interaction/index.Rmd at main · ehsanx/interaction · GitHub

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---
title: "Assessing interation in epidemiological studies"
author: "Ehsan Karim, ehsan.karim@ubc.ca, https://ehsank.com/"
date: "`r Sys.Date()`"
site: bookdown::bookdown_site
documentclass: book
bibliography: [ref.bib]
description: |
  Interactions and effect modifications.
link-citations: yes
github-repo: ehsanx/interaction
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
require(SASxport)
require(DiagrammeR)
require(DiagrammeRsvg)
require(rsvg)
library(magrittr)
library(svglite)
library(png)
require(nhanesA)
require(survey)
require(Publish)
require(knitr)
require(jtools)
require(interactions)
require(interactionR)
require(mosaic)
require(epiR)
cache.ON = TRUE
```

# Definitions

## Effect modification

Causal effect of exposure (A) on outcome (Y) depends upon levels of a third factor (B). This is the scenario when the exposure-outcome association differs within the strata of a 2nd exposure (2nd exposure = effect modifier). Interaction term is often added on a logistic regression model to assess the impact.

```{r dagem, echo=FALSE, fig.cap="An illustration of possible effect modification by a dichotomous factor $B$ (tobacco smoking [**smk**]) while investigating the impact of a dichotomous factor $A$ (alcohol [**alc**]) on the dichotomous outcome $Y$ (oral cancer [**oc**]).\\label{fig:dagem}", out.width = '50%'}
knitr::include_graphics("images/dagem.png")
```

## Interaction

Causal effect of combination of multiples exposures (A and B) on outcome (Y). Interaction is the joint causal effect of two exposures on an outcome.

```{r dag, echo=FALSE, fig.cap="An illustration of possible interaction by  while investigating the impact of two dichotomous factors: $A$ (alcohol [**alc**]) and $B$ (tobacco smoking [**smk**]) on the dichotomous outcome $Y$ (oral cancer [**oc**]).\\label{fig:dag}", out.width = '50%'}
knitr::include_graphics("images/dag.png")
```


## Example data

**Data source**: @rothman1972effect

```{r}
require(interactionR)
data(OCdata)
dim(OCdata)
summary(OCdata)
```

Variables

- **oc**, oral cancer, outcome (Y)
- **alc**, alcohol use, first exposure (A)
- **smk**, smoking, second exposure (B)

```{r}
outcome = "oc"
ex = "alc"
dataset = OCdata
M <- table(dataset[[ex]], dataset[[outcome]])
rownames(M) <- c("Exposure -", "Exposure +")
colnames(M) <- c("Outcome -", "Outcome +")
M
```

### Crude risk ratio
```{r}
require(mosaic)
relrisk(M, verbose = TRUE)
```


### Change exposure label if RR <1

This step is not necessary of RR > 1. The following calculattion assumes that exposure and stratification factors are risk factors for the outcome (RR > 1), not protective factors. If protective, estimates of RERI and AP will be invalid, although the estimate of SI is not affected by this condition.

```{r}
M3 <- matrix(c(M[2,2],M[2,1],M[1,2],M[1,1]), nrow = 2, byrow = TRUE)
require(epiR)
```

### Get detailed estimates from 2x2 table

```{r}
require(epiR)
res <- epi.2by2(dat = M3, method = "cross.sectional",
         conf.level = 0.95, units = 1,
         interpret = FALSE,
         outcome = "as.columns")
res
```

Check the results yourself
```{r}
p1 <- as.numeric(strsplit(as.character(res$tab$`              Prevalence *`), " ")[[1]][1])
p0 <- as.numeric(strsplit(as.character(res$tab$`              Prevalence *`), " ")[[2]][1])
RR <- p1/p0
RR
RD <- p1 - p0
RD
OR <- (p1/(1-p1))/(p0/(1-p0))
OR
```

## Further reading

Useful references

- @vanderweele2009distinction,
- @vanderweele2011interpretation,
- @rothman2012epidemiology,
- @vanderweele2014tutorial,
- @bours2021tutorial,
- @whitcomb2023interaction