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---
title: Prediction when testing and training are stratified by a collider
---

## Background

In Menni et al 2020 they look for risk factors that associate with testing positive. They then create a model to predict test status in untested individuals using those risk factors.

The risk factors, and testing positive, both influence whether individuals are tested. Therefore, the associations in the tested sample are likely biased due to colliders, and not transportable to those in the untested sample.

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---
title: Data generating process underlying causal inference using Mendelian randomization
author: Gibran Hemani
date: '`r format(Sys.Date())`'
---


## Background

Causal inference between two traits, the exposure's ($x$) effect on the outcome ($y$) can be made using associations of genetic variants $g$ on $x$ and $y$. This method is known as Mendelian randomization (MR), a special case of instrumental variable (IV) analysis where the instrument is a genetic variant. Assume the following causal structure:

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library(mvtnorm)
library(psych)

n <- 100000
dn <- rmvnorm(n, c(0,0), matrix(c(1,0.5, 0.5,1), 2))

# 50% prevalence
d <- dn
d[,1] <- rbinom(n, 1, pnorm(d[,1]))

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maf <- function(x) { sum(x) / (length(x) * 2)}

hwe <- function(x) {
	observed <- table(x)
	m <- maf(x)
	expected <- c(
		(1-m)^2, 2 * m * (1-m), m^2
	) * length(x) 
	chisq.test(rbind(observed, round(expected)))
	print(rbind(observed, round(expected)))

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library(ggplot2)
library(tidyr)
library(alspac)
data(current)
vars <- c("cf040", "cf041", "cf042", "cf043", "fh3000")
b <- extractVars(subset(current, name %in% vars))

b1 <- subset(b, select=c("aln", "qlet", vars)) %>% filter(!apply(., 1, function(x) any(is.na(x))))

for(i in vars)

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for i in {1..22}
do
plink --bfile /mnt/storage/private/mrcieu/research/mr-eve/vcf-reference-datasets/1000g_filtered/data_maf0.01_rs --chr $i --make-bed --out ld/ref/data_$i
done

for i in {1..22}
do
bcftools query -r $i -f '%ID\t%POS\t%REF\t%ALT\t%B\t%SE\n' ../data.bcf | awk 'BEGIN {print "rsID\tpos\tA0\tA1\tZ"; OFS="\t"}; { print $1, $2, $3, $4, $5/$6}' > ld/ref/z_2_$i.txt
done

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library(TwoSampleMR)
library(RadialMR)
library(MendelianRandomization)

# Read in example data
a <- extract_instruments(2)
b <- extract_outcome_data(a$SNP, 7)
ab <- harmonise_data(a,b)
ab$SNP <- as.character(ab$SNP)
# IVW in TwoSampleMR package

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#!/bin/bash

# Download 1000 genomes

wget ALL.chr1.phase3_shapeit2_mvncall_integrated_v5a.20130502.genotypes.vcf.gz
wget ALL.chr1.phase3_shapeit2_mvncall_integrated_v5a.20130502.genotypes.vcf.gz.tbi
wget ALL.chr10.phase3_shapeit2_mvncall_integrated_v5a.20130502.genotypes.vcf.gz
wget ALL.chr10.phase3_shapeit2_mvncall_integrated_v5a.20130502.genotypes.vcf.gz.tbi
wget ALL.chr11.phase3_shapeit2_mvncall_integrated_v5a.20130502.genotypes.vcf.gz
wget ALL.chr11.phase3_shapeit2_mvncall_integrated_v5a.20130502.genotypes.vcf.gz.tbi

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#===================================#
#          GWAS Practical           #
#      iBSC Genomic Medicine        #
#       Lavinia Paternoster         #
#           08/11/2018              #
#===================================#


# Run the GWAS without PCs but using the cleaned genetic data