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Multiple imputation in Cox regression when there are time-varying effects of covariates

Keogh, RH; Morris, TP; (2018) Multiple imputation in Cox regression when there are time-varying effects of covariates. Statistics in Medicine , 37 (25) pp. 3661-3678. 10.1002/sim.7842. Green open access

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Abstract

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time‐varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a “complete‐case” analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive‐model‐compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive‐model‐compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete‐case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided.

Type: Article
Title: Multiple imputation in Cox regression when there are time-varying effects of covariates
Open access status: An open access version is available from UCL Discovery
DOI: 10.1002/sim.7842
Publisher version: https://doi.org/10.1002/sim.7842
Language: English
Additional information: Copyright © 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
Keywords: Cox regression, missing data, multiple imputation, restricted cubic spline, time‐varying effect
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Inst of Clinical Trials and Methodology
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences > Faculty of Population Health Sciences > Inst of Clinical Trials and Methodology > MRC Clinical Trials Unit at UCL
URI: https://discovery.ucl.ac.uk/id/eprint/10040889
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