isniglmmbin: Function for ISNI computation when the longitudinal/clustered...
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 mixed-effects models (GLMMs) for binary outcomes.

1 2	isniglmmbin(formula, data, random, id, weights, subset, predprobobs, misni = FALSE, nAGQ = 10, method = 1)

`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.
`random`	an object of class "formula": an one-sided linear formula description of the random-effects part of the model to be fitted for the outcome
`id`	the name of the level-2 clustering variable.
`weights`	frequency weights to be assigned to each `id`. when supplied, indicates differential weights are used; otherwise each `id` is weighted equally.
`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.
`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.
`nAGQ`	integer scalar - the number of points per axis for evaluating the adaptive Gauss-Hermite approximation to the log-likelihood for obtaining MAR estimates using the R function glmer(). Defaults to 10, corresponding to the 10-points Gaussian quarature. A value of 1 corresponds to Laplace approximation. Values greater than 1 produce greater accuracy in the evaluation of the log-likelihood at the expense of speed. A value of zero uses a faster but less exact form of parameter estimation for GLMMs by optimizing the random effects and the fixed-effects coefficients in the penalized iteratively reweighted least squares step. (See documentation for glmer() for Details.)
`method`	Indicate the method to obtain the MAR estimates: 1: GLMER(); 2: OPTIM()

The ISNI analysis is based on a joint selection model and requires specifying two model equations: the outcome model and the missingness mechanism model. 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 binnary 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 isniglmm 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 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 isniglmmbin() 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 | miss + missprior ~ Xterms | Sterms, which specifies the formula for the outcome model as response ~ Xterms and that for the missingness mechanism model as miss | missprior ~ Sterms, where Xterms and Sterms can be different, miss and missprior are the variable names in data denoting the missingness status at the current and prior visits, respectively.

For isniglmm, response ~ Xterms specfied the fixed-effect part of the linear mixed-effects model for the outcome. The random-effect part of the model is specified as a one-sided formula via the argument random.

Xie H. A Local Sensitivity Analysis Approach to Longitudinal Non-Gaussian Data with Non-Ignorable Dropout. Statist Med. 2008;27:3155-3177.
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.

data(skquit)

formula=quit~time
## formula=quit~time + helmert1:as.factor(time) +helmert2:as.factor(time)+ helmert3:as.factor(time)
random=~1

## Uncomment the following two lines of codes to run isniglmmbin() and report result with summary()
##result=isniglmmbin(formula, skquit, random, id,misni=FALSE,method=1)
##summary(result)