Article Handling ties in continuous outcomes for confounder adjustment with rank-ordered logit and its application to ordinal outcomes Yilin Ning, 1,2 Chuen Seng Tan, 3 Angeliki Maraki, 4 Peh Joo Ho, 3 Sheilagh Hodgins, 5,6 Erika Comasco, 7 Kent W Nilsson, 8 Philippe Wagner, 8 Eric YH Khoo, 9,10 E-Shyong Tai, 9,10 Shih Ling Kao, 9,10 Mikael Hartman, 1,2 Marie Reilly 11 and Nathalie C Støer 11,12 Abstract The rank-ordered logit (rologit) model was recently introduced as a robust approach for analysing continuous outcomes, with the linear exposure effect estimated by scaling the rank-based log-odds estimate. Here we extend the application of the rologit model to continuous outcomes with ties and ordinal outcomes treated as imperfectly-observed continuous outcomes. By identifying the functional relationship between survival times and continuous outcomes, we explicitly establish the equivalence between the rologit and Cox models to justify the use of the Breslow, Efron and perturbation methods in the analysis of continuous outcomes with ties. Using simulation, we found all three methods perform well with few ties. Although an increasing extent of ties increased the bias of the log-odds and linear effect estimates and resulted in reduced power, which was somewhat worse when the model was mis-specified, the perturbation method maintained a type I error around 5%, while the Efron method became conservative with heavy ties but outperformed Breslow. In general, the perturbation method had the highest power, followed by the Efron and then the Breslow method. We applied our approach to three real-life datasets, demonstrating a seamless analytical workflow that uses stratification for confounder adjustment in studies of continuous and ordinal outcomes. Keywords Rank-ordered logit model, stratification, tied observations, continuous outcome, ordinal outcome 1 Introduction The goal of much epidemiological research is the identification of exposures that are risk factors for disease. While such exposures might be interpreted as causal agents in a randomised clinical trial, associations between exposure and disease in observational studies may be confounded by other factors. Adjustment for such confounding can be 1 NUS Graduate School for Integrative Sciences and Engineering, National University of Singapore, Singapore 2 Yong Loo Lin School of Medicine, Department of Surgery, National University of Singapore and National University Health System, Singapore 3 Saw Swee Hock School of Public Health, National University of Singapore and National University Health System, Singapore 4 Department of Mathematics, Stockholm University, Stockholm, Sweden 5 Institut Universitaire en Sante ´ Mentale de Montre ´al, et De ´partement de Psychiatrie et Addictologie, Universite ´ de Montre ´al, Montre ´al, Canada 6 Department of Clinical Neuroscience, Karolinska Institute, Stockholm, Sweden 7 Science for Life Laboratory, Department of Neuroscience, Uppsala University, Uppsala, Sweden 8 Centre for Clinical Research, Uppsala University, Va ¨stmanland County Hospital, Va ¨stera ˚s, Sweden 9 Yong Loo Lin School of Medicine, Department of Medicine, National University of Singapore and National University Health System, Singapore 10 University Medicine Cluster, Division of Endocrinology, National University Health System, Singapore 11 Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden 12 Norwegian National Advisory Unit on Women’s Health, Oslo University Hospital, Oslo, Norway Corresponding authors: Nathalie C Støer, Norwegian National Advisory Unit on Women’s Health, Oslo University Hospital, Oslo 0424, Norway. Email: Nathalie.C.Stoer@kreftregisteret.no Chuen Seng Tan, Saw Swee Hock School of Public Health, National University of Singapore, Singapore 119077, Singapore. Email: ephtcs@nus.edu.sg. Statistical Methods in Medical Research 0(0) 1–18 ! The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0962280219837656 journals.sagepub.com/home/smm