---
title: "CMR Extensions"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{CMR Extensions}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

This vignette shows three extension workflows that keep the same applied
pattern: pass simulated pilot outcomes and design labels, inspect the main-wave
allocation, and record the CMR certificate.

```{r setup}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")
library(cmrdesign)
```

## Shared-control multi-arm designs

Use `cmr_multiarm()` when the pilot has multiple treatment arms and one shared
control group. The outcome vector `y` has one entry per pilot unit, and `arm`
labels the corresponding arm. The control arm is standardized to `"0"` in the
result.

```{r multiarm}
set.seed(505)

n_per_arm <- 180
arm <- rep(c(0, 1, 2), each = n_per_arm)
y <- c(
  rbeta(n_per_arm, shape1 = 4, shape2 = 4),
  rbeta(n_per_arm, shape1 = 2.5, shape2 = 6),
  rbeta(n_per_arm, shape1 = 5, shape2 = 3)
)

fit_multi <- cmr_multiarm(y, arm, alpha = 0.05, method = "bounded")

round(fit_multi$pi, 3)
fit_multi$U_CMR
fit_multi$method
fit_multi$pilot$n
```

The returned `pi` is a named vector of total main-wave assignment shares across
control and all treatment arms.

## Stratified designs

Use `cmr_stratified()` when the main-wave allocation should adapt across known
target-population strata. The `strata_share` input should describe the target
population shares, not only the realized pilot composition.

```{r stratified}
set.seed(506)

n_per_cell <- 100
strata <- rep(c("urban", "rural"), each = 2 * n_per_cell)
d <- rep(c(rep(1, n_per_cell), rep(0, n_per_cell)), times = 2)
y <- c(
  rbeta(n_per_cell, shape1 = 2, shape2 = 5),
  rbeta(n_per_cell, shape1 = 4, shape2 = 4),
  rbeta(n_per_cell, shape1 = 3, shape2 = 6),
  rbeta(n_per_cell, shape1 = 5, shape2 = 4)
)
strata_share <- c(urban = 0.55, rural = 0.45)

fit_strata <- cmr_stratified(
  y = y,
  d = d,
  strata = strata,
  strata_share = strata_share,
  alpha = 0.05,
  method = "bounded"
)

round(fit_strata$pi_matrix, 3)
round(fit_strata$sampling_margin, 3)
round(fit_strata$treatment_margin, 3)
fit_strata$U_CMR
```

`pi_matrix` gives the total assignment share for each treatment/control by
stratum cell. `sampling_margin` gives the total sample share assigned to each
stratum, and `treatment_margin` gives the treatment share within each stratum.

## Raw unbounded outcomes

Use `cmr_unbounded()` when the two-arm outcome is raw and finite but not
assumed to be bounded on a known scale. This method requires a bounded-kurtosis
input `psi`. It is currently a two-arm extension only.

```{r unbounded}
set.seed(507)

n_per_arm <- 1500
d <- c(rep(1, n_per_arm), rep(0, n_per_arm))
y <- c(
  0.20 + 1.10 * rt(n_per_arm, df = 8),
  0.00 + 0.70 * rt(n_per_arm, df = 8)
)

fit_unbounded <- cmr_unbounded(
  y = y,
  d = d,
  psi = c(treatment = 6, control = 6),
  alpha = 0.10
)

fit_unbounded$pi
fit_unbounded$U_CMR
fit_unbounded$pilot[c("rho", "b", "active", "status")]
```

If the median-of-means variance interval is inactive because the pilot is too
small, the relative radius is too large, or the variance estimate is zero, the
function returns the balanced assignment with no finite certificate. Check
`fit_unbounded$pilot$status` before using the result.