, condition1 = "2", condition2 = "5"),
ate_Y_4_3 = difference_in_means(formula = Y ~ Z, data = data, clusters = clusters,
condition1 = "3", condition2 = "4"),
ate_Y_5_3 = difference_in_means(formula = Y ~
Z, data = data, clusters = clusters, condition1 = "3", condition2 = "5"),
ate_Y_5_4 = difference_in_means(formula = Y ~ Z, data = data, clusters = clusters,
condition1 = "4", condition2 = "5"))
estimates\$estimator_label <- "DIM"
estimates\$estimand_label <- rownames(estimates)
estimates\$estimate <- estimates\$coefficients
estimates\$term <- NULL
return(estimates)
})

multi_arm__cluster_design <- population + potential_outcomes + assignment +
reveal_Y + estimand + estimator
``````

# Using the design

Simulated data for this design looks like this

``````kable(head(draw_data(multi_arm__cluster_design)))
``````

A diagnosis looks like this:

``````sims <- 500

diagnosis <- diagnose_design(multi_arm__cluster_design, sims = sims)

kable(reshape_diagnosis(diagnosis))
``````

A diagnosis for different numbers of clusters would look like this:

``````designs <- redesign(multi_arm__cluster_design, N_clusters = c(40, 50))
diagnoses <- diagnose_design(designs, sims = sims)
kable(reshape_diagnosis(diagnoses))

``````

# Note

Say you are interested in a 2*2+1 design. This is a 5 arm trial and so you could use the code above. However you might want to rethink the estimands and estimators. The current estimands compare each cell to each other but you might instead be interested in comparing combinations of cells. To get a sense of factorial estimands like this have a look at the `simple_factorial_designer` code.