Handling missing data when estimating causal effects with targeted maximum likelihood estimation.

Targeted maximum likelihood estimation (TMLE) is increasingly used for doubly robust causal inference, but how missing data should be handled when using TMLE with data-adaptive approaches is unclear. Based on data (1992-1998) from the Victorian Adolescent Health Cohort Study, we conducted a simulation study to evaluate 8 missing-data methods in this context: complete-case analysis, extended TMLE incorporating an outcome-missingness model, the missing covariate missing indicator method, and 5 multiple imputation (MI) approaches using parametric or machine-learning models. We considered 6 scenarios that varied in terms of exposure/outcome generation models (presence of confounder-confounder interactions) and missingness mechanisms (whether outcome influenced missingness in other variables and presence of interaction/nonlinear terms in missingness models). Complete-case analysis and extended TMLE had small biases when outcome did not influence missingness in other variables. Parametric MI without interactions had large bias when exposure/outcome generation models included interactions. Parametric MI including interactions performed best in bias and variance reduction across all settings, except when missingness models included a nonlinear term. When choosing a method for handling missing data in the context of TMLE, researchers must consider the missingness mechanism and, for MI, compatibility with the analysis method. In many settings, a parametric MI approach that incorporates interactions and nonlinearities is expected to perform well.

The forgotten girls: the state of evidence for health interventions for pregnant adolescents and their newborns in low-income and middle-income countries.

Every year, an estimated 21 million girls aged 15-19 years become pregnant in low-income and middle-income countries (LMICs). Policy responses have focused on reducing the adolescent birth rate whereas efforts to support pregnant adolescents have developed more slowly. We did a systematic review of interventions addressing any health-related outcome for pregnant adolescents and their newborn babies in LMICs and mapped its results to a framework describing high-quality health systems for pregnant adolescents. Although we identified some promising interventions, such as micronutrient supplementation, conditional cash transfers, and well facilitated group care, most studies were at high risk of bias and there were substantial gaps in evidence. These included major gaps in delivery, abortion, and postnatal care, and mental health, violence, and substance misuse-related outcomes. We recommend that the fields of adolescent, maternal, and sexual and reproductive health collaborate to develop more adolescent-inclusive maternal health care and research, and specific interventions for pregnant adolescents. We outline steps to develop high-quality, evidence-based care for the millions of pregnant adolescents and their newborns who currently do not receive this.

Recoverability and estimation of causal effects under typical multivariable missingness mechanisms.

In the context of missing data, the identifiability or "recoverability" of the average causal effect (ACE) depends not only on the usual causal assumptions but also on missingness assumptions that can be depicted by adding variable-specific missingness indicators to causal diagrams, creating missingness directed acyclic graphs (m-DAGs). Previous research described canonical m-DAGs, representing typical multivariable missingness mechanisms in epidemiological studies, and examined mathematically the recoverability of the ACE in each case. However, this work assumed no effect modification and did not investigate methods for estimation across such scenarios. Here, we extend this research by determining the recoverability of the ACE in settings with effect modification and conducting a simulation study to evaluate the performance of widely used missing data methods when estimating the ACE using correctly specified g-computation. Methods assessed were complete case analysis (CCA) and various implementations of multiple imputation (MI) with varying degrees of compatibility with the outcome model used in g-computation. Simulations were based on an example from the Victorian Adolescent Health Cohort Study (VAHCS), where interest was in estimating the ACE of adolescent cannabis use on mental health in young adulthood. We found that the ACE is recoverable when no incomplete variable (exposure, outcome, or confounder) causes its own missingness, and nonrecoverable otherwise, in simplified versions of 10 canonical m-DAGs that excluded unmeasured common causes of missingness indicators. Despite this nonrecoverability, simulations showed that MI approaches that are compatible with the outcome model in g-computation may enable approximately unbiased estimation across all canonical m-DAGs considered, except when the outcome causes its own missingness or causes the missingness of a variable that causes its own missingness. In the latter settings, researchers may need to consider sensitivity analysis methods incorporating external information (e.g., delta-adjustment methods). The VAHCS case study illustrates the practical implications of these findings.

A comparison of strategies for selecting auxiliary variables for multiple imputation.

