Ordinal Methods

Motivated by a simple question we encountered in our collaborative research, 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 ( R01AI093234). 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. In addition to Chun, I have had many fabulous contributors on this work, in particular, Qi Liu, Svetlana Eden, Yuqi Tian, Shengxin Tu, Donglin Zeng, Jonathan Schildcrout, and Frank Harrell. Frank's blog, Statistical Thinking, also contains a lot of interesting ideas about ordinal data analysis (and many other things).

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

Li C, Shepherd BE. A new residual for ordinal outcomes. Biometrika 2012; 99: 473-480. paper; R package: PResiduals

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; R package: PResiduals

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

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; R package: PResiduals

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 2022; 78:421-434. paper; code; R package: survSpearman

Schildcrout JS, Harrell FE, Heagerty PJ, Haneuse S, Di Gravio C, Garbett S, Rathouz PJ, Shepherd BE. Model-assisted analyses of longitudinal, ordinal outcomes with absorbing states. Statistics in Medicine 2022; 41: 2497-2512. paper; code

Li C, Tian Y, Zeng D, Shepherd BE. Asymptotic properties for cumulative probability models for continuous outcomes. Mathematics 2023; 11; 4896. paper; code

Tian Y, Shepherd BE, Li C, Zeng D, Schildcrout JS. Analyzing clustered continuous response variables with ordinal regression models. Biometrics 2023; 79: 3764-3777. paper; code; R packages: rms, cpmgee

Eden S, Li C, Shepherd BE. Spearman-like correlation measure adjusting for covariates in bivariate survival data. Biometrical Journal 2023; 65: 2200137. paper; code

Tu S, Li C, Zeng D, Shepherd BE. Rank intraclass correlation for clustered data. Statistics in Medicine 2023; 42: 4333-4348. paper; code; R package: rankICC

Tian Y, Li C, Tu S, James NT, Harrell FE, Shepherd BE. Addressing multiple detection limits with semiparametric cumulative probability models. Journal of the American Statistical Association (in press) paper; code; R package: multipleDL

Li C, Chen G, Shepherd BE. Fitting semiparametric cumulative probability models for big data. (submitted) paper; R package: cpmBigData

Tu S, Li C, Shepherd BE. Between- and within-cluster Spearman rank correlations. (submitted) paper; code; R package: rankCorr

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