stdReg (version 3.4.1)

stdGlm: Regression standardization in generalized linear models

Description

stdGlm performs regression standardization in generalized linear models, at specified values of the exposure, over the sample covariate distribution. Let \(Y\), \(X\), and \(Z\) be the outcome, the exposure, and a vector of covariates, respectively. stdGlm uses a fitted generalized linear model to estimate the standardized mean \(\theta(x)=E\{E(Y|X=x,Z)\}\), where \(x\) is a specific value of \(X\), and the outer expectation is over the marginal distribution of \(Z\).

Usage

stdGlm(fit, data, X, x, clusterid, case.control = FALSE, subsetnew)

Arguments

fit

an object of class "glm", as returned by the glm function in the stats package. If arguments weights and/or subset are used when fitting the model, then the same weights and subset are used in stdGlm.

data

a data frame containing the variables in the model. This should be the same data frame as was used to fit the model in fit.

X

a string containing the name of the exposure variable \(X\) in data.

x

an optional vector containing the specific values of \(X\) at which to estimate the standardized mean. If \(X\) is binary (0/1) or a factor, then x defaults to all values of \(X\). If \(X\) is numeric, then x defaults to the mean of \(X\). If x is set to NA, then \(X\) is not altered. This produces an estimate of the marginal mean \(E(Y)=E\{E(Y|X,Z)\}\).

clusterid

an optional string containing the name of a cluster identification variable when data are clustered.

case.control

logical. Do data come from a case-control study? Defaults to FALSE.

subsetnew

an optional logical statement specifying a subset of observations to be used in the standardization. This set is assumed to be a subset of the subset (if any) that was used to fit the regression model.

Value

An object of class "stdGlm" is a list containing

call

the matched call.

input

input is a list containing all input arguments.

est

a vector with length equal to length(x), where element j is equal to \(\hat{\theta}\)(x[j]).

vcov

a square matrix with length(x) rows, where the element on row i and column j is the (estimated) covariance of \(\hat{\theta}\)(x[i]) and \(\hat{\theta}\)(x[j]).

Details

stdGlm assumes that a generalized linear model $$\eta\{E(Y|X,Z)\}=h(X,Z;\beta)$$ has been fitted. The maximum likelihood estimate of \(\beta\) is used to obtain estimates of the mean \(E(Y|X=x,Z)\): $$\hat{E}(Y|X=x,Z)=\eta^{-1}\{h(X=x,Z;\hat{\beta})\}.$$ For each \(x\) in the x argument, these estimates are averaged across all subjects (i.e. all observed values of \(Z\)) to produce estimates $$\hat{\theta}(x)=\sum_{i=1}^n \hat{E}(Y|X=x,Z_i)/n,$$ where \(Z_i\) is the value of \(Z\) for subject \(i\), \(i=1,...,n\). The variance for \(\hat{\theta}(x)\) is obtained by the sandwich formula.

References

Rothman K.J., Greenland S., Lash T.L. (2008). Modern Epidemiology, 3rd edition. Lippincott, Williams \& Wilkins.

Sjolander A. (2016). Regression standardization with the R-package stdReg. European Journal of Epidemiology 31(6), 563-574.

Sjolander A. (2016). Estimation of causal effect measures with the R-package stdReg. European Journal of Epidemiology 33(9), 847-858.

Examples

# NOT RUN {
##Example 1: continuous outcome
n <- 1000
Z <- rnorm(n)
X <- rnorm(n, mean=Z)
Y <- rnorm(n, mean=X+Z+0.1*X^2)
dd <- data.frame(Z, X, Y)
fit <- glm(formula=Y~X+Z+I(X^2), data=dd)
fit.std <- stdGlm(fit=fit, data=dd, X="X", x=seq(-3,3,0.5))
print(summary(fit.std))
plot(fit.std)

##Example 2: binary outcome
n <- 1000
Z <- rnorm(n)
X <- rnorm(n, mean=Z)
Y <- rbinom(n, 1, prob=(1+exp(X+Z))^(-1))
dd <- data.frame(Z, X, Y)
fit <- glm(formula=Y~X+Z+X*Z, family="binomial", data=dd)
fit.std <- stdGlm(fit=fit, data=dd, X="X", x=seq(-3,3,0.5))
print(summary(fit.std))
plot(fit.std)
# }