isniglm: Function for ISNI computation when the outcome follows GLMs.
In isni: Index of Local Sensitivity to Nonignorability

Description Usage Arguments Details References Examples

Calculate the ISNI when the regression outcome is subject to missingness and follows generalized linear models (GLMs)

1 2	isniglm(formula, family = gaussian, data, weights, subset, start = NULL, offset)

`formula`	an object of class "Formula": a symbolic description of the models to be fitted for the outcome and missingness status variable. The details of model specification are given under "Details".
`family`	a description of the error distribution to be used in the GLM for the outcome.
`data`	the name of data frame containing the variables in the model and all the observations including those intended to be collected but became missing.
`weights`	an optional vector of "prior weights" to be used in the fitting process for the outcome model and the missingness mechanism model. Should be NULL or a numeric vector.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process for the outcome model and the missingness mechanism model.
`start`	starting values for the parameters in the linear predictor of the outcome model.
`offset`	an optional vector to specify an a priori known component to be included in the linear predictor during fitting the GLM for the outcome. This should be NULL or a numeric vector of length equal to the number of observations.

The ISNI analysis is based on a joint selection model and requires specifying two model equations: the complete-data model and the missing data mechanism model. To specify the variables in the models and required for computing the ISNI measures, we make use of the R package "Formula" designed for handling model equations with multiple responses and multiple sets of predictors. At a minimum, the user should supply a single-equation in the typical form: response ~ Xterms where response is the (numeric or factor) vector for the outcome of interest and Xterms is a series of terms, separated by + operators, which specify a linear predictor for response. With the signle-equation specification, the isnimgm function will by default use (is.na(response)) as the missingness status variable and Xterms as the observed predictors for missingness. The isniglm then computes the MAR estimates and conducts ISNI computation to evaluate the rate of change of model estimates in the neighborhood of the MAR model where the missingness probability is allowed to depend on the unobserved value of response, even after conditioning on the other missingness predictors.

The above single-equation formula specification uses the same set of predictors for the outcome model and the missingness mechanism model for computing ISNI. To use different sets of predictors, one can explicitly specifiy a two-equation formula as: response | is.na(response) ~ Xterms | Sterms, which specifies the formula for the complete-data model as response ~ Xterms and that for the missing data mechanism model as is.na(response) ~ Sterms, and Xterms and the observed predictors for missingness Sterms can be different.

Troxel AB, Ma G, Heitjan DF. An Index of Local Sensitivity to Nonignorability. Stat Sin. 2004;14:1221-1237.

## load data set
data(sos)

## Perform the MAR analysis
ymodel= sexact  ~ gender*faculty
summary(glm(ymodel,family=binomial, data=sos))

## Perform ISNI analysis
sos.isni<-isniglm(ymodel, family=binomial, data=sos)
sos.isni
summary(sos.isni)

## specifying the missing data model explicitly
ygmodel= sexact | is.na(sexact)  ~ gender*faculty | gender *faculty
summary(isniglm(ygmodel, family=binomial, data=sos))
 

 ## ISNI for grouped binomial regression. 
gender <- c(0,0,1,1,0,0,1,1)
faculty    <- c(0,0,0,0,1,1,1,1)
gender = factor(gender, levels = c(0, 1), labels =c("male", "female"))
faculty = factor(faculty, levels = c(0, 1), labels =c("other", "mdv"))
 
SAcount <- c(NA, 1277, NA, 1247, NA, 126, NA, 152)
total       <- c(1189,1710,978,1657,68,215,73,246)
sosgrp <- data.frame(gender=gender, faculty=faculty, SAcount=SAcount, total=total)
ymodel <- SAcount/total ~gender*faculty
sosgrp.isni<-isniglm(ymodel, family=binomial, data=sosgrp, weight=total)