stdReg2 (version 1.0.3)

standardize_glm: Get regression standardized estimates from a glm

Description

Get regression standardized estimates from a glm

Usage

standardize_glm(
  formula,
  data,
  values,
  clusterid,
  matched_density_cases,
  matched_density_controls,
  matching_variable,
  p_population,
  case_control = FALSE,
  ci_level = 0.95,
  ci_type = "plain",
  contrasts = NULL,
  family = "gaussian",
  reference = NULL,
  transforms = NULL
)

Value

An object of class std_glm. Obtain numeric results in a data frame with the tidy.std_glm function. This is a list with the following components:

res_contrast

An unnamed list with one element for each of the requested contrasts. Each element is itself a list with the elements:

estimates

Estimated counterfactual means and standard errors for each exposure level

covariance

Estimated covariance matrix of counterfactual means

fit_outcome

The estimated regression model for the outcome

fit_exposure

The estimated exposure model

exposure_names

A character vector of the exposure variable names

est_table

Data.frame of the estimates of the contrast with inference

transform

The transform argument used for this contrast

contrast

The requested contrast type

reference

The reference level of the exposure

ci_type

Confidence interval type

ci_level

Confidence interval level

res

A named list with the elements:

estimates

Estimated counterfactual means and standard errors for each exposure level

covariance

Estimated covariance matrix of counterfactual means

fit_outcome

The estimated regression model for the outcome

fit_exposure

The estimated exposure model

exposure_names

A character vector of the exposure variable names

Arguments

formula

The formula which is used to fit the model for the outcome.

data

The data.

values

A named list or data.frame specifying the variables and values at which marginal means of the outcome will be estimated.

clusterid

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

matched_density_cases

A function of the matching variable. The probability (or density) of the matched variable among the cases.

matched_density_controls

A function of the matching variable. The probability (or density) of the matched variable among the controls.

matching_variable

The matching variable extracted from the data set.

p_population

Specifies the incidence in the population when case_control=TRUE.

case_control

Whether the data comes from a case-control study.

ci_level

Coverage probability of confidence intervals.

ci_type

A string, indicating the type of confidence intervals. Either "plain", which gives untransformed intervals, or "log", which gives log-transformed intervals.

contrasts

A vector of contrasts in the following format: If set to "difference" or "ratio", then \(\psi(x)-\psi(x_0)\) or \(\psi(x) / \psi(x_0)\) are constructed, where \(x_0\) is a reference level specified by the reference argument. Has to be NULL if no references are specified.

family

The family argument which is used to fit the glm model for the outcome.

reference

A vector of reference levels in the following format: If contrasts is not NULL, the desired reference level(s). This must be a vector or list the same length as contrasts, and if not named, it is assumed that the order is as specified in contrasts.

transforms

A vector of transforms in the following format: If set to "log", "logit", or "odds", the standardized mean \(\theta(x)\) is transformed into \(\psi(x)=\log\{\theta(x)\}\), \(\psi(x)=\log[\theta(x)/\{1-\theta(x)\}]\), or \(\psi(x)=\theta(x)/\{1-\theta(x)\}\), respectively. If the vector is NULL, then \(\psi(x)=\theta(x)\).

Details

standardize_glm 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. standardize_glm 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 \(Z\).

References

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

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

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

Examples

# basic example
# needs to correctly specify the outcome model and no unmeasered confounders
# (+ standard causal assunmptions)
set.seed(6)
n <- 100
Z <- rnorm(n)
X <- cut(rnorm(n, mean = Z), breaks = c(-Inf, 0, Inf), labels = c("low", "high"))
Y <- rbinom(n, 1, prob = (1 + exp(as.numeric(X) + Z))^(-1))
dd <- data.frame(Z, X, Y)
x <- standardize_glm(
  formula = Y ~ X * Z,
  family = "binomial",
  data = dd,
  values = list(X = c("low", "high")),
  contrasts = c("difference", "ratio"),
  reference = "low"
)
x
# different transformations of causal effects

# example from Sjölander (2016) with case-control data
# here the matching variable needs to be passed as an argument
singapore <- AF::singapore
Mi <- singapore$Age
m <- mean(Mi)
s <- sd(Mi)
d <- 5
standardize_glm(
  formula = Oesophagealcancer ~ (Everhotbev + Age + Dial + Samsu + Cigs)^2,
  family = binomial, data = singapore,
  values = list(Everhotbev = 0:1), clusterid = "Set",
  case_control = TRUE,
  matched_density_cases = function(x) dnorm(x, m, s),
  matched_density_controls = function(x) dnorm(x, m - d, s),
  matching_variable = Mi,
  p_population = 19.3 / 100000
)

# multiple exposures
set.seed(7)
n <- 100
Z <- rnorm(n)
X1 <- rnorm(n, mean = Z)
X2 <- rnorm(n)
Y <- rbinom(n, 1, prob = (1 + exp(X1 + X2 + Z))^(-1))
dd <- data.frame(Z, X1, X2, Y)
x <- standardize_glm(
  formula = Y ~ X1 + X2 + Z,
  family = "binomial",
  data = dd, values = list(X1 = 0:1, X2 = 0:1),
  contrasts = c("difference", "ratio"),
  reference = c(X1 = 0, X2 = 0)
)
x
tidy(x)

# continuous exposure
set.seed(2)
n <- 100
Z <- rnorm(n)
X <- rnorm(n, mean = Z)
Y <- rnorm(n, mean = X + Z + 0.1 * X^2)
dd <- data.frame(Z, X, Y)
x <- standardize_glm(
  formula = Y ~ X * Z,
  family = "gaussian",
  data = dd,
  values = list(X = seq(-1, 1, 0.1))
)

# plot standardized mean as a function of x
plot(x)
# plot standardized mean - standardized mean at x = 0 as a function of x
plot(x, contrast = "difference", reference = 0)