Testing the proportional odds assumption in multiply imputed ordinal longitudinal data

Abstract

A popular choice when analyzing ordinal data is to consider the cumulative proportional odds model to relate the marginal probabilities of the ordinal outcome to a set of covariates. However, application of this model relies on the condition of identical cumulative odds ratios across the cut-offs of the ordinal outcome; the well-known proportional odds assumption. This paper focuses on the assessment of this assumption while accounting for repeated and missing data. In this respect, we develop a statistical method built on multiple imputation (MI) based on generalized estimating equations that allows to test the proportionality assumption under the missing at random setting. The performance of the proposed method is evaluated for two MI algorithms for incomplete longitudinal ordinal data. The impact of both MI methods is compared with respect to the type I error rate and the power for situations covering various numbers of categories of the ordinal outcome, sample sizes, rates of missingness, well-balanced and skewed data. The comparison of both MI methods with the complete-case analysis is also provided. We illustrate the use of the proposed methods on a quality of life data from a cancer clinical trial.

Keywords:

• categorical outcome
• clinical trials
• longitudinal analysis
• proportional odds assumption
• missing data
• multivariate normal imputation
• ordinal imputation model

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

The authors thank the European Organization for Research and Treatment of Cancer for permission to use the data from EORTC trial 26981 for this research. This publication is supported by Fondation Contre le Cancer (Belgium) through the EORTC Charitable Trust. The third author also acknowledges support from the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy) and from the contract ‘Projet d'Actions de Recherche Concertées’ (ARC) 11/16-039 of the ‘Communauté française de Belgique’.