Analyzing endpoints with many ordered categories: theory and applications

Background: Longitudinal exposure-response (E-R) modeling of clinical endpoints is important in drug development to identify optimal dose regimens. Clinical endpoints are often ordinal composite scores. Typically, endpoints with few (e.g., <6) categories are analyzed as categorical, and endpoints with many (≥10) categories are analyzed as continuous. Endpoints with many categories often show skewed distributions that require special handling. The bounded outcome score (BOS) approach emerged in the last decade aims to parsimoniously model endpoints with moderate to large number of categories, and has been put under a general ordinal data analysis framework [1]. Most recently, benefits of the categorical analysis approach have been argued even in situations with many categories [2].

Objective: To provide an overview of the analysis approaches, discuss developments up to date, and facilitate an understanding of when best to use what approaches in the context of longitudinal E-R modelling of clinical endpoints with many categories.

Methods: Under the unifying statistical framework [1], theoretical characteristics of BOS [3] and categorical analysis approaches are discussed. The ability of these approaches in describing and predicting the endpoints of interest are compared with the continuous analysis approach though some recent applications [2]. The implications on dosing regimen selection are discussed.

Results: The continuous analysis approach requires symmetric distributional assumptions, and suitable transformations are often difficult to find for clinical endpoints that show skewness. BOS approaches may be parsimonious but often lead to significant biases in predicting derived endpoints, e.g., responder/non-responder rates based on the clinical endpoint. The ordered categorical analysis approach has appealing theoretical characteristics, and may work well with sufficient sample sizes, e.g. as in phase 3 clinical trials. Impact of the appropriateness of E-R analysis approach can be significant, e.g., those used for phase 3 dose selections may lead to the difference of with or without post-marketing requirements at the approval stage.

Conclusion: Appropriate analysis approach for clinical endpoints with many categories require careful considerations and may or may not need to be technically complex. Important influential factors include characteristics of the endpoint, whether any additional derived endpoints are of interest, and sample size. The analysis choice may directly impact clinical dosing decisions where the stakes are high.


  1. Iannario MP, D. (2016) A comprehensive framework of regression models for ordinal data. METRON 74 (2):233–252.
  2. Hu C, Adedokun O, Zhang, L, Sharma A, Zhou H (2018) Modeling near-continuous clinical endpoint as categorical: application to longitudinal exposure-response modeling of Mayo scores for golimumab in patients with Ulcerative Colitis, J Pharmacokinet Pharmacodyn, 45(6), 803-816.
  3. Hu C, Yeilding N, Davis H, Zhou H, Bounded outcome score modeling: application to treating psoriasis with ustekinumab (2011) J Pharmacokinet Pharmacodyn, 38(4):497-517.