Multiple imputation (MI) is a popular method for handling missing data. Auxiliary variables can be added to the imputation model(s) to improve MI estimates. However, the choice of which auxiliary variables to include is not always straightforward. Several data-driven auxiliary variable selection strategies have been proposed, but there has been limited evaluation of their performance. Using a simulation study we evaluated the performance of eight auxiliary variable selection strategies: (1, 2) two versions of selection based on correlations in the observed data; (3) selection using hypothesis tests of the "missing completely at random" assumption; (4) replacing auxiliary variables with their principal components; (5, 6) forward and forward stepwise selection; (7) forward selection based on the estimated fraction of missing information; and (8) selection via the least absolute shrinkage and selection operator (LASSO). A complete case analysis and an MI analysis using all auxiliary variables (the "full model") were included for comparison. We also applied all strategies to a motivating case study. The full model outperformed all auxiliary variable selection strategies in the simulation study, with the LASSO strategy the best performing auxiliary variable selection strategy overall. All MI analysis strategies that we were able to apply to the case study led to similar estimates, although computational time was substantially reduced when variable selection was employed. This study provides further support for adopting an inclusive auxiliary variable strategy where possible. Auxiliary variable selection using the LASSO may be a promising alternative when the full model fails or is too burdensome.

Analysis and Reporting of Randomized Trials in Cleft Palate Surgery: Learning from the Timing of Primary Surgery (TOPS) Trial.

The Timing of Primary Surgery (TOPS) trial was published August 2023 in the New England Journal of Medicine and is a milestone achievement for a study focused on cleft palate. Due to the complexity of outcome reporting in cleft and the rarity of such comparative trials, TOPS presents a useful opportunity to critically review the design, analysis and reporting strategies utilised. This perspective article focused on the inclusion of participants, the choice of the primary outcome measure and the analysis of ordinal data within the trial. Considerations for future comparative studies in cleft care are discussed.

On the use of multiple imputation to address data missing by design as well as unintended missing data in case-cohort studies with a binary endpoint.

BACKGROUND: Case-cohort studies are conducted within cohort studies, with the defining feature that collection of exposure data is limited to a subset of the cohort, leading to a large proportion of missing data by design. Standard analysis uses inverse probability weighting (IPW) to address this intended missing data, but little research has been conducted into how best to perform analysis when there is also unintended missingness. Multiple imputation (MI) has become a default standard for handling unintended missingness and is typically used in combination with IPW to handle the intended missingness due to the case-control sampling. Alternatively, MI could be used to handle both the intended and unintended missingness. While the performance of an MI-only approach has been investigated in the context of a case-cohort study with a time-to-event outcome, it is unclear how this approach performs with a binary outcome. METHODS: We conducted a simulation study to assess and compare the performance of approaches using only MI, only IPW, and a combination of MI and IPW, for handling intended and unintended missingness in the case-cohort setting. We also applied the approaches to a case study. RESULTS: Our results show that the combined approach is approximately unbiased for estimation of the exposure effect when the sample size is large, and was the least biased with small sample sizes, while MI-only and IPW-only exhibited larger biases in both sample size settings. CONCLUSIONS: These findings suggest that a combined MI/IPW approach should be preferred to handle intended and unintended missing data in case-cohort studies with binary outcomes.

Should multiple imputation be stratified by exposure group when estimating causal effects via outcome regression in observational studies?

BACKGROUND: Despite recent advances in causal inference methods, outcome regression remains the most widely used approach for estimating causal effects in epidemiological studies with a single-point exposure and outcome. Missing data are common in these studies, and complete-case analysis (CCA) and multiple imputation (MI) are two frequently used methods for handling them. In randomised controlled trials (RCTs), it has been shown that MI should be conducted separately by treatment group. In observational studies, causal inference is now understood as the task of emulating an RCT, which raises the question of whether MI should be conducted by exposure group in such studies. METHODS: We addressed this question by evaluating the performance of seven methods for handling missing data when estimating causal effects with outcome regression. We conducted an extensive simulation study based on an illustrative case study from the Victorian Adolescent Health Cohort Study, assessing a range of scenarios, including seven outcome generation models with exposure-confounder interactions of differing strength. RESULTS: The simulation results showed that MI by exposure group led to the least bias when the size of the smallest exposure group was relatively large, followed by MI approaches that included the exposure-confounder interactions. CONCLUSIONS: The findings from our simulation study, which was designed based on a real case study, suggest that current practice for the conduct of MI in causal inference may need to shift to stratifying by exposure group where feasible, or otherwise including exposure-confounder interactions in the imputation model.

