qgcomp (version 2.2.2)

pointwisebound.noboot: estimating pointwise comparisons for qgcomp.noboot objects

Description

Calculates: expected outcome (on the link scale), mean difference (link scale) and the standard error of the mean difference (link scale) for pointwise comparisons

Usage

pointwisebound.noboot(x, alpha = 0.05, pointwiseref = 1)

Arguments

x

"qgcompfit" object from `qgcomp.boot`,

alpha

alpha level for confidence intervals

pointwiseref

referent quantile (e.g. 1 uses the lowest joint-exposure category as the referent category for calculating all mean differences/standard deviations)

Value

A data frame containing expected values of the outcome at each quantized value of all exposures as well as a mean difference contrasting the expected outcome at each quantized value of all exposures, and associated standard error and confidence intervals.

Details

The comparison of interest following a qgcomp fit is often comparisons of model predictions at various values of the joint-exposures (e.g. expected outcome at all exposures at the 1st quartile vs. the 3rd quartile). The expected outcome at a given joint exposure and at a given level of non-exposure covariates (W) is given as E(Y|S,W=w), where S takes on integer values 0 to q-1. Thus, comparisons are of the type E(Y|S=s,W=w) - E(Y|S=s2,W=w) where s and s2 are two different values of the joint exposures (e.g. 0 and 2). This function yields E(Y|S,W=w) as well as E(Y|S=s,W=w) - E(Y|S=p,W=w) where s is any value of S and p is the value chosen via "pointwise ref" - e.g. for binomial variables this will equal the risk/ prevalence difference at all values of S, with the referent category S=p-1. For the non-boostrapped version of quantile g-computation (under a linear model)

\(f(\beta) = \sum_i^p \beta_i\) given gradient vector $$G = [\partial(f(\beta))/\partial\beta_1 = 1, ..., \partial(f(\beta))/\partial\beta_3k= 1] $$ \(t(G) Cov(\beta) G\) = delta method variance, where t() is the transpose operator and \(\partial y/ \partial x\) denotes the partial derivative/gradient and G is the "gradient vector". The vector G takes on values that equal the difference in quantiles of S for each pointwise comparison (e.g. for a comparison of the 3rd vs the 5th category, G is a vector of 2s)

This is used to create pointwise confidence intervals

See Also

qgcomp.noboot, pointwisebound.boot

Examples

# NOT RUN {
set.seed(12)
# }
# NOT RUN {
n = 100
dat <- data.frame(x1=(x1 <- runif(n)), x2=(x2 <- runif(n)), x3=(x3 <- runif(n)), z=(z <- runif(n)),
                  y=rnorm(n)+x1 + x2 - x3 +z)
ft <- qgcomp.noboot(y ~ z + x1 + x2 + x3, expnms=c('x1','x2','x3'), data=dat, q=10)
ft2 <- qgcomp.boot(y ~ z + x1 + x2 + x3, expnms=c('x1','x2','x3'), data=dat, q=10)
pointwisebound.noboot(ft, alpha=0.05, pointwiseref=3)
pointwisebound.boot(ft2, alpha=0.05, pointwiseref=3)
dat <- data.frame(x1=(x1 <- runif(n)), x2=(x2 <- runif(n)), x3=(x3 <- runif(n)), z=(z <- runif(n)),
                  y=rbinom(n, 1, 1/(1+exp(-(x1 + x2 - x3 +z)))))
ft <- qgcomp.noboot(y ~ z + x1 + x2 + x3, expnms=c('x1','x2','x3'), data=dat, q=10)
ft2 <- qgcomp.boot(y ~ z + x1 + x2 + x3, expnms=c('x1','x2','x3'), data=dat, q=10)
pointwisebound.noboot(ft, alpha=0.05, pointwiseref=3)
pointwisebound.boot(ft2, alpha=0.05, pointwiseref=3)
# }