Clustered Ordinal Respiratory Disorder

The respdis data frame has 111 rows and 3 columns. The study described in Miller et. al. (1993) is a randomized clinical trial of a new treatment of respiratory disorder. The study was conducted in 111 patients who were randomly assigned to one of two treatments (active, placebo). At each of four visits during the follow-up period, the response status of each patients was classified on an ordinal scale.

respdis

Format

This data frame contains the following columns:

y1, y2, y3, y4

ordered factor measured at 4 visits for the response with levels, 1 < 2 < 3, 1 = poor, 2 = good, and 3 = excellent

trt

a factor for treatment with levels, 1 = active, 0 = placebo.

References

Miller, M.E., David, C.S., and Landis, R.J. (1993) The analysis of longitudinal polytomous data: Generalized estimating equation and connections with weighted least squares, Biometrics 49: 1033-1048.

Examples

data(respdis)
resp.l <- reshape(respdis, varying = list(c("y1", "y2", "y3", "y4")),
                  v.names = "resp", direction = "long")
resp.l <- resp.l[order(resp.l$id, resp.l$time),]
fit <- ordgee(ordered(resp) ~ trt, id = id, data = resp.l, int.const = FALSE)
summary(fit)
#> 
#> Call:
#> ordgee(formula = ordered(resp) ~ trt, id = id, data = resp.l, 
#>     int.const = FALSE)
#> 
#> Mean Model:
#>  Mean Link:                 logit 
#>  Variance to Mean Relation: binomial 
#> 
#>  Coefficients:
#>           estimate san.se   wald         p
#> Inter:1:1   1.5796 0.3276 23.246 1.425e-06
#> Inter:1:2  -1.2367 0.2887 18.346 1.842e-05
#> Inter:2:1   1.1587 0.3010 14.821 1.182e-04
#> Inter:2:2  -1.2160 0.2578 22.244 2.401e-06
#> Inter:3:1   1.0449 0.2907 12.923 3.246e-04
#> Inter:3:2  -1.0623 0.2728 15.158 9.887e-05
#> Inter:4:1   0.8388 0.2724  9.479 2.078e-03
#> Inter:4:2  -1.0745 0.2771 15.041 1.052e-04
#> trt         0.9943 0.3204  9.633 1.911e-03
#> 
#> Scale is fixed.
#> 
#> Correlation Model:
#>  Correlation Structure:     independence 
#> 
#> Returned Error Value:    0 
#> Number of clusters:   111   Maximum cluster size: 4 
#> 

z <- model.matrix( ~ trt - 1, data = respdis)
ind <- rep(1:111, 4*3/2 * 2^2)
zmat <- z[ind,,drop=FALSE]
fit <- ordgee(ordered(resp) ~ trt, id = id, data = resp.l, int.const = FALSE,
              z = zmat, corstr = "exchangeable")
summary(fit)
#> 
#> Call:
#> ordgee(formula = ordered(resp) ~ trt, id = id, data = resp.l, 
#>     z = zmat, corstr = "exchangeable", int.const = FALSE)
#> 
#> Mean Model:
#>  Mean Link:                 logit 
#>  Variance to Mean Relation: binomial 
#> 
#>  Coefficients:
#>           estimate san.se   wald         p
#> Inter:1:1   1.4899 0.3386 19.365 1.080e-05
#> Inter:1:2  -1.2431 0.2921 18.106 2.089e-05
#> Inter:2:1   1.1133 0.3049 13.332 2.609e-04
#> Inter:2:2  -1.2296 0.2744 20.083 7.414e-06
#> Inter:3:1   1.0606 0.2988 12.599 3.860e-04
#> Inter:3:2  -1.0259 0.2816 13.268 2.700e-04
#> Inter:4:1   0.8054 0.2765  8.486 3.579e-03
#> Inter:4:2  -1.0246 0.2835 13.067 3.006e-04
#> trt         1.0633 0.3449  9.505 2.049e-03
#> 
#> Scale is fixed.
#> 
#> Correlation Model:
#>  Correlation Structure:     exchangeable 
#>  Correlation Link:          log 
#> 
#>  Estimated Correlation Parameters:
#>     estimate san.se  wald        p
#> trt    4.092  1.302 9.877 0.001673
#> 
#> Returned Error Value:    1 
#> Number of clusters:   111   Maximum cluster size: 4 
#>