Primary health care utilization and hospital readmission in children with asthma: a multi-site linked data cohort study.

OBJECTIVES: To (1) describe primary health care utilization and (2) estimate the effect of primary care early follow-up, continuity, regularity, frequency, and long consultations on asthma hospital readmission, including secondary outcomes of emergency (ED) presentations, asthma preventer adherence, and use of rescue oral corticosteroids within 12 months. METHODS: An Australian multi-site cohort study of 767 children aged 3-18 years admitted with asthma between 2017 and 2018, followed up for at least 12 months with outcome and primary care exposure data obtained through linked administrative datasets. We estimated the effect of primary care utilization through a modified Poisson regression adjusting for child age, asthma severity, socioeconomic status and self-reported GP characteristics. RESULTS: The median number of general practitioner (GP) consultations, unique GPs and clinics visited was 9, 5, and 4, respectively. GP care was irregular and lacked continuity, only 152 (19.8%) children visited their usual GP on more than 60% of occasions. After adjusting for confounders, there was overall weak indication of effects due to any of the exposures. Increased frequency of GP visits was associated with reduced readmissions (4-14 visits associated with risk ratio of 0.71, 95% CI 0.50-1.00, p = 0.05) and ED presentations (>14 visits associated risk ratio 0.62, 95% CI 0.42-0.91, p = 0.02). CONCLUSIONS: Our study demonstrates that primary care use by children with asthma is often irregular and lacking in continuity. This highlights the importance of improving accessibility, consistency in care, and streamlining discharge communication from acute health services.

Modifiable factors associated with pediatric asthma readmissions: a multi-center linked cohort study.

OBJECTIVES: To (a) identify rates of hospital readmission and emergency department (ED) re-presentation for asthma within a 12-month period, (b) estimate the effects of modifiable hospital, general practitioner (GP) and home environmental factors on hospital readmission, ED re-presentations and rescue oral corticosteroid use. METHODS: We recruited 767 children aged 3-18 years who were admitted to 3 hospitals in Victoria, Australia between 2017 and 2018 with a validated diagnosis of asthma on chart review. Primary outcome was hospital readmission with asthma within 12 months of index admission. Secondary outcomes were ED re-presentation for asthma and rescue oral corticosteroid use. All outcomes were identified through linked administrative datasets. Their caregivers and 277 nominated GPs completed study surveys regarding the home environment and their usual asthma management practices respectively. RESULTS: Within 12 months of an index admission for asthma 263 (34.3%) participants were readmitted to a hospital for asthma, with participants between the ages of 3-5 years accounting for 69.2% of those readmitted. The estimated effect of GP reported guideline discordant care on the odds of readmission was OR 1.57, 95% CI 1.00-2.47, p = 0.05. None of the hospital or home environmental factors appeared to be associated with hospital readmissions. CONCLUSIONS: Hospital readmissions among Australian children with asthma are increasing, and linked datasets are important for objectively identifying the health services burden of asthma. They also confirm the important role of the GP in the management of pediatric asthma.

Success of blinding a procedural intervention in a randomised controlled trial in preterm infants receiving respiratory support.

BACKGROUND: Blinding of treatment allocation from treating clinicians in neonatal randomised controlled trials can minimise performance bias, but its effectiveness is rarely assessed. METHODS: To examine the effectiveness of blinding a procedural intervention from treating clinicians in a multicentre randomised controlled trial of minimally invasive surfactant therapy versus sham treatment in preterm infants of gestation 25-28 weeks with respiratory distress syndrome. The intervention (minimally invasive surfactant therapy or sham) was performed behind a screen within the first 6 h of life by a 'study team' uninvolved in clinical care including decision-making. Procedure duration and the study team's words and actions during the sham treatment mimicked those of the minimally invasive surfactant therapy procedure. Post-intervention, three clinicians completed a questionnaire regarding perceived group allocation, with the responses matched against actual intervention and categorised as correct, incorrect, or unsure. Success of blinding was calculated using validated blinding indices applied to the data overall (James index, successful blinding defined as > 0.50), or to the two treatment allocation groups (Bang index, successful blinding: -0.30 to 0.30). Blinding success was measured within staff role, and the associations between blinding success and procedural duration and oxygenation improvement post-procedure were estimated. RESULTS: From 1345 questionnaires in relation to a procedural intervention in 485 participants, responses were categorised as correct in 441 (33%), incorrect in 142 (11%), and unsure in 762 (57%), with similar proportions for each of the response categories in the two treatment arms. The James index indicated successful blinding overall 0.67 (95% confidence interval (CI) 0.65-0.70). The Bang index was 0.28 (95% CI 0.23-0.32) in the minimally invasive surfactant therapy group and 0.17 (95% CI 0.12-0.21) in the sham arm. Neonatologists more frequently guessed the correct intervention (47%) than bedside nurses (36%), neonatal trainees (31%), and other nurses (24%). For the minimally invasive surfactant therapy intervention, the Bang index was linearly related to procedural duration and oxygenation improvement post-procedure. No evidence of such relationships was seen in the sham arm. CONCLUSION: Blinding of a procedural intervention from clinicians is both achievable and measurable in neonatal randomised controlled trials.

