isnimgm: Function for ISNI computation when the outcome follows...
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 marginal multivaraite Gaussian models.

1 2	isnimgm(formula, data, cortype = "CS", id, subset, weights, predprobobs, misni = FALSE)

`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".
`data`	the name of data frame containing all the variables in the model and all the observations including those intended to be collected but became missing.
`cortype`	the type of within-subject correlation structure.
`id`	the name of variable for the level-2 clustering variable.
`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.
`weights`	frequency weights to be assigned to each `id`. when supplied, indicates differential weights are used; otherwise each `id` is weighted equally.
`predprobobs`	Null if using buil-in multinomial transitional logistic model to obtain predicted probabilities of being observed; otherwise user supply the name of the variable in `data` that gives these probabilities for all the observations in the data.
`misni`	FALSE if using the default approach to computing ISNI with a scalar nonignorability parameter; TRUE when computing ISNI with multiple nonignorability parameters.

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 that are 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 isniglm function will by default use the utility function definemissingstatus provided in the package to generate the missingness status variables at the current and prior visits and then use Xterms as the observed missingness predictors for fitting a first-order transitional missing data model. It is important to sort within-id observations by time so that the missingness status variables can be defined correctly in this default setting. The isnimgm 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 missing data mechanism model for computing ISNI. To use different sets of predictors, one can explicitly specifiy a two-equation formula as: response | miss + missprior ~ Xterms | Sterms, which specifies the formula for the outcome model as response ~ Xterms and that for the missing data mechanism model as miss + missprior ~ Sterms, where Xterms and the observed missingness predictors Sterms can be different, miss and missprior are the variable names in data denoting the missingness status at the current and prior visits, respectively.

Ma G, Troxel AB, Heitjan DF. An Index of Local Sensitivity to Nonignorable Dropout in Longitudinal Modeling. Stat Med. 2005;24:2129-2150.
Xie H. Analyzing Longitudinal Clinical Trial Data with Nonignorable Missingness and Unknown Missingness Reasons. Comput Stat Data Anal. 2012;56:1287-1300.
Xie H, Qian Y. Measuring the Impact of Nonignorability in Panel Data with Non-Monotone Nonresponse. Journal of Applied Econometrics. 2012;27:129-159.

models= y | g+gp ~   perf + sever+ as.factor(time) + group +as.factor(time):group   |
       as.factor(time) * group + yp+ perf + sever
qolef.isni=isnimgm(models, data=qolef, id=id)
summary(qolef.isni)