Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls

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Abstract

Most studies have some missing data. Jonathan Sterne and colleagues describe the appropriate use and reporting of the multiple imputation approach to dealing with them

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Using the outcome for imputation of missing predictor values was preferred.

Karel Moons, Rogier A. R. T. Donders, Theo Stijnen … (2006)

Epidemiologic studies commonly estimate associations between predictors (risk factors) and outcome. Most software automatically exclude subjects with missing values. This commonly causes bias because missing values seldom occur completely at random (MCAR) but rather selectively based on other (observed) variables, missing at random (MAR). Multiple imputation (MI) of missing predictor values using all observed information including outcome is advocated to deal with selective missing values. This seems a self-fulfilling prophecy. We tested this hypothesis using data from a study on diagnosis of pulmonary embolism. We selected five predictors of pulmonary embolism without missing values. Their regression coefficients and standard errors (SEs) estimated from the original sample were considered as "true" values. We assigned missing values to these predictors--both MCAR and MAR--and repeated this 1,000 times using simulations. Per simulation we multiple imputed the missing values without and with the outcome, and compared the regression coefficients and SEs to the truth. Regression coefficients based on MI including outcome were close to the truth. MI without outcome yielded very biased--underestimated--coefficients. SEs and coverage of the 90% confidence intervals were not different between MI with and without outcome. Results were the same for MCAR and MAR. For all types of missing values, imputation of missing predictor values using the outcome is preferred over imputation without outcome and is no self-fulfilling prophecy.

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A comparison of inclusive and restrictive strategies in modern missing data procedures.

Linda Collins, Joseph Schafer, Chi-Ming Kam (2001)

Two classes of modern missing data procedures, maximum likelihood (ML) and multiple imputation (MI), tend to yield similar results when implemented in comparable ways. In either approach, it is possible to include auxiliary variables solely for the purpose of improving the missing data procedure. A simulation was presented to assess the potential costs and benefits of a restrictive strategy, which makes minimal use of auxiliary variables, versus an inclusive strategy, which makes liberal use of such variables. The simulation showed that the inclusive strategy is to be greatly preferred. With an inclusive strategy not only is there a reduced chance of inadvertently omitting an important cause of missingness, there is also the possibility of noticeable gains in terms of increased efficiency and reduced bias, with only minor costs. As implemented in currently available software, the ML approach tends to encourage the use of a restrictive strategy, whereas the MI approach makes it relatively simple to use an inclusive strategy.

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Are missing outcome data adequately handled? A review of published randomized controlled trials in major medical journals.

Tammara A. Wood, Ian R White, P. Thompson … (2003)

Randomized controlled trials almost always have some individuals with missing outcomes. Inadequate handling of these missing data in the analysis can cause substantial bias in the treatment effect estimates. We examine how missing outcome data are handled in randomized controlled trials in order to assess whether adequate steps have been taken to reduce nonresponse bias and to identify ways to improve procedures for missing data. We reviewed all randomized trials published between July and December 2001 in BMJ, JAMA, Lancet and New England Journal of Medicine, excluding trials in which the primary outcome was described as a time-to-event. We focused on trial designs, how missing outcome data were described and the statistical methods used to deal with the missing outcome data, including sensitivity analyses. We identified 71 trials of which 63 (89%) reported having partly missing outcome data: 13 trials had more than 20% of patients with missing outcomes. In 26 trials that measured the outcome at a single time point, 92% performed a complete case analysis and 8% imputed the missing outcomes using baseline values or the worst case value. In 37 trials with repeated measures of the outcome, 46% performed complete case analyses, potentially excluding individuals with some follow-up data, while 14% performed a repeated measures analysis, 19% used the last observation carried forward, 11% imputed with the worst case value and 2% imputed using regression predictions. Thirteen (21%) of trials with missing data reported a sensitivity analysis. Our review shows that missing outcome data are a common problem in randomized controlled trials, and are often inadequately handled in the statistical analysis in the top tier medical journals. Authors should explicitly state the assumptions underlying the handling of the missing outcomes and justify them through data descriptions and sensitivity analyses.

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Author and article information

Contributors

: Role: professor of medical statistics and epidemiology

: Role: senior scientist

: Role: director of clinical epidemiology and biostatistics unit

: Role: research associate

: Role: senior scientist

: Role: professor of biostatistics

: Role: lecturer in biostatistics

: Role: reader in medical and social statistics

Journal

Journal ID (nlm-ta): BMJ

Journal ID (publisher-id): bmj

Title: BMJ : British Medical Journal

Publisher: BMJ Publishing Group Ltd.

ISSN (Print): 0959-8138

ISSN (Electronic): 1468-5833

Publication date Collection: 2009

Publication date (Print): 2009

Publication date (Electronic): 29 June 2009

Volume: 338

Electronic Location Identifier: b2393

Affiliations

[1 ]Department of Social Medicine, University of Bristol, Bristol BS8 2PR

[2 ]MRC Biostatistics Unit, Institute of Public Health, Cambridge CB2 0SR

[3 ]Clinical Epidemiology and Biostatistics Unit, Murdoch Children’s Research Institute, and University of Melbourne, Parkville, Victoria 3052, Australia

[4 ]Cancer and Statistical Methodology Groups, MRC Clinical Trials Unit, London NW1 2DA

[5 ]Medical Statistics Unit, London School of Hygiene and Tropical Medicine London, WC1E 7HT

[6 ]Department of Public Health and Primary Care, Institute of Public Health, Cambridge

Author notes

Correspondence to: J A C Sterne jonathan.sterne@ 123456bristol.ac.uk

Article

Publisher ID: stej610915

DOI: 10.1136/bmj.b2393

PMC ID: 2714692

PubMed ID: 19564179

SO-VID: 83ca01f8-e465-4955-9ae6-564a71ead7b7

License:

This is an open-access article distributed under the terms of the Creative Commons Attribution Non-commercial License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

History

Date accepted : 30 January 2009

Multiple imputation for missing data in epidemiological and clinical research: potential and pitfalls

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Most cited references 8

Using the outcome for imputation of missing predictor values was preferred.

A comparison of inclusive and restrictive strategies in modern missing data procedures.

Are missing outcome data adequately handled? A review of published randomized controlled trials in major medical journals.

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