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

This vignette shows the CMR extensions for multiple bounded outcomes. Outcomes
can be combined into a weighted index or protected as co-primary outcomes.
The outcome object `y` is a matrix with one row per pilot unit and one column
per outcome.

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

## Simulate a pilot with two outcomes

The simulated pilot has a test-score outcome and an attendance outcome, both
scaled to `[0, 1]`.

```{r simulate-multiple-outcomes}
set.seed(303)

n_pilot <- 180
d <- rbinom(n_pilot, size = 1, prob = 0.5)

test_score <- numeric(n_pilot)
attendance <- numeric(n_pilot)

test_score[d == 1] <- rbeta(sum(d == 1), shape1 = 5.5, shape2 = 3.5)
test_score[d == 0] <- rbeta(sum(d == 0), shape1 = 4, shape2 = 4)

attendance[d == 1] <- rbeta(sum(d == 1), shape1 = 7, shape2 = 2.5)
attendance[d == 0] <- rbeta(sum(d == 0), shape1 = 5, shape2 = 3.5)

y <- cbind(test_score = test_score, attendance = attendance)
weights <- c(test_score = 0.7, attendance = 0.3)

by_arm_mean <- rbind(
  treatment = colMeans(y[d == 1, , drop = FALSE]),
  control = colMeans(y[d == 0, , drop = FALSE])
)
round(by_arm_mean, 3)
```

## Weighted-index CMR

With `estimand = "index"`, the package forms the weighted index first and then
constructs the two-arm confidence rectangle for that index.

```{r index-cmr}
fit_index <- cmr_multiple_outcomes(
  y = y,
  d = d,
  weights = weights,
  estimand = "index",
  method = "bounded"
)

fit_index$pi
round(fit_index$rectangle, 4)
fit_index$estimand
fit_index$weights
```

This is the natural option when the main estimand is a prespecified index.

## Co-primary Outcome CMR

With `estimand = "coprimary"`, the package builds outcome-by-arm confidence
bounds and combines them into an effective two-arm variance rectangle using the
prespecified weights.

```{r coprimary-cmr}
fit_coprimary <- cmr_multiple_outcomes(
  y = y,
  d = d,
  weights = weights,
  estimand = "coprimary",
  method = "bounded"
)

fit_coprimary$pi
round(fit_coprimary$rectangle, 4)
fit_coprimary$joint_error_bound
```

The outcome-specific pieces remain available for audit.

```{r outcome-specific-bounds}
names(fit_coprimary$confidence_set$outcome_bounds)
round(fit_coprimary$confidence_set$outcome_vhat$treatment, 4)
round(fit_coprimary$confidence_set$outcome_vhat$control, 4)
```

## Compare index and co-primary designs

```{r compare-index-coprimary}
comparison <- rbind(
  index = c(pi = fit_index$pi, U_CMR = fit_index$U_CMR),
  coprimary = c(pi = fit_coprimary$pi, U_CMR = fit_coprimary$U_CMR)
)

round(comparison, 4)
```

The two designs need not agree because they place different requirements on
the pilot confidence set.