Multiple imputation strategies for missing event times in a multi-state model analysis.

In clinical studies, multi-state model (MSM) analysis is often used to describe the sequence of events that patients experience, enabling better understanding of disease progression. A complicating factor in many MSM studies is that the exact event times may not be known. Motivated by a real dataset of patients who received stem cell transplants, we considered the setting in which some event times were exactly observed and some were missing. In our setting, there was little information about the time intervals in which the missing event times occurred and missingness depended on the event type, given the analysis model covariates. These additional challenges limited the usefulness of some missing data methods (maximum likelihood, complete case analysis, and inverse probability weighting). We show that multiple imputation (MI) of event times can perform well in this setting. MI is a flexible method that can be used with any complete data analysis model. Through an extensive simulation study, we show that MI by predictive mean matching (PMM), in which sampling is from a set of observed times without reliance on a specific parametric distribution, has little bias when event times are missing at random, conditional on the observed data. Applying PMM separately for each sub-group of patients with a different pathway through the MSM tends to further reduce bias and improve precision. We recommend MI using PMM methods when performing MSM analysis with Markov models and partially observed event times.

Quantitative bias analysis in practice: review of software for regression with unmeasured confounding.

BACKGROUND: Failure to appropriately account for unmeasured confounding may lead to erroneous conclusions. Quantitative bias analysis (QBA) can be used to quantify the potential impact of unmeasured confounding or how much unmeasured confounding would be needed to change a study's conclusions. Currently, QBA methods are not routinely implemented, partly due to a lack of knowledge about accessible software. Also, comparisons of QBA methods have focused on analyses with a binary outcome. METHODS: We conducted a systematic review of the latest developments in QBA software published between 2011 and 2021. Our inclusion criteria were software that did not require adaption (i.e., code changes) before application, was still available in 2022, and accompanied by documentation. Key properties of each software tool were identified. We provide a detailed description of programs applicable for a linear regression analysis, illustrate their application using two data examples and provide code to assist researchers in future use of these programs. RESULTS: Our review identified 21 programs with [Formula: see text] created post 2016. All are implementations of a deterministic QBA with [Formula: see text] available in the free software R. There are programs applicable when the analysis of interest is a regression of binary, continuous or survival outcomes, and for matched and mediation analyses. We identified five programs implementing differing QBAs for a continuous outcome: treatSens, causalsens, sensemakr, EValue, and konfound. When applied to one of our illustrative examples, causalsens incorrectly indicated sensitivity to unmeasured confounding whereas the other four programs indicated robustness. sensemakr performs the most detailed QBA and includes a benchmarking feature for multiple unmeasured confounders. CONCLUSIONS: Software is now available to implement a QBA for a range of different analyses. However, the diversity of methods, even for the same analysis of interest, presents challenges to their widespread uptake. Provision of detailed QBA guidelines would be highly beneficial.

Time-sensitive testing pressures and COVID-19 outcomes: are socioeconomic inequalities over the first year of the pandemic explained by selection bias?

BACKGROUND: There are many ways in which selection bias might impact COVID-19 research. Here we focus on selection for receiving a polymerase-chain-reaction (PCR) SARS-CoV-2 test and how known changes to selection pressures over time may bias research into COVID-19 infection. METHODS: Using UK Biobank (N = 420,231; 55% female; mean age = 66.8 [SD = 8·11]) we estimate the association between socio-economic position (SEP) and (i) being tested for SARS-CoV-2 infection versus not being tested (ii) testing positive for SARS-CoV-2 infection versus testing negative and (iii) testing negative for SARS-CoV-2 infection versus not being tested. We construct four distinct time-periods between March 2020 and March 2021, representing distinct periods of testing pressures and lockdown restrictions and specify both time-stratified and combined models for each outcome. We explore potential selection bias by examining associations with positive and negative control exposures. RESULTS: The association between more disadvantaged SEP and receiving a SARS-CoV-2 test attenuated over time. Compared to individuals with a degree, individuals whose highest educational qualification was a GCSE or equivalent had an OR of 1·27 (95% CI: 1·18 to 1·37) in March-May 2020 and 1·13 (95% CI: 1.·10 to 1·16) in January-March 2021. The magnitude of the association between educational attainment and testing positive for SARS-CoV-2 infection increased over the same period. For the equivalent comparison, the OR for testing positive increased from 1·25 (95% CI: 1·04 to 1·47), to 1·69 (95% CI: 1·55 to 1·83). We found little evidence of an association between control exposures, and any considered outcome. CONCLUSIONS: The association between SEP and SARS-CoV-2 testing changed over time, highlighting the potential of time-specific selection pressures to bias analyses of COVID-19. Positive and negative control analyses suggest that changes in the association between SEP and SARS-CoV-2 infection over time likely reflect true increases in socioeconomic inequalities.