Two-Year Outcomes After Minimally Invasive Surfactant Therapy in Preterm Infants: Follow-Up of the OPTIMIST-A Randomized Clinical Trial.

Importance: The long-term effects of surfactant administration via a thin catheter (minimally invasive surfactant therapy [MIST]) in preterm infants with respiratory distress syndrome remain to be definitively clarified. Objective: To examine the effect of MIST on death or neurodevelopmental disability (NDD) at 2 years' corrected age. Design, Setting, and Participants: Follow-up study of a randomized clinical trial with blinding of clinicians and outcome assessors conducted in 33 tertiary-level neonatal intensive care units in 11 countries. The trial included 486 infants with a gestational age of 25 to 28 weeks supported with continuous positive airway pressure (CPAP). Collection of follow-up data at 2 years' corrected age was completed on December 9, 2022. Interventions: Infants assigned to MIST (n = 242) received exogenous surfactant (200 mg/kg poractant alfa) via a thin catheter; those assigned to the control group (n = 244) received sham treatment. Main Outcomes and Measures: The key secondary outcome of death or moderate to severe NDD was assessed at 2 years' corrected age. Other secondary outcomes included components of this composite outcome, as well as hospitalizations for respiratory illness and parent-reported wheezing or breathing difficulty in the first 2 years. Results: Among the 486 infants randomized, 453 had follow-up data available (median gestation, 27.3 weeks; 228 females [50.3%]); data on the key secondary outcome were available in 434 infants. Death or NDD occurred in 78 infants (36.3%) in the MIST group and 79 (36.1%) in the control group (risk difference, 0% [95% CI, -7.6% to 7.7%]; relative risk [RR], 1.0 [95% CI, 0.81-1.24]); components of this outcome did not differ significantly between groups. Secondary respiratory outcomes favored the MIST group. Hospitalization with respiratory illness occurred in 49 infants (25.1%) in the MIST group vs 78 (38.2%) in the control group (RR, 0.66 [95% CI, 0.54-0.81]) and parent-reported wheezing or breathing difficulty in 73 (40.6%) vs 104 (53.6%), respectively (RR, 0.76 [95% CI, 0.63-0.90]). Conclusions and Relevance: In this follow-up study of a randomized clinical trial of preterm infants with respiratory distress syndrome supported with CPAP, MIST compared with sham treatment did not reduce the incidence of death or NDD by 2 years of age. However, infants who received MIST had lower rates of adverse respiratory outcomes during their first 2 years of life. Trial Registration: anzctr.org.au Identifier: ACTRN12611000916943.

Multiple imputation approaches for handling incomplete three-level data with time-varying cluster-memberships.

Three-level data arising from repeated measures on individuals clustered within higher-level units are common in medical research. A complexity arises when individuals change clusters over time, resulting in a cross-classified data structure. Missing values in these studies are commonly handled via multiple imputation (MI). If the three-level, cross-classified structure is modeled in the analysis, it also needs to be accommodated in the imputation model to ensure valid results. While incomplete three-level data can be handled using various approaches within MI, the performance of these in the cross-classified data setting remains unclear. We conducted simulations under a range of scenarios to compare these approaches in the context of an acute-effects cross-classified random effects substantive model, which models the time-varying cluster membership via simple additive random effects. The simulation study was based on a case study in a longitudinal cohort of students clustered within schools. We evaluated methods that ignore the time-varying cluster memberships by taking the first or most common cluster for each individual; pragmatic extensions of single- and two-level MI approaches within the joint modeling (JM) and the fully conditional specification (FCS) frameworks, using dummy indicators (DI) and/or imputing repeated measures in wide format to account for the cross-classified structure; and a three-level FCS MI approach developed specifically for cross-classified data. Results indicated that the FCS implementations performed well in terms of bias and precision while JM approaches performed poorly. Under both frameworks approaches using the DI extension should be used with caution in the presence of sparse data.

