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Additive interactions function.R
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############## ESTIMATES AND INFERENCE FOR ADDITIVE AND MECHANISTIC INTERACTIONS ##############
##### Please cite as follows:
##### Mathur MB & VanderWeele TJ (2018). R function for additive interaction measures. Epidemiology 29(1), e5-e6.
##### Fn: Checks whether both exposure ORs are > 1
causative = function( OR10, OR01 ) {
return( (OR10 > 1) & (OR01 > 1) )
}
##### Fn: Compute additive interaction measures with inference
additive_interactions = function( model, dat=NULL, monotone=0, CI.level=0.95, recode=FALSE ) {
# check for valid logistic regression model
if ( is.null(model$family$link) ) {
stop ("Argument 'model' must be a logistic regression fit with glm()")
} else if ( !model$family$link == "logit" ) {
stop ("Argument 'model' must be a logistic regression fit with glm()")
}
# extract exposure variable names
exposure1 = names(coef(model))[2]
exposure2 = names(coef(model))[3]
# variables to keep for delta method
# requires that the two exposures of interest be listed first in model
# in order to get the right variables in the interaction string
interaction.string = paste(exposure1, exposure2, sep=":")
if ( !(interaction.string %in% names( coef(model) ) ) ) {
stop("Could not identify the interaction coefficient in the model formula, possibly because you used the I() operator. Please enter the interaction using * instead.")
}
keepers = c(exposure1, exposure2, interaction.string)
# get variance-covariance matrix of the GLM
V = as.matrix( vcov(model) )
V2 = V[keepers, keepers] # subset to just the coefficients of interest
# calculate various coefficients and ORs
b10 = coef(model)[exposure1]
b01 = coef(model)[exposure2]
bint = coef(model)[interaction.string]
OR00 = 1.0 # reference
OR10 = exp(b10)
OR01 = exp(b01)
OR11 = exp( b10 + b01 + bint )
# check if we are already in causative case
if( !causative( OR10 = OR10, OR01 = OR01 ) ) {
if(!recode) stop("Error: At least one exposure has negative association with outcome. Set argument recode=TRUE if you would like the exposures to be automatically recoded.")
if(recode) {
# attempt recoding
if (is.null(dat)) stop("Error: Provide data in order to recode preventive exposures")
# find stratum with lowest overall risk, conditional on covariates
temp = data.frame( cat = c("OR10", "OR01", "OR11"), value = c(OR10, OR01, OR11) )
refcat = temp$cat[ which.min(temp$value) ] # get category's name
# extract first "subscript" number
E1.ref = substr( refcat, 3, 3 )
# extract second "subscript" number
E2.ref = substr( refcat, 4, 4 )
# recode each exposure based on new reference category
dat[[exposure1]] = ifelse( dat[[exposure1]] == E1.ref, 0, 1 )
dat[[exposure2]] = ifelse( dat[[exposure2]] == E2.ref, 0, 1 )
# tell user what happened
warning("Recoding exposures; new reference category for ", exposure1, " is ", E1.ref,
" and for ", exposure2, " is ", E2.ref)
# refit model by refitting user's original call
# but with newly recoded dataframe
model = update(model, .~., data=dat)