Mendelian randomisation with coarsened exposures.

A key assumption in Mendelian randomisation is that the relationship between the genetic instruments and the outcome is fully mediated by the exposure, known as the exclusion restriction assumption. However, in epidemiological studies, the exposure is often a coarsened approximation to some latent continuous trait. For example, latent liability to schizophrenia can be thought of as underlying the binary diagnosis measure. Genetically driven variation in the outcome can exist within categories of the exposure measurement, thus violating this assumption. We propose a framework to clarify this violation, deriving a simple expression for the resulting bias and showing that it may inflate or deflate effect estimates but will not reverse their sign. We then characterise a set of assumptions and a straight-forward method for estimating the effect of SD increases in the latent exposure. Our method relies on a sensitivity parameter which can be interpreted as the genetic variance of the latent exposure. We show that this method can be applied in both the one-sample and two-sample settings. We conclude by demonstrating our method in an applied example and reanalysing two papers which are likely to suffer from this type of bias, allowing meaningful interpretation of their effect sizes.

Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies.

BACKGROUND: Longitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories. METHODS: This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5-40 years. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts. RESULTS: Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence. CONCLUSIONS: LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software.

Combining Longitudinal Data From Different Cohorts to Examine the Life-Course Trajectory.

Longitudinal data are necessary to reveal changes within an individual as he or she ages. However, rarely will a single cohort study capture data throughout a person's entire life span. Here we describe in detail the steps needed to develop life-course trajectories from cohort studies that cover different and overlapping periods of life. Such independent studies are probably from heterogenous populations, which raises several challenges, including: 1) data harmonization (deriving new harmonized variables from differently measured variables by identifying common elements across all studies); 2) systematically missing data (variables not measured are missing for all participants in a cohort); and 3) model selection with differing age ranges and measurement schedules. We illustrate how to overcome these challenges using an example which examines the associations of parental education, sex, and race/ethnicity with children's weight trajectories. Data were obtained from 5 prospective cohort studies (carried out in Belarus and 4 regions of the United Kingdom) spanning data collected from birth to early adulthood during differing calendar periods (1936-1964, 1972-1979, 1990-2012, 1996-2016, and 2007-2015). Key strengths of our approach include modeling of trajectories over wide age ranges, sharing of information across studies, and direct comparison of the same parts of the life course in different geographical regions and time periods. We also introduce a novel approach of imputing individual-level covariates of a multilevel model with a nonlinear growth trajectory and interactions.

Multiple imputation strategies for a bounded outcome variable in a competing risks analysis.

In patient follow-up studies, events of interest may take place between periodic clinical assessments and so the exact time of onset is not observed. Such events are known as "bounded" or "interval-censored." Methods for handling such events can be categorized as either (i) applying multiple imputation (MI) strategies or (ii) taking a full likelihood-based (LB) approach. We focused on MI strategies, rather than LB methods, because of their flexibility. We evaluated MI strategies for bounded event times in a competing risks analysis, examining the extent to which interval boundaries, features of the data distribution and substantive analysis model are accounted for in the imputation model. Candidate imputation models were predictive mean matching (PMM); log-normal regression with postimputation back-transformation; normal regression with and without restrictions on the imputed values and Delord and Genin's method based on sampling from the cumulative incidence function. We used a simulation study to compare MI methods and one LB method when data were missing at random and missing not at random, also varying the proportion of missing data, and then applied the methods to a hematopoietic stem cell transplantation dataset. We found that cumulative incidence and median event time estimation were sensitive to model misspecification. In a competing risks analysis, we found that it is more important to account for features of the data distribution than to restrict imputed values based on interval boundaries or to ensure compatibility with the substantive analysis by sampling from the cumulative incidence function. We recommend MI by type 1 PMM.

Selection Bias When Estimating Average Treatment Effects Using One-sample Instrumental Variable Analysis.

