---
title: "Simulations for Non-inferiority trials"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Simulations for Non-inferiority trials}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## Introduction

Non-inferiority tests are used in clinical trials when the objective is to
demonstrate that a new treatment is not significantly worse than a reference
treatment by more than a pre-specified margin.

In designs involving multiple outcomes, it may be required that some outcomes
meet strict non-inferiority criteria (e.g., the primary outcomes) while others
can meet more flexible conditions (e.g., at least two out of three secondary
outcomes).

This vignette shows how to use the `sim_power_ni_normal()` function from the
**ssutil** package to estimate power in such a design.

## Example

What is the empirical power of a trial that wants to evaluate non-inferiority
of the immune response for a vaccine against 7 serotypes? Non-inferiority is
achieved if the geometric mean ratio between the candidate vaccine and the
reference is greater than 0.5 for the first two antigens, and for three of the 
other five.

This example simulates 1000 trials with 125 participants per group, 
7 independent outcomes, a standard deviation of 0.8 on the log10 scale for all 
outcomes, and a common non-inferiority margin equivalent to log10(2/3). 
Non-inferiority is required in the first two outcomes, and in at least three 
of the remaining five.

```{r noninferiority-example}
library(ssutil)
set.seed(123)

res <- sim_power_ni_normal(
  nsim = 1000,
  npergroup = 125,
  ntest = 7,
  ni_limit = log10(2/3),
  test_req = 2,
  test_opt = 3,
  sd = 0.8,
  corr = 0,
  t_level = 0.05
)

res
```

The result shows the proportion of simulations in which the full
non-inferiority rule was satisfied.

```{r setup}
library(ssutil)
```
