simulation 2018 07 02 appendix.rmd

---
title: "Appendix - Simulation experiment mediation analysis"
author: "Elmar W. Tobi, Erik W. van Zwet, L.H. Lumey, Bastiaan T. Heijmans"
date: "July 2, 2018"
output: 
  html_document:
    toc: true
---

Set options.
```{r set-options}
options(width = 200)
```

# Introduction

Simulation.

```{r, echo = TRUE, message=FALSE,warning=FALSE}
setwd("M:\\projects\\Tobi\\mediation artikel\\rebuttal")
set.seed(123)    # fix seed of RNG for reproducibility
library(bda)     # for Sobel test

n1=350
n2=650
n=n1+n2
Famine  = c(rep(0,n1),rep(1,n2))  # Exposure to Famine

K=1000          # number of simulations
```

# Scenario Mediation

![](5-PartialMediation.png){width=50%}

\bigskip


```{r, echo = TRUE, message=FALSE,warning=FALSE}
a=0.4
b=0.1
c=0.2

pval=numeric(K)
for (ind in 1:K){
  DNAm    = a * Famine + rnorm(n,0,1)
  Health  = c * Famine + b *DNAm + rnorm(n,0,1)
  fit  = mediation.test(mv=DNAm,iv=Famine,dv=Health)
  pval[ind] = fit[2,1]
}
power = mean(pval<0.05)
power
```


# Scenario Reverse Causation


![](6-PartialReverseCausation.png){width=50%}

\bigskip


```{r, echo = TRUE, message=FALSE,warning=FALSE}
d=0.3
e=0.1
f=0.1

pval=numeric(K)
for (ind in 1:K){
  Health  = d * Famine + rnorm(n,0,1)
  DNAm    = f * Famine + e * Health + rnorm(n,0,1)
  fit  = mediation.test(mv=DNAm,iv=Famine,dv=Health)
  pval[ind] = fit[2,1]
}
power = mean(pval<0.05)
power
```

# Session information

```{r, warning=FALSE, message=FALSE}
sessionInfo()
```