### Ordinal Methods

Motivated by a simple question we encountered in our collaborative research, my colleague, Chun Li and I developed a new statistical method to test for association between two ordered categorical variables while adjusting for covariates. In the process, we developed a new residual for ordinal outcomes, which we have since discovered to be useful for many other outcome types. This work has opened up new directions for the analysis of ordinal data based on fewer assumptions than traditional approaches and is currently funded by an R01 from the National Institutes of Health. Some of our more recent work includes developing covariate-adjusted Spearman's rank correlation, extensions of Spearman's rank correlation to bivariate survival data, and analysis of continuous response variables using ordinal regression models.

Li C, Shepherd BE (2010). Test of association between two ordinal variables while adjusting for covariates. *Journal of the American Statistical Association* 105: 612--620. code; paper- the published version can be found at Journal of the American Statistical Association

Li C, Shepherd BE (2012). A new residual for ordinal outcomes. *Biometrika* 99: 473-480. paper.

Shepherd BE, Li C, and Liu Q. Probability-scale residuals for continuous, discrete, and censored data. *Canadian Journal of Statistics* 2016; 44: 463-479. paper; code

Liu Q, Shepherd BE, Li C, Harrell FE. Modeling continuous response variables using ordinal regression. *Statistics in Medicine* 2017; 36: 4316-4335. paper; code

Liu Q, Li C, Wanga V, Shepherd BE. Covariate-adjusted Spearman's rank correlation with probability-scale residuals. *Biometrics* 2018; 74: 595-605. paper; code

Tian Y, Hothorn T, Li C, Harrell FE, Shepherd BE. An empirical comparison of two novel transformation models. *Statistics in Medicine* 2020; 39: 562-576. paper; code

Eden S, Li C, Shepherd BE. Non-parametric estimation of Spearman's rank correlation with bivariate survival data. *Biometrics* (in press).

### Software

PResiduals Package; Vignette for package:

Liu Q, Shepherd BE, Li C. PResiduals: an R package for residual analysis using probability-scale residuals.

*Journal of Statistical Software* 2020; 94: 12. doi: 10.18637/jss.v094.i12