Analysis of Partially Ordered Data.

poset

The poset package provides simple and efficient statistical routines for partially ordered data, such as multivariate ordinal response under consensus or prioritized order. The current version focuses on the win ratio/net benefit approach (Mao 2024) via generalized pairwise comparisons (Buyse 2010).

Installation

Install poset from CRAN with:

install.packages("poset")

You can install the development version from GitHub with:

# install.packages("devtools")
devtools::install_github("lmaowisc/poset")

Examples

Here is a basic example for two-sample testing and regression.

library(poset)
## data example
head(liver)
#>   R1NASH R2NASH Sex    AF Steatosis  SSF2  LSN
#> 1      3      2   M FALSE        30  0.21 2.33
#> 2      1      1   F FALSE         5  0.38 2.86
#> 3      4      2   M FALSE        70  0.58 3.65
#> 4      4      4   F  TRUE        30 -0.08 2.73
#> 5      4      3   M  TRUE        70 -0.04 2.53
#> 6      3      3   M FALSE        10  0.02 2.88

Compare bivariate ratings by fibrosis stage

Y1 <- liver[liver$AF, c("R1NASH", "R2NASH")] # advanced
Y0 <- liver[!liver$AF, c("R1NASH", "R2NASH")] # not advanced
wrtest(Y1, Y0)
#> Call:
#> wrtest(Y1 = Y1, Y0 = Y0)
#> 
#> Two-sample (Y1 vs Y0) win ratio/net benefit analysis
#> 
#> Number of pairs: N1 x N0 =  69 x 116  =  8004 
#>   Win: 4251 (53.1%)
#>   Loss: 2392 (29.9%)
#>   Tie: 1361 (17%)
#> 
#> Win ratio (95% CI): 1.78 (1.16, 2.73), p-value = 0.00856547
#> Net benefit (95% CI): 0.232 (0.065, 0.4), p-value = 0.006577537

Regression analysis

Y <- 5 - liver[, c("R1NASH", "R2NASH")] # lower score is better
Z <- cbind("Female" = liver$Sex == "F",
           liver[, c("AF", "Steatosis",   "SSF2",  "LSN")]) # covariates
obj <- wreg(Y, Z) # fit model
obj
#> Call:
#> wreg(Y = Y, Z = Z)
#> 
#> n = 154 subjects with complete data
#> Comparable (win/loss) pairs: 9548/11781 = 81%
#> 
#>    Female         AF   Steatosis         SSF2        LSN
#>  -0.18956 -0.9660827 -0.02779146 -0.007926333 -0.1029914

summary(obj)
#> Call:
#> wreg(Y = Y, Z = Z)
#> 
#> n = 154 subjects with complete data
#> Comparable (win/loss) pairs: 9548/11781 = 81%
#> 
#> Newton-Raphson algoritm converged in 7 iterations
#> 
#>                coef exp(coef)  se(coef)      z Pr(>|z|)    
#> Female    -0.189560    0.8273  0.259988 -0.729 0.465934    
#> AF        -0.966083    0.3806  0.280313 -3.446 0.000568 ***
#> Steatosis -0.027791    0.9726  0.005281 -5.262 1.42e-07 ***
#> SSF2      -0.007926    0.9921  0.003953 -2.005 0.044953 *  
#> LSN       -0.102991    0.9021  0.125718 -0.819 0.412657    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#>           exp(coef) exp(-coef) lower .95 upper .95
#> Female      0.82732    1.20872   0.49702    1.3771
#> AF          0.38057    2.62763   0.21970    0.6592
#> Steatosis   0.97259    1.02818   0.96258    0.9827
#> SSF2        0.99210    1.00796   0.98445    0.9998
#> LSN         0.90213    1.10848   0.70512    1.1542
#> 
#> Overall Wald test = 79.129 on 5 df,  p = 1.221245e-15

References