qgcomp (version 2.7.0)

modelbound.boot: Estimating qgcomp regression line confidence bounds

Description

Calculates: expected outcome (on the link scale), and upper and lower confidence intervals (both pointwise and simultaneous)

Usage

modelbound.boot(x, alpha = 0.05, pwonly = FALSE)

Arguments

x

"qgcompfit" object from qgcomp.boot,

alpha

alpha level for confidence intervals

pwonly

logical: return only pointwise estimates (suppress simultaneous estimates)

Value

A data frame containing

linpred:

The linear predictor from the marginal structural model

r/o/m:

The canonical measure (risk/odds/mean) for the marginal structural model link

se....:

the stndard error of linpred

ul..../ll....:

Confidence bounds for the effect measure, and bounds centered at the canonical measure (for plotting purposes)

The confidence bounds are either "pointwise" (pw) and "simultaneous" (simul) confidence intervals at each each quantized value of all exposures.

Details

This method leverages the bootstrap distribution of qgcomp model coefficients to estimate pointwise regression line confidence bounds. These are defined as the bounds that, for each value of the independent variable X (here, X is the joint exposure quantiles) the 95% bounds (for example) for the model estimate of the regression line E(Y|X) are expected to include the true value of E(Y|X) in 95% of studies. The "simultaneous" bounds are also calculated, and the 95% simultaneous bounds contain the true value of E(Y|X) for all values of X in 95% of studies. The latter are more conservative and account for the multiple testing implied by the former. Pointwise bounds are calculated via the standard error for the estimates of E(Y|X), while the simultaneous bounds are estimated using the bootstrap method of Cheng (reference below). All bounds are large sample bounds that assume normality and thus will be underconservative in small samples. These bounds may also inclue illogical values (e.g. values less than 0 for a dichotomous outcome) and should be interpreted cautiously in small samples.

Reference:

Cheng, Russell CH. "Bootstrapping simultaneous confidence bands." Proceedings of the Winter Simulation Conference, 2005.. IEEE, 2005.

See Also

qgcomp.boot

Examples

# NOT RUN {
set.seed(12)
# }
# NOT RUN {
dat <- data.frame(x1=(x1 <- runif(50)), x2=runif(50), x3=runif(50), z=runif(50),
                  y=runif(50)+x1+x1^2)
ft <- qgcomp.boot(y ~ z + x1 + x2 + x3, expnms=c('x1','x2','x3'), data=dat, q=5)
modelbound.boot(ft, 0.05)
# }