---
title: "Simulations for Negative Binomial outcomes"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Negative Binomial outcomes}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

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


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

## Introduction

The `sim_power_nbinom` function is used to estimate the empirical power of a 
negative binomial regression model. This method is useful when outcomes consist 
of over dispersed count data, and the objective is to test whether the relative 
risk (RR) between two groups differs significantly from a null boundary.

Data are simulated under a negative binomial distribution, a model is fit 
using `glm.nb`, and it is determined whether the null hypothesis is rejected 
based on confidence interval limits relative to a specified boundary. The 
procedure accounts for whether the true RR is below or above 1, applying the 
appropriate directional test logic.


## Example

What is the empirical power using negative binomial regression to detect efficacy of
vaccine with a 95% lower vaccine efficacy boundary above 30% assuming the true vaccine efficacy is 60%?
if the sample size is 500 per group average follow-up of 1 year, the event rate is 0.25 
episode per person-year in the control group, and the dispersion parameter is 2?

```{r example-sim-power-vaccine, message=FALSE}
library(ssutil)
set.seed(123)
result <- sim_power_nbinom(
  n1 = 500, n2 = 500,
  ir1 = 0.2, tm = 1,
  rr = 0.4, boundary = 0.7,
  dispersion = 2,
  alpha = 0.05,
  nsim = 1000
)

result
```


