A comparison of multiple imputation methods for missing data in longitudinal studies

Abstract

Background: Multiple imputation (MI) is now widely used to handle missing data in longitudinal studies. Several MI techniques have been proposed to impute incomplete longitudinal covariates, including standard fully conditional specification (FCS-Standard) and joint multivariate normal imputation (JM-MVN), which treat repeated measurements as distinct variables, and various extensions based on generalized linear mixed models. Although these MI approaches have been implemented in various software packages, there has not been a comprehensive evaluation of the relative performance of these methods in the context of longitudinal data.

Method: Using both empirical data and a simulation study based on data from the six waves of the Longitudinal Study of Australian Children (N = 4661), we investigated the performance of a wide range of MI methods available in standard software packages for investigating the association between child body mass index (BMI) and quality of life using both a linear regression and a linear mixed-effects model.

Results: In this paper, we have identified and compared 12 different MI methods for imputing missing data in longitudinal studies. Analysis of simulated data under missing at random (MAR) mechanisms showed that the generally available MI methods provided less biased estimates with better coverage for the linear regression model and around half of these methods performed well for the estimation of regression parameters for a linear mixed model with random intercept. With the observed data, we observed an inverse association between child BMI and quality of life, with available data as well as multiple imputation.

Conclusion: Both FCS-Standard and JM-MVN performed well for the estimation of regression parameters in both analysis models. More complex methods that explicitly reflect the longitudinal structure for these analysis models may only be needed in specific circumstances such as irregularly spaced data.

Keywords: FCS; Joint modelling; Linear mixed model; Longitudinal missing data; MICE; Multilevel multiple imputation; Multiple imputation.

Conflict of interest statement

Ethics approval and consent to participate

Not applicable. De-identified secondary (LSAC) datasets were obtained from the National Centre for Longitudinal Data (NCLD).

Consent for publication

Not applicable.

Competing interests

The authors declare that they have no competing interests.

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Figures

Fig. 1

Distribution of the bias in the estimated regression coefficients (i.e., mean changes in the QoL z-score associated with each covariate) for analysis model (1) across the 1000 simulated datasets following complete data, available data and 12 multiple imputation methods. Top and bottom panel show the distribution of the bias in the estimated regression coefficients for covariates with missing data whereas the middle panel shows the distribution of the bias associated with fully observed covariate

Fig. 2

Estimated coverage of the 95% confidence interval for the regression coefficients in analysis model (1), derived from 1000 simulated datasets. The dotted lines indicate the nominal value of 95%

Fig. 3

Distribution of the bias in the estimated regression coefficients (i.e., mean changes in the QoL z-score associated with each covariate) for analysis model (2) across the 1000 simulated datasets following complete data, available data and 12 multiple imputation methods. Top, left and bottom right panels show the distribution of the bias in the estimated regression coefficients for covariates with missing data and all other panels show the distribution of the bias associated with fully observed covariate

Fig. 4

Estimated coverage of the 95% confidence interval for the regression coefficients in analysis model (2), derived from 1000 simulated datasets. The dotted lines indicate the nominal value of 95%

Fig. 5

Average computational time (in seconds) for single imputation for each of the MI methods when applied to a single simulated dataset

Fig. 6

Estimated regression coefficients and 95% CI for analysis model (1) applying available data and all the approaches to handle missing data in LSAC

Fig. 7

Estimated regression coefficients with 95% CI for analysis model (2) applying available data and all the MI approaches to handle missing data in LSAC