In this document, we illustrate the main features of the
ememax R package through examples. Additional information
on the statistical methodology and computational details are provided in
the accompanying documentation and research articles.
The package applies methods introduced in the paper:
Zhang J, Pradhan V, Zhao Y. Robust Emax model fitting: Addressing nonignorable missing binary outcome in dose–response analysis. Statistical Methods in Medical Research. 2026;0(0). doi:10.1177/09622802251403356
Open the R console and run the following command to install the package from source:
install.packages("devtools") # When you have not installed devtools package
devtools::install_github("Celaeno1017/ememax")First, load the R package.
library(ememax)To illustrate the main features of the R package ememax,
let’s first generate some data. We have built in a few functions
directly into the R package for this purpose.
theta_true=matrix(c(qlogis(0.1),qlogis(0.8)-qlogis(0.1),log(7.5)),1,3) #true parmaeter of emax model
colnames(theta_true)<- c('e_0','emax','led_50')
theta_true <- as.data.frame(theta_true)
dose_set <- c(0,7.5,22.5,75,225) #doseage definition
n=355 #total number of sample size. The sample will be evenly allocated.
alpha_true = c(0.5,1,-0.5,0,0) #mis 15 typical
data <-sim_data(theta_true,n,dose_set,alpha_true)To fit the emEmax model with Firth type correction, we use the fitEmaxEM_firth function which implements the proposed methodology.
res <- fitEmaxEM_firth(data=data$data,mis_form=as.formula(mis~y+dose) )Key parameters include: - mis_form: The pre-defined
logistic model for missingness. If y is included as a covariate, that
means one considers the missingness is non-ignorable.
The result will contain the following values: - theta:
the final fitted parameters of Emax model
alpha: the final fitted parameters of the logistic
missing model
weight: the final fitted weight for each observation
in EM
Q: the value of Q function for maximizationfor each
iteration of EM
K: the total number of iterations of EM to
converge
vcov_theta: the estimated variance covariance matrix
of theta
vcov_alpha: the estimated variance covariance matrix
of alpha