Quantile G-Computation

G-computation for a set of time-fixed exposures with quantile-based basis functions, possibly under linearity and homogeneity assumptions. This approach estimates a regression line corresponding to the expected change in the outcome (on the link basis) given a simultaneous increase in the quantile-based category for all exposures. Reference: Alexander P. Keil, Jessie P. Buckley, Katie M. OBrien, Kelly K. Ferguson, Shanshan Zhao Alexandra J. White (2019) A quantile-based g-computation approach to addressing the effects of exposure mixtures; [stat.ME].

Quick start

#install.packages("devtools") # if devtools package not already installed, uncomment this line
# developers version
devtools::install_github("alexpkeil1/qgcomp", build_opts = c("--no-resave-data", "--no-manual", "--build-vignettes"))
library("qgcomp")
# using data from the qgcomp package
data("metals", package="qgcomp")

Xnm <- c(
'arsenic','barium','cadmium','calcium','chloride','chromium','copper',
'iron','lead','magnesium','manganese','mercury','selenium','silver',
'sodium','zinc'
)

# continuous outcome
results = qc.fit <- qgcomp.noboot(y~.,dat=metals[,c(Xnm, 'y')], family=gaussian())
print(results)
>  calcium manganese   mercury  chloride      zinc    sodium  selenium 
>   0.5974    0.0791    0.0761    0.0739    0.0704    0.0658    0.0373 
>
>Scaled effect size (negative direction, sum of negative coefficients = -0.0732)
>magnesium   cadmium    silver      lead   arsenic    copper  chromium    barium      iron 
>   0.2673    0.1758    0.1303    0.1047    0.0872    0.0831    0.0796    0.0584    0.0136 
>
>Mixture slope parameters (Delta method CI):
>
>     Estimate Std. Error  Lower CI Upper CI t value Pr(>|t|)
>psi1 0.044589   0.019180 0.0069964 0.082182  2.3247  0.02055    
plot(results)

# binary outcome
results2 = qgcomp.noboot(disease_state~., expnms=Xnm, 
           data = metals[,c(Xnm, 'disease_state')], family=binomial(), q=4)
print(results2)

>Scaled effect size (positive direction, sum of positive coefficients = 1.83)
> mercury  arsenic  cadmium selenium   silver   copper chloride   sodium chromium   barium 
> 0.41512  0.22194  0.11081  0.11037  0.03762  0.03140  0.02883  0.02714  0.01515  0.00161 
>
>Scaled effect size (negative direction, sum of negative coefficients = -0.851)
>manganese      lead      zinc      iron magnesium   calcium 
>   0.5635    0.2145    0.1342    0.0358    0.0307    0.0213 
>
>Mixture log(OR) (Delta method CI):
>
>     Estimate Std. Error Lower CI Upper CI Z value Pr(>|z|)
>psi1  0.97669    0.37724   0.2373   1.7161   2.589 0.009625
>
    
plot(results2)

adjusting for covariate(s)

results3 = qgcomp.noboot(y ~ mage35 + arsenic + barium + cadmium + calcium + chloride + 
                       chromium + copper + iron + lead + magnesium + manganese + 
                       mercury + selenium + silver + sodium + zinc,
                     expnms=Xnm,
                     metals, family=gaussian(), q=4)
print(results3)

> Scaled effect size (positive direction, sum of positive coefficients = 0.117)
>   calcium manganese   mercury  chloride      zinc    sodium  selenium 
>    0.5989    0.0800    0.0749    0.0736    0.0681    0.0599    0.0445 
> 
> Scaled effect size (negative direction, sum of negative coefficients = -0.0689)
> magnesium   cadmium    silver      lead  chromium    copper    barium   arsenic      iron 
>    0.2793    0.1454    0.1378    0.0967    0.0930    0.0865    0.0727    0.0647    0.0239 
> 
> Mixture slope parameters (Delta method CI):
> 
>      Estimate Std. Error Lower CI Upper CI t value Pr(>|t|)
> psi1 0.048393   0.019269 0.010627 0.086159  2.5115  0.01238
# coefficient for confounder
results3$fit$coefficients['mage35']
>      mage35 
> -0.02099359 

Bootstrapping to get population average risk ratio via g-computation using qgcomp.boot

results4 = qgcomp.boot(disease_state~., expnms=Xnm, 
      data = metals[,c(Xnm, 'disease_state')], family=binomial(), 
      q=4, B=10,# B should be 200-500+ in practice
      seed=125, rr=TRUE)
print(results4)

> Mixture log(RR) (bootstrap CI):
> 
>      Estimate Std. Error Lower CI Upper CI Z value  Pr(>|z|)
> psi1  0.31318    0.07747  0.16134  0.46502  4.0426 5.286e-05

# checking whether model fit seems appropriate 
plot(results4)

Allowing for interactions and non-linear terms using qgcomp.boot

results5 = qgcomp(y~. + .^2 + arsenic*cadmium,
                     expnms=Xnm,
                     metals[,c(Xnm, 'y')], family=gaussian(), q=4, B=10, 
                     seed=125, degree=2)

print(results5)

> Mixture slope parameters (bootstrap CI):
> 
>         Estimate  Std. Error Lower CI Upper CI t value Pr(>|t|)
> psi1 -0.00090979  0.27733904 -0.54448  0.54266 -0.0033   0.9974
> psi2  0.01124374  0.09166007 -0.16841  0.19089  0.1227   0.9024

# some apparent non-linearity, but would require more bootstrap iterations for
# proper test of non-linear mixture effect
plot(results5)