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Does pattern mixture modelling reduce bias due to informative attrition compared to fitting a mixed effects model to the available cases or data imputed using multiple imputation?: a simulation study.pdf (758.58 kB)

Does pattern mixture modelling reduce bias due to informative attrition compared to fitting a mixed effects model to the available cases or data imputed using multiple imputation?: a simulation study.

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posted on 2019-09-09, 14:48 authored by Catherine A. Welch, Séverine Sabia, Eric Brunner, Mika Kivimäki, Martin J. Shipley
BACKGROUND: Informative attrition occurs when the reason participants drop out from a study is associated with the study outcome. Analysing data with informative attrition can bias longitudinal study inferences. Approaches exist to reduce bias when analysing longitudinal data with monotone missingness (once participants drop out they do not return). However, findings may differ when using these approaches to analyse longitudinal data with non-monotone missingness. METHODS: Different approaches to reduce bias due to informative attrition in non-monotone longitudinal data were compared. To achieve this aim, we simulated data from a Whitehall II cohort epidemiological study, which used the slope coefficients from a linear mixed effects model to investigate the association between smoking status at baseline and subsequent decline in cognition scores. Participants with lower cognitive scores were thought to be more likely to drop out. By using a simulation study, a range of scenarios using distributions of variables which exist in real data were compared. Informative attrition that would introduce a known bias to the simulated data was specified and the estimates from a mixed effects model with random intercept and slopes when fitted to: available cases; data imputed using multiple imputation (MI); imputed data adjusted using pattern mixture modelling (PMM) were compared. The two-fold fully conditional specification MI approach, previously validated for non-monotone longitudinal data under ignorable missing data assumption, was used. However, MI may not reduce bias because informative attrition is non-ignorable missing. Therefore, PMM was applied to reduce the bias, usually unknown, by adjusting the values imputed with MI by a fixed value equal to the introduced bias. RESULTS: With highly correlated repeated outcome measures, the slope coefficients from a mixed effects model were found to have least bias when fitted to available cases. However, for moderately correlated outcome measurements, the slope coefficients from fitting a mixed effects model to data adjusted using PMM were least biased but still underestimated the true coefficients. CONCLUSIONS: PMM may potentially reduce bias in studies analysing longitudinal data with suspected informative attrition and moderately correlated repeated outcome measurements. Including additional auxiliary variables in the imputation model may also reduce any remaining bias.


This work was supported by the British Heart Foundation (RG/13/2/30098), British Medical Research Council (K013351), the British Health and Safety Executive, the British Department of Health, the British Stroke Association (TSA 2008/05), the US National Heart, Lung, and Blood Institute (R01HL036310), and the US National Institute on Aging (R01AG013196 and R01AG034454). MK is additionally supported by a professorial fellowship from the Economic and Social Research Council and by NordForsk. MJS is partly supported by the British Heart Foundation. The funding bodies did not have any role in the design of the study, or in the collection, analysis, and interpretation of data or in writing the manuscript.



BMC Medical Research Methodology, 2018, volume 18, Article number: 89

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/Organisation/COLLEGE OF LIFE SCIENCES/School of Medicine/Department of Cardiovascular Sciences


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Whitehall II data are available to bona fide researchers for research purposes. Please refer to the Whitehall II data sharing policy at The simulated datasets used and analysis described in the current study are available from the corresponding author on reasonable request.



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