explodecomputer

explodecomputer

# simulation
n <- 10000
a <- rbinom(n, 2, 0.5)
b <- rbinom(n, 2, 0.49)

# perform fisher's exact test to obtain odds ratio for two allele frequencies being different
cont <- matrix(
	c(sum(a==0) * 2 + sum(a==1), sum(a==2) * 2 + sum(a==1), sum(b==0) * 2 + sum(b==1), sum(b==2) * 2 + sum(b==1)), 2, 2)

fisher.test(cont)

explodecomputer

# Number of individuals in the population
npop <- 100000

# Distribution of variable in the population
x <- rnorm(npop)

# Individuals selected into sample with high x value
s <- rbinom(npop, 1, plogis(x * 0.4))

# Population mean of x

explodecomputer

library(dplyr)
library(data.table)
library(TwoSampleMR)

bmi_id <- "ukb-b-19953"

chd_id <- "ukb-b-3983"

datadir <- "/mnt/storage/private/mrcieu/research/mr-eve/UKBB_replication/replication/results"

explodecomputer

---
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.

explodecomputer

---
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:

explodecomputer

explodecomputer

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]))

explodecomputer

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)))

explodecomputer

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)