# get new coefficients and ORs
b10 = coef(model)[exposure1]
b01 = coef(model)[exposure2]
bint = coef(model)[interaction.string]
OR00 = 1.0 # reference
OR10 = exp(b10)
OR01 = exp(b01)
OR11 = exp( b10 + b01 + bint )
}
}
# RERI (VanderWeele pg. 258-259)
RERI = OR11 - exp(b10) - exp(b01) + 1
require(msm)
SE.RERI = deltamethod( ~ exp( x1 + x2 + x3 ) - exp(x1) - exp(x2) + 1,
mean=c( coef(model)[exposure1], coef(model)[exposure2], coef(model)[interaction.string] ),
cov=V2) # this is its SE
# attributable proportion (VanderWeele pg. 256)
AP = RERI / OR11
SE.AP = deltamethod( ~ ( exp( x1 + x2 + x3 ) - exp(x1) - exp(x2) + 1 ) / exp( x1 + x2 + x3 ),
mean=c( coef(model)[exposure1], coef(model)[exposure2], coef(model)[interaction.string] ),
cov=V2) # this is its SE
alpha = 1-CI.level
z = qnorm( 1 - alpha/2 ) # critical value
# RERI p-values for tests vs. nulls of 0, 1, or 2
# for mechanistic conclusions (VanderWeele pg. 275)
p.0 = 1 - pnorm( RERI/SE.RERI )
p.1 = 1 - pnorm( (RERI-1) / SE.RERI )
p.2 = 1 - pnorm( (RERI-2) / SE.RERI )
# based on monotonicity assumption, give p-value for epistatic and sufficient-cause interactions
if (monotone==0) {
p.val.epi = p.2
p.val.suff.cause = p.1
} else if (monotone==1) {
p.val.epi = p.val.suff.cause = p.1
} else if (monotone==2) {
p.val.epi = p.val.suff.cause = p.0
} else {
stop("Argument 'monotone' must be 0, 1, or 2")
}
##### Prop. of joint effect due to each exposure separately or to their interaction ####
# VanderWeele pg. 282
denom = OR11 - 1
E1.contrib = ( exp( coef(model)[exposure1] ) - 1 ) / denom
E2.contrib = ( exp( coef(model)[exposure2] ) - 1 ) / denom
int.contrib = RERI / denom
SE.1 = deltamethod( ~ ( exp(x1) - 1 ) / ( exp( x1 + x2 + x3 ) - 1 ),
mean=c( coef(model)[exposure1], coef(model)[exposure2], coef(model)[interaction.string] ),
cov=V2)
SE.2 = deltamethod( ~ ( exp(x2) - 1 ) / ( exp( x1 + x2 + x3 ) - 1 ),
mean=c( coef(model)[exposure1], coef(model)[exposure2], coef(model)[interaction.string] ),
cov=V2)
SE.3 = deltamethod( ~ ( exp( x1 + x2 + x3 ) - exp(x1) - exp(x2) + 1 ) / ( exp( x1 + x2 + x3 ) - 1 ),
mean=c( coef(model)[exposure1], coef(model)[exposure2], coef(model)[interaction.string] ),
cov=V2)
alpha = 1-CI.level
z = qnorm( 1 - alpha/2 ) # critical value
##### Return results #####
rs = data.frame( Stat = c( "RERI", "AP", exposure1, exposure2, interaction.string ),
Est = c( RERI, AP, E1.contrib, E2.contrib, int.contrib ),
CI.lo = c( RERI - z*SE.RERI, AP - z*SE.AP, E1.contrib - z*SE.1, E2.contrib - z*SE.2, int.contrib - z*SE.3 ),
CI.hi = c( RERI + z*SE.RERI, AP + z*SE.AP, E1.contrib + z*SE.1, E2.contrib + z*SE.2, int.contrib + z*SE.3 ),
p.val.0 = c( p.0, ( 1 - pnorm( abs(AP)/SE.AP) ), ( 1 - pnorm(E1.contrib/SE.1) ), ( 1 - pnorm(E2.contrib/SE.2) ), ( 1 - pnorm(int.contrib/SE.3) ) ),
p.val.epi = c( p.val.epi, NA, NA, NA, NA ),
p.val.suff.cause = c( p.val.suff.cause, NA, NA, NA, NA )
)
rownames(rs) = NULL
if (monotone == 1) cat("\nAssuming AT LEAST ONE of exposures has positive monotonic effect\n\n")
if (monotone == 2) cat("\nAssuming BOTH exposures have positive monotonic effect\n\n")
print(rs)
invisible(rs)
}