CIEE: sandwich_se – R documentation

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sandwich_se

Sandwich standard error estimates

Description

Function to obtain consistent and robust sandwich standard error estimates based on estimating equations, for the parameter estimates of the get_estimates function, under the GLM or AFT setting for the analysis of a normally-distributed or censored time-to-event primary outcome.

Usage

sandwich_se(setting = "GLM", scores = NULL, hessian = NULL)

Arguments

`setting`	String with value `"GLM"` or `"AFT"` indicating whether standard error estimates are obtained for a normally-distributed (`"GLM"`) or censored time-to-event (`"AFT"`) primary outcome `Y`.
`scores`	Score matrix of the parameters, which can be obtained using the `scores` function.
`hessian`	Hessian matrix of the parameters, which can be obtained using the `hessian` function.

Details

Under the GLM setting for the analysis of a normally-distributed primary outcome Y, robust sandwich standard error estimates are obtained for the estimates of the parameters α0, α1, α2, α3, σ1^2, α4, αXY, σ2^2 in the model

Y = α0 + α1*K + α2*X + α3*L + ε1, ε1 ~ N(0,σ1^2)

Y* = Y - mean(Y) - α1*(K-mean(K))

Y* = α0 + αXY*X + ε2, ε2 ~ N(0,σ2^2)

by using the score and hessian matrices of the parameters.

Under the AFT setting for the analysis of a censored time-to-event primary outcome, robust sandwich standard error estimates are similarly obtained of the parameter estimates of α0, α1, α2, α3, σ1, α4, αXY, σ2^2. For more details and the underlying model, see the vignette.

Value

Returns a vector with the CIEE sandwich standard error estimates of the parameter estimates.

Examples

# Generate data including Y, K, L, X under the GLM setting
dat <- generate_data(setting = "GLM")

# Obtain estimating functions expressions
estfunct <- est_funct_expr(setting = "GLM")

# Obtain point estimates of the parameters
estimates <- get_estimates(setting = "GLM", Y = dat$Y, X = dat$X,
                           K = dat$K, L = dat$L)

# Obtain matrices with all first and second derivatives
derivobj <- deriv_obj(setting = "GLM", logL1 = estfunct$logL1,
                      logL2 = estfunct$logL2, Y = dat$Y, X = dat$X,
                      K = dat$K, L = dat$L, estimates = estimates)

# Obtain score and hessian matrices
results_scores <- scores(derivobj)
results_hessian <- hessian(derivobj)

# Obtain sandwich standard error estimates of the parameters
sandwich_se(scores = results_scores, hessian = results_hessian)

CIEE

Estimating and Testing Direct Effects in Directed Acyclic Graphs using Estimating Equations

v0.1.1

GPL-2

Authors

Stefan Konigorski [aut, cre], Yildiz E. Yilmaz [ctb]

Initial release