Calculates: expected outcome (on the link scale), mean difference (link scale) and the standard error of the mean difference (link scale) for pointwise comparisons
pointwisebound.boot(x, pointwiseref = 1, alpha = 0.05)
"qgcompfit" object from
referent quantile (e.g. 1 uses the lowest joint-exposure category as the referent category for calculating all mean differences/standard deviations)
alpha level for confidence intervals
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 marginalized over non-exposure covariates (W), is given as E(Y^s|S) = sum_w E_w(Y|S,W)Pr(W) = sum_i E(Y_i|S) where Pr(W) is the emprical distribution of W and S takes on integer values 0 to q-1. Thus, comparisons are of the type E_w(Y|S=s) - E_w(Y|S=s2) where s and s2 are two different values of the joint exposures (e.g. 0 and 2). This function yields E_w(Y|S) as well as E_w(Y|S=s) - E_w(Y|S=p) 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. The standard error of E(Y|S=s) - E(Y|S=p) is calculated from the bootstrap covariance matrix of E_w(Y|S), such that the standard error for E_w(Y|S=s) - E_w(Y|S=p) is given by
Var(E_w(Y|S=s)) + - Var(E_w(Y|S=p)) - 2*Cov(E_w(Y|S=p), - E_w(Y|S=s))
This is used to create pointwise confidence intervals. Note that this differs slightly from the
pointwisebound.noboot function, which estimates the variance of the conditional
regression line given by E(Y|S,W=w), where w is a vector of medians of W (i.e. predictions
are made at the median value of all covariates).
A data frame containing
The linear predictor from the marginal structural model
The canonical effect measure (risk ratio/odds ratio/mean difference) for the marginal structural model link
the stndard error of the effect measure
Confidence bounds for the effect measure, and bounds centered at the linear predictor (for plotting purposes)
1 2 3 4 5 6 7 8 9 10
set.seed(12) ## Not run: n=100 # non-linear model for continuous outcome dat <- data.frame(x1=(x1 <- runif(100)), x2=runif(100), x3=runif(100), z=runif(100), y=runif(100)+x1+x1^2) ft <- qgcomp.boot(y ~ z + x1 + x2 + x3, expnms=c('x1','x2','x3'), data=dat, q=10) pointwisebound.boot(ft, alpha=0.05, pointwiseref=3) ## End(Not run)
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