MR.mean {MultiRobust}

Multiply Robust Estimation of the Marginal Mean

Description

MR.mean() is used to estimate the marginal mean of a variable which is subject to missingness. Multiple missingness probability models and outcome regression models can be accommodated.

Usage

MR.mean(response, reg.model = NULL, mis.model = NULL, moment = NULL,
  order = 1, data, bootstrap = FALSE, bootstrap.size = 300,
  alpha = 0.05)

Arguments

response

The response variable of interest whose marginal mean is to be estimated.

reg.model

A list of outcome regression models defined by glm.work.

mis.model

A list of missingness probability models defined by glm.work. The dependent variable is always specified as R.

moment

A vector of auxiliary variables whose moments are to be calibrated.

order

A numeric value. The order of moments up to which to be calibrated.

data

A data frame with missing data encoded as NA.

bootstrap

Logical. If bootstrap = TRUE, the bootstrap will be applied to calculate the standard error and construct a Wald confidence interval.

bootstrap.size

A numeric value. Number of bootstrap resamples generated if bootstrap = TRUE.

alpha

Significance level used to construct the 100(1 - alpha)% Wald confidence interval.

Value

mu

The estimated value of the marginal mean.

SE

The bootstrap standard error of mu when bootstrap = TRUE.

CI

A Wald-type confidence interval based on mu and SE when bootstrap = TRUE.

weights

The calibration weights if any reg.model, mis.model or moment is specified.

References

Han, P. and Wang, L. (2013). Estimation with missing data: beyond double robustness. Biometrika, 100(2), 417–430.

Han, P. (2014). A further study of the multiply robust estimator in missing data analysis. Journal of Statistical Planning and Inference, 148, 101–110.

Examples

# Simulated data set
set.seed(123)
n <- 400
gamma0 <- c(1, 2, 3)
alpha0 <- c(-0.8, -0.5, 0.3)
X <- runif(n, min = -2.5, max = 2.5)
p.mis <- 1 / (1 + exp(alpha0[1] + alpha0[2] * X + alpha0[3] * X ^ 2))
R <- rbinom(n, size = 1, prob = 1 - p.mis)
a.x <- gamma0[1] + gamma0[2] * X + gamma0[3] * exp(X)
Y <- rnorm(n, a.x, sd = sqrt(4 * X ^ 2 + 2))
dat <- data.frame(X, Y)
dat[R == 0, 2] <- NA

# Define the outcome regression models and missingness probability models
reg1 <- glm.work(formula = Y ~ X + exp(X), family = gaussian)
reg2 <- glm.work(formula = Y ~ X + I(X ^ 2), family = gaussian)
mis1 <- glm.work(formula = R ~ X + I(X ^ 2), family = binomial(link = logit))
mis2 <- glm.work(formula = R ~ X + exp(X), family = binomial(link = cloglog))
MR.mean(response = Y, reg.model = list(reg1, reg2), 
        mis.model = list(mis1, mis2), data = dat)
MR.mean(response = Y, moment = c(X), order = 2, data = dat)