grepolr: Polynomial Cut-point Models for repolr

Description

Regression models are fitted to repeated ordinal scores, for the proportional odds model, using a modified version of the generalized estimating equation (GEE) method. The algorithm used estimates the correlation parameter by minimizing the generalized variance of the regression parameters at each step of the fitting algorithm. Parameter estimation is available for the uniform and first-order autoregressive correlation models, for data potentially recorded at irregularly spaced time intervals.

Usage

grepolr(formula, subjects, data, times, categories, scalevalue = 1, corstr = "independence", maxiter = 10, tol = 0.001, alpha = 0.5, po.test = FALSE, fixed = FALSE, poly = 3, space = NULL)

Arguments

formula

a formula, as for other regression models.

subjects

a character string specifying the name of the subject variable.

data

a dataframe in which to interpret the variables occurring in the formula.

times

a vector of times which occur within subject clusters; e.g. for four evenly spaced times c(1,2,3,4).

Value

The fitted model is an object of class gee and the correlation model has the following values in addition to the model set-up variables:
critconvergence criterion.
score.testscore test statistic.
iternumber of iterations.
alphaestimate of the correlation parameter.
grad1first derivative of generalized variance at convergence.
grad2second derivative of generalized variance at convergence.

Details

The grepolr function fits generalized estimating equations using the same algorithm as repolr, and the majority of arguments are the same for both functions. However, rather than estimate K-1 cut-point parameters, as function repolr does, function grepolr fits orthogonal polynomial contrasts to model the cut-point parameters. This is particularly useful for long ordinal scores, where K is large, or where a particular form for the cut-point parameters is preferred; e.g. increasing uniformaly at the extremes of the score scale. The function requires two additional arguments, poly and space, that indicate the order of the polynomial and the spacing between categories. The latter is normally set to 1:{categories} when all categories are observed, but can be modified to provide more realsitic models if for instance some categories are not observed.

References

Parsons, N.R. (2013). Proportional-odds models for repeated composite and long ordinal outcome scales. Statistics in Medicine In Press.

Examples

Run this code

## conventional equal spacing model
data(QoL)
base.mod <- repolr(QoL~factor(Time)+factor(Treat),subjects="Patient",
         data=QoL, categories=10, times=c(1,2,3))

## linear polynomial
space <- 1:10
mod1 <- grepolr(QoL~factor(Time)+factor(Treat),subjects="Patient",
         data=QoL, categories=10, times=c(1,2,3),poly=1,space=space)
## cubic polynomial
mod3 <- grepolr(QoL~factor(Time)+factor(Treat),subjects="Patient",
         data=QoL, categories=10, times=c(1,2,3),poly=3,space=space)
summary(mod3[["gee"]])
print(paste(round(QIC(base.mod),2),round(QIC(mod3),2),round(QIC(mod1),2)))
## plot cut-point models
plot(x=space[2:10],y=base.mod$gee$coeff[1:9],type="p",xlim=c(1,10),ylab="Cut-points",
          xlab="Category Divisions")
lines(x=space[2:length(space)],y=polycuts(mod1),type="l",lty=2)
lines(x=space[2:length(space)],y=polycuts(mod3),type="l",lty=1)

## alternative spacing model
space2 <- c(1,1.5,3,5,5.5,7,7.25,8,9,10)
base.modx <- grepolr(QoL~factor(Time)+factor(Treat),subjects="Patient",
   data=QoL, categories=10, times=c(1,2,3),corstr="uniform",poly=8,space=space2)
## cubic polynomial
modx <- grepolr(QoL~factor(Time)+factor(Treat),subjects="Patient",
   data=QoL, categories=10, times=c(1,2,3),corstr="uniform",poly=3,space=space2)
summary(modx[["gee"]])
lines(x=space2[2:length(space2)],y=polycuts(modx),type="l",lty=1,col=2)
points(x=space2[2:length(space2)],y=polycuts(base.modx),type="p",col=2)

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