Evaluation of multiple imputation approaches for handling missing covariate information in a case-cohort study with a binary outcome.

BACKGROUND: In case-cohort studies a random subcohort is selected from the inception cohort and acts as the sample of controls for several outcome investigations. Analysis is conducted using only the cases and the subcohort, with inverse probability weighting (IPW) used to account for the unequal sampling probabilities resulting from the study design. Like all epidemiological studies, case-cohort studies are susceptible to missing data. Multiple imputation (MI) has become increasingly popular for addressing missing data in epidemiological studies. It is currently unclear how best to incorporate the weights from a case-cohort analysis in MI procedures used to address missing covariate data. METHOD: A simulation study was conducted with missingness in two covariates, motivated by a case study within the Barwon Infant Study. MI methods considered were: using the outcome, a proxy for weights in the simple case-cohort design considered, as a predictor in the imputation model, with and without exposure and covariate interactions; imputing separately within each weight category; and using a weighted imputation model. These methods were compared to a complete case analysis (CCA) within the context of a standard IPW analysis model estimating either the risk or odds ratio. The strength of associations, missing data mechanism, proportion of observations with incomplete covariate data, and subcohort selection probability varied across the simulation scenarios. Methods were also applied to the case study. RESULTS: There was similar performance in terms of relative bias and precision with all MI methods across the scenarios considered, with expected improvements compared with the CCA. Slight underestimation of the standard error was seen throughout but the nominal level of coverage (95%) was generally achieved. All MI methods showed a similar increase in precision as the subcohort selection probability increased, irrespective of the scenario. A similar pattern of results was seen in the case study. CONCLUSIONS: How weights were incorporated into the imputation model had minimal effect on the performance of MI; this may be due to case-cohort studies only having two weight categories. In this context, inclusion of the outcome in the imputation model was sufficient to account for the unequal sampling probabilities in the analysis model.

Evaluating the performance of Bayesian and restricted maximum likelihood estimation for stepped wedge cluster randomized trials with a small number of clusters.

BACKGROUND: Stepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials. METHODS: We conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect. RESULTS: Both REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias. CONCLUSIONS: The use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

Decreased in-hospital mortality rate following implementation of a comprehensive electronic medical record system.

AIM: To evaluate changes in in-hospital mortality rate following implementation of a comprehensive electronic medical record (EMR) system. METHODS: Before and after study of 355,709 hospital discharges, over an 8-year period, at a paediatric teaching hospital. The major outcome measures were crude number of in-hospital deaths, deaths per 1000 discharges, and standardised mortality ratio. RESULTS: Primary analysis of data from 2 years before and 2 years after EMR go-live showed a reduction in absolute mortality of 33 deaths, a reduction in the mortality rate of 0.48 per 1000 discharges (95% CI 0.09, 0.88 per 1000): and a relative 22% decrease (95% CI: 4%, 36%, P = 0.02) in deaths per 1000 discharges from 2.20 to 1.72. There was also a reduction in standardised mortality ratio of 47% (95% CI: 18%, 66%, P = 0.004). Post-hoc analysis of mortality rates for an additional 2-year pre-intervention period indicated that these changes in the mortality rate were not part of a pre-existing downward trend. Further analysis of an additional 20-month post-intervention period suggests that the reduced mortality rate has been sustained. CONCLUSION: We documented evidence of a clinically important decrease in in-hospital mortality rate following the implementation of a modern comprehensive EMR system in an Australian paediatric teaching hospital. The study does not prove a causal relationship, and it is possible that other factors explain some, or all, of this difference, but no changes in the hospital population or other major interventions were identified as alternative explanations for this observed change.

Evaluation of approaches for accommodating interactions and non-linear terms in multiple imputation of incomplete three-level data.

