---
title: "CompAREdesign: Binary endpoints"
author: "Marta Bofill Roig, Jordi Cortés Martínez and Guadalupe Gómez Melis"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Binary endpoints}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include=FALSE, echo=FALSE}
library('CompAREdesign')            # Load library
knitr::opts_chunk$set(echo = TRUE)  # Show code
```

## Binary endpoint: TUXEDO TRIAL

This example is based on the data from the [TUXEDO trial](https://doi.org/10.1056/nejmoa1510188) [1].

The Taxus Element versus Xience Prime in a Diabetic Population (TUXEDO)–India study is an investigator-initiated, multicenter, randomized clinical trial. The trial protocol is available with the full text of this article at NEJM.org. The trial was funded by Boston Scientific, the manufacturer of the paclitaxeleluting stent (Taxus Element). 

### Input Parameters

To use the functions in CompAREdesign, we first of all need to include the information for the components of the composite endpoint.

```{r}
## Probabilities of observing the event in control arm at the end of follow-up
p0_e1 <- 0.059    # Ischemia-driven target-lesion revascularization 
p0_e2 <- 0.032    # Cardiac death or target-vessel MI 

## Effect size (absolute reduction) for each endpoint
AR_e1 <- -0.0196  # Ischemia-driven target-lesion revascularization 
AR_e2 <- -0.0098  # Cardiac death or target-vessel MI

## Correlation
rho   <- 0.4
```

### ARE: Asymptotic Relatively Efficiency

Aiming to compare the gain in power of using the composite endpoint over the most relevant of its components. One can use the function ARE. 
As the ARE is greater than 1, we can state that the design using the composite endpoint is more efficient.

```{r}
ARE_cbe(p0_e1   = p0_e1  , p0_e2   = p0_e2, 
        eff_e1  = AR_e1  , eff_e2  = AR_e2, 
        effm_e1 = "diff" , effm_e2 = "diff", effm_ce = "or",
        rho     = rho) 
```

### Effect size of the Composite Endpoint

If we can anticipate the baseline information of the composite components and expected effect sizes together with the correlation between the components, we can obtain the expected treatment effect on the composite endpoint (odds ratio, *OR*).

```{r}
effectsize_cbe(p0_e1   = p0_e1  , p0_e2   = p0_e2, 
               eff_e1  = AR_e1  , eff_e2  = AR_e2, 
               effm_e1 = "diff" , effm_e2 = "diff", effm_ce = "or",
               rho     = rho) 
```

### Sample size

Lastly, we can compute the required sample size for the design using the composite endpoint, in this case obtaining **2644**.

```{r}
samplesize_cbe(p0_e1   = p0_e1  , p0_e2   = p0_e2, 
               eff_e1  = AR_e1  , eff_e2  = AR_e2, 
               effm_e1 = "diff" , effm_e2 = "diff", effm_ce = "or",
               rho     = rho,
               alpha   = 0.05, beta = 0.2) 
```

## References

1. Kaul U, Bangalore S, Seth A, Priyadarshini A, Rajpal KA, Tejas MP et al. Paclitaxel-Eluting versus EverolimusEluting Coronary Stents in Diabetes. N Engl J Med. 2015;373(18):1709-19.



```{r, echo = FALSE}
rm(list = ls())
```