Multiple imputation strategies for a bounded outcome variable in a competing risks analysis

E Curnow*, R A Hughes, K Birnie, M J Crowther, M T May, K Tilling

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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In patient follow-up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as ‘bounded’ or ‘interval-censored’. Methods for handling such events can be categorised as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood-based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log-normal regression with postimputation back-transformation; normal regression with and without restrictions on the imputed values and Delord and Genin’s method1 based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a haematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.
Original languageEnglish
Pages (from-to)1917-1929
Number of pages13
JournalStatistics in Medicine
Issue number8
Early online date19 Oct 2021
Publication statusE-pub ahead of print - 19 Oct 2021

Bibliographical note

Funding Information:
We are grateful to Eurocord for supplying the UK NHS CBB patient data and to the reviewer and associate editor for their helpful comments. This research received no specific grant from any funding agency in the public, commercial, or not‐for‐profit sectors. Elinor Curnow is supported by funding from NHS Blood and Transplant. Kate Tilling, Kate Birnie and Rachael Hughes work in the Medical Research Council Integrative Epidemiology Unit at the University of Bristol which is supported by the Medical Research Council and the University of Bristol MC_UU_00011/3. Rachael Hughes is supported by a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (Grant Number 215408/Z/19/Z).

Publisher Copyright:
© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.


  • bounded data
  • competing risks
  • missing data
  • multiple imputation
  • predictive mean matching


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