This package is used to assess non-linear exposure-outcome relationships using instrumental variable (IV) analysis in the context of Mendelian randomisation (MR). In this package, there are two IV methods for investigating the shape of the exposure-outcome relationship: a fractional polynomial method (frac_poly_mr) and a piecewise linear method (piecewise_mr). The population (i.e. one-sample) is divided into strata using the exposure distribution, and a causal effect is estimated, referred to as a localized average causal effect (LACE), in each stratum. The fractional polynomial method fits across these LACE using meta-regression. The piecewise linear method estimates a continuous piecewise linear function by consecutively adding the LACE together.

• frac_poly_mr - this method performs IV analysis using fractional polynomials
• piecewise_mr - this method performs IV analysis using piecewise linear function

1. install.packages("devtools")
2. library(devtools)
3. install_github("jrs95/nlmr")
4. library(nlmr)

### IV (g), exposure (x) & outcome (y)
epsx = rexp(10000)
u = runif(10000, 0, 1)
g = rbinom(10000, 2, 0.3)
epsy = rnorm(10000)
ag = 0.25
x = 1 + ag*g + u + epsx
y = 0.15*x^2 + 0.8*u + epsy

### Covariates (c) & covariate types (c_type)
c1 = rnorm(10000)
c2 = rnorm(10000)
c3 = rbinom(10000,2,0.33)
c = data.frame(c1=c1, c2=c2, c3=as.factor(c3))
c_type = c("numeric", "numeric", "factor")

### Analyses
fp = frac_poly_mr(y, x, g, c, c_type, family="gaussian", q=10, d=1, ci="model_se", fig=T)
summary(fp)
plm = piecewise_mr(y, x, g, c, c_type, family="gaussian", q=10, nboot=50, fig=T)
summary(plm)

James R Staley & Stephen Burgess, Semiparametric methods for estimation of a non-linear exposure-outcome relationship using instrumental variables with application to Mendelian randomization. Genetic Epidemiology. 2017;41(4):341-352. Link: http://onlinelibrary.wiley.com/doi/10.1002/gepi.22041/abstract