Bias in longitudinal data analysis with missing data using typical linear mixed-effects modelling and pattern-mixture approach: an analytical illustration

Appropriately estimating the standardized average treatment effect with missing data: A simulation and primer

Reporting standardized effects in randomized treatment studies aids interpretation and facilitates future meta-analyses and policy considerations. However, when outcome data are missing, achieving an unbiased, accurate estimate of the standardized average treatment effect, sATE, can pose challenges even for those with general knowledge of missing data handling, given that the sATE is a ratio of a mean difference to a (within-group) standard deviation. Under both homogeneity and heterogeneity of variance, a Monte Carlo simulation study was conducted to compare missing data handling strategies in terms of bias and accuracy in the sATE, under specific missingness patterns plausible for randomized pretest posttest studies. Within two broad missing data handling approaches, maximum likelihood and multiple imputation, modeling choices were thoroughly investigated including the analysis model, variance estimator, imputation algorithm, and method of pooling results across imputed datasets. Results demonstrated that although the sATE can be estimated with little bias using either maximum likelihood or multiple imputation, particular attention should be paid to the model and variance estimator, especially at smaller sample sizes (i.e., N = 50). Differences in accuracy were driven by differences in bias. To improve estimation of the sATE in practice, recommendations and a software demonstration are provided. Moreover, a pedagogical explanation of the causes of bias, described separately for the numerator and denominator of the sATE is provided, demonstrating visually how and why bias occurs with certain methods.

Vasomotor symptoms and lipids/lipoprotein subclass metrics in midlife women: Does level of endogenous estradiol matter? The SWAN HDL Ancillary Study

BACKGROUND

A greater frequency of vasomotor symptoms (VMSs) has been associated with higher low-density lipoprotein cholesterol (LDL-C), but the association with high-density lipoprotein cholesterol (HDL-C) remains unclear. Endogenous estradiol (E2) levels are associated with both VMS and lipid levels and thus may confound such associations.

OBJECTIVES

To assess the relationship of VMS frequency with HDL-C, LDL-C, and lipoprotein concentrations (HDL and LDL particles [HDL-P; LDL-P]) and lipoprotein sizes in midlife women and to evaluate whether these associations are explained by E2.

METHODS

Participants were from the Study of Women's Health Across the Nation (SWAN) HDL ancillary study who had both nuclear magnetic resonance (NMR) spectroscopy lipoprotein subclass metrics and self-reported frequency of VMS measured 2-5 times over the menopause transition. VMS frequency was categorized into none, 1-5 days (infrequent), or ≥6 days (frequent) within the past 2 weeks.

RESULTS

We evaluated 522 women [at baseline: mean age 50.3 (SD: 2.8) years; infrequent VMS: 29.8%, frequent VMS: 16.5%]. Adjusting for potential confounders except E2, frequent VMS was associated with smaller HDL size [β(SE): -0.06 (0.03); P = .04] and higher concentrations of LDL-C [β(SE): 3.58 (1.77); P = .04] and intermediate LDL-P [β(SE): 0.09 (0.05); P = .04] than no VMS. These associations were largely explained by E2, all P's > .05.

CONCLUSIONS

Frequent VMSs were associated with smaller HDL size and higher concentrations of LDL-C and intermediate LDL-P. These associations were explained by endogenous E2. Whether treating frequent VMS with exogenous E2 could simultaneously improve lipids/lipoproteins profile should be assessed in future studies.

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

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.

To what degree does the missing-data technique influence the estimated growth in learning strategies over time? A tutorial example of sensitivity analysis for longitudinal data

Longitudinal data is almost always burdened with missing data. However, in educational and psychological research, there is a large discrepancy between methodological suggestions and research practice. The former suggests applying sensitivity analysis in order to the robustness of the results in terms of varying assumptions regarding the mechanism generating the missing data. However, in research practice, participants with missing data are usually discarded by relying on listwise deletion. To help bridge the gap between methodological recommendations and applied research in the educational and psychological domain, this study provides a tutorial example of sensitivity analysis for latent growth analysis. The example data concern students’ changes in learning strategies during higher education. One cohort of students in a Belgian university college was asked to complete the Inventory of Learning Styles–Short Version, in three measurement waves. A substantial number of students did not participate on each occasion. Change over time in student learning strategies was assessed using eight missing data techniques, which assume different mechanisms for missingness. The results indicated that, for some learning strategy subscales, growth estimates differed between the models. Guidelines in terms of reporting the results from sensitivity analysis are synthesised and applied to the results from the tutorial example.