| 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  [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