Title: Alternating Logistic Regression with Orthogonalized Residuals for Correlated Ordinal Outcomes
Version: 1.0.1
Description: A modified version of alternating logistic regressions (ALR) with estimation based on orthogonalized residuals (ORTH) is implemented, which use paired estimating equations to jointly estimate parameters in marginal mean and within-association models. The within-cluster association between ordinal responses is modeled by global pairwise odds ratios (POR). A finite-sample bias correction is provided to POR parameter estimates based on matrix multiplicative adjusted orthogonalized residuals (MMORTH) for correcting estimating equations, and different bias-corrected variance estimators such as BC1, BC2, and BC3.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding: UTF-8
RoxygenNote: 7.3.1
Depends: R (≥ 4.0), magic, MASS
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
LazyData: true
NeedsCompilation: no
Packaged: 2024-08-20 17:14:39 UTC; cmeng
Author: Can Meng ORCID iD [aut, cre], Fan Li [aut]
Maintainer: Can Meng <can.meng@yale.edu>
Repository: CRAN
Date/Publication: 2024-08-26 13:10:02 UTC

function: ORTH.Ord

Description

This function is designed for analyzing correlated ordinal data with ability to correct small-sample bias.

Usage

ORTH.Ord(
  formula_mean,
  data_mean,
  cluster,
  formula_por = NULL,
  data_por = NULL,
  MMORTH = FALSE,
  BC = NULL,
  init_beta = NULL,
  init_alpha = NULL,
  miter = 30,
  crit_level = 1e-04
)

Arguments

formula_mean

the symbolic description of the marginal mean model that contains the ordinal outcome and marginal mean covariates.

data_mean

the data set containing the ordinal outcome and marginal mean covariates.

cluster

cluster ID (consecutive integers) in data_mean.

formula_por

the symbolic description of marginal association model in the form of a one-sided formula, default is NULL. When leaving formula_por as default, independence working correlation will be used.

data_por

a data set for marginal association model, default is NULL. When leaving data_por as default, independence working correlation will be used.

MMORTH

a logical value to indicate if matrix-adjusted estimating equations will be applied for the association estimation, default is FALSE.

BC

an option to apply bias-correction on covariance estimation, default is NULL. Possible values are "BC1", "BC2", or "BC3".

init_beta

pre-specified starting values for parameters in the mean model, default is NULL.

init_alpha

pre-specified starting values for parameters in the association model, default is NULL.

miter

maximum number of iterations for Fisher scoring, default is 30.

crit_level

tolerance for convergence, default is 0.0001.

Details

The method is a modified version of alternating logistic regressions with estimation based on orthogonalized residuals (ORTH). The within-cluster association between ordinal responses is modeled by global pairwise odds ratios (POR). A small-sample bias correction to POR parameter estimates based on matrix multiplicative adjusted orthogonalized residuals (MMORTH) for correcting estimating equations, and bias-corrected sandwich estimators with different options for covariance estimation, i.e. BC1 (Kauermann & Zeger (1986)), BC2 (Mancl & DeRouen (2001)), and BC3 (Fay & Graubard (2001)).

Value

A list is returned. The first element is a matrix for model parameter estimates; the second element is a variance-covariance matrix for model parameters without bias correction (BC0). Additional variance-covarianc matrices will be added if argument BC is specified.

References

Can Meng, Mary Ryan, Paul Rathouz, Elizabeth Turner, John S Preisser, and Fan Li. 2023. ORTH.Ord: An R package for analyzing correlated ordinal outcomes using alternating logistic regressions with orthogonalized residuals. Computer Methods and Programs in Biomedicine, 237, doi:10.1016/j.cmpb.2023.107567.

A simulated data with correlated ordinal outcome for cluster randomized trial

Description

A dataset contains 50 clusters, in which 25 clusters are in group 1 and the other 25 clusters are in group 0 Each cluster has 9 observations, each observation has an ordinal outcome Y with three levels (i.e., 0, 1, 2). The outcomes within each cluster are correlated.

Usage

simdata

Format

a data frame with 450 rows and 5 variables:

Obs

number of observations per cluster

Y

ordinal outcome with three levels, possible values are 0, 1, and 2

Cluster

number of clusters

X1

a cluster-level binary covariate: X1=1 if in group 1 and X1=0 otherwise

X2

an observation-level continuous covariate: generatd from normal distribution with mean=1 and SD=1