Three-level data structures arising from repeated measures on individuals clustered within larger units are common in health research studies. Missing data are prominent in such studies and are often handled via multiple imputation (MI). Although several MI approaches can be used to account for the three-level structure, including adaptations to single- and two-level approaches, when the substantive analysis model includes interactions or quadratic effects, these too need to be accommodated in the imputation model. In such analyses, substantive model compatible (SMC) MI has shown great promise in the context of single-level data. Although there have been recent developments in multilevel SMC MI, to date only one approach that explicitly handles incomplete three-level data is available. Alternatively, researchers can use pragmatic adaptations to single- and two-level MI approaches, or two-level SMC-MI approaches. We describe the available approaches and evaluate them via simulations in the context of three three-level random effects analysis models involving an interaction between the incomplete time-varying exposure and time, an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. Results showed that all approaches considered performed well in terms of bias and precision when the target analysis involved an interaction with time, but the three-level SMC MI approach performed best when the target analysis involved an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. We illustrate the methods using data from the Childhood to Adolescence Transition Study.

When should matching be used in the design of cluster randomized trials?

For cluster randomized trials (CRTs) with a small number of clusters, the matched-pair (MP) design, where clusters are paired before randomizing one to each trial arm, is often recommended to minimize imbalance on known prognostic factors, add face-validity to the study, and increase efficiency, provided the analysis recognizes the matching. Little evidence exists to guide decisions on when to use matching. We used simulation to compare the efficiency of the MP design with the stratified and simple designs, based on the mean confidence interval width of the estimated intervention effect. Matched and unmatched analyses were used for the MP design; a stratified analysis was used for the stratified design; and analyses without and with post-stratification adjustment for factors that would otherwise have been used for restricted allocation were used for the simple design. Results showed the MP design was generally the most efficient for CRTs with 10 or more pairs when the correlation between cluster-level outcomes within pairs (matching correlation) was moderate to strong (0.3-0.5). There was little gain in efficiency for the MP or stratified designs compared to simple randomization when the matching correlation was weak (0.05-0.1). For trials with four pairs of clusters, the simple and stratified designs were more efficient than the MP design because greater degrees of freedom were available for the analysis, although an unmatched analysis of the MP design recovered precision for weak matching correlations. Practical guidance on choosing between the MP, stratified, and simple designs is provided.

A comparison of multiple imputation strategies for handling missing data in multi-item scales: Guidance for longitudinal studies.

Medical research often involves using multi-item scales to assess individual characteristics, disease severity, and other health-related outcomes. It is common to observe missing data in the scale scores, due to missing data in one or more items that make up that score. Multiple imputation (MI) is a popular method for handling missing data. However, it is not clear how best to use MI in the context of scale scores, particularly when they are assessed at multiple waves of data collection resulting in large numbers of items. The aim of this article is to provide practical advice on how to impute missing values in a repeatedly measured multi-item scale using MI when inference on the scale score is of interest. We evaluated the performance of five MI strategies for imputing missing data at either the item or scale level using simulated data and a case study based on four waves of the Longitudinal Study of Australian Children (LSAC). MI was implemented using both multivariate normal imputation and fully conditional specification, with two rules for calculating the scale score. A complete case analysis was also performed for comparison. Based on our results, we caution against the use of a MI strategy that does not include the scale score in the imputation model(s) when the scale score is required for analysis.

Multiple imputation of semi-continuous exposure variables that are categorized for analysis.

Semi-continuous variables are characterized by a point mass at one value and a continuous range of values for remaining observations. An example is alcohol consumption quantity, with a spike of zeros representing non-drinkers and positive values for drinkers. If multiple imputation is used to handle missing values for semi-continuous variables, it is unclear how this should be implemented within the standard approaches of fully conditional specification (FCS) and multivariate normal imputation (MVNI). This question is brought into focus by the use of categorized versions of semi-continuous exposure variables in analyses (eg, no drinking, drinking below binge level, binge drinking, heavy binge drinking), raising the question of how best to achieve congeniality between imputation and analysis models. We performed a simulation study comparing nine approaches for imputing semi-continuous exposures requiring categorization for analysis. Three methods imputed the categories directly: ordinal logistic regression, and imputation of binary indicator variables representing the categories using MVNI (with two variants). Six methods (predictive mean matching, zero-inflated binomial imputation, and two-part imputation methods with variants in FCS and MVNI) imputed the semi-continuous variable, with categories derived after imputation. The ordinal and zero-inflated binomial methods had good performance across most scenarios, while MVNI methods requiring rounding after imputation did not perform well. There were mixed results for predictive mean matching and the two-part methods, depending on whether the estimands were proportions or regression coefficients. The results highlight the need to consider the parameter of interest when selecting an imputation procedure.