Participants in epidemiologic and genetic studies are rarely true random samples of the populations they are intended to represent, and both known and unknown factors can influence participation in a study (known as selection into a study). The circumstances in which selection causes bias in an instrumental variable (IV) analysis are not widely understood by practitioners of IV analyses. We use directed acyclic graphs (DAGs) to depict assumptions about the selection mechanism (factors affecting selection) and show how DAGs can be used to determine when a two-stage least squares IV analysis is biased by different selection mechanisms. Through simulations, we show that selection can result in a biased IV estimate with substantial confidence interval (CI) undercoverage, and the level of bias can differ between instrument strengths, a linear and nonlinear exposure-instrument association, and a causal and noncausal exposure effect. We present an application from the UK Biobank study, which is known to be a selected sample of the general population. Of interest was the causal effect of staying in school at least 1 extra year on the decision to smoke. Based on 22,138 participants, the two-stage least squares exposure estimates were very different between the IV analysis ignoring selection and the IV analysis which adjusted for selection (e.g., risk differences, 1.8% [95% CI, -1.5%, 5.0%] and -4.5% [95% CI, -6.6%, -2.4%], respectively). We conclude that selection bias can have a major effect on an IV analysis, and further research is needed on how to conduct sensitivity analyses when selection depends on unmeasured data.

Childhood neurodevelopmental difficulties and risk of adolescent depression: the role of irritability.

BACKGROUND: Children with neurodevelopmental disorders are at increased risk of developing depression. Irritability predicts depression in the general population and is common in children with neurodevelopmental disorders. Thus, it is possible that irritability in children with neurodevelopmental disorders contributes to the link with later depression. This study aimed to (a) examine the association between childhood neurodevelopmental difficulties and adolescent depression and (b) test whether irritability explains this association. METHODS: Children with any neurodevelopmental difficulty at the age of 7-9 (n = 1,697) and a selected, comparison group without any neurodevelopmental difficulty (n = 3,177) were identified from a prospective, UK population-based cohort, the Avon Longitudinal Study of Parents and Children. Neurodevelopmental difficulties were defined as a score in the bottom 5% of the sample on at least one measure of cognitive ability, communication, autism spectrum symptoms, attention-deficit/hyperactivity symptoms, reading or motor coordination. The Development and Well-Being Assessment measured parent-reported child irritability at the age of 7, parent-reported adolescent depression at the age of 10 and 13, and self-reported depression at the age of 15. Depression measures were combined, deriving an outcome of major depressive disorder (MDD) in adolescence. Logistic regression examined the association between childhood neurodevelopmental difficulties and adolescent MDD, controlling for gender. Path analysis estimated the proportion of this association explained by irritability. Analyses were repeated for individual neurodevelopmental problems. RESULTS: Childhood neurodevelopmental difficulties were associated with adolescent MDD (OR = 2.11, 95% CI = 1.24, 3.60, p = .006). Childhood irritability statistically accounted for 42% of this association. On examining each neurodevelopmental difficulty separately, autistic, communication and ADHD problems were each associated with depression, with irritability explaining 29%-51% of these links. CONCLUSIONS: Childhood irritability appears to be a key contributor to the link between childhood neurodevelopmental difficulties and adolescent MDD. High rates of irritability in children with autistic and ADHD difficulties may explain elevated rates of depression in the neurodevelopmental group.

Socioeconomic differences in childhood BMI trajectories in Belarus.

OBJECTIVE: To examine associations of parental socioeconomic position with early-life offspring body mass index (BMI) trajectories in a middle-income country. SUBJECTS: Overall, 12,385 Belarusian children born 1996-97 and enrolled in a randomised breastfeeding promotion trial at birth, with 3-14 measurements of BMI from birth to 7 years. METHODS: Cohort analysis in which exposures were parental education (common secondary or less; advanced secondary or partial university; completed university) and occupation (manual; non-manual) at birth, and the outcome was BMI z-score trajectories estimated using multilevel linear spline models, controlling for trial arm, location, parental BMI, maternal smoking status and number of older siblings. RESULTS: Infants born to university-educated mothers were heavier at birth than those born to secondary school-educated mothers [by 0.13 BMI z-score units (95% confidence interval, CI: 0.07, 0.19) for girls and 0.11 (95% CI: 0.05, 0.17) for boys; equivalent for an infant of average birth length to 43 and 38 g, respectively]. Between the ages of 3-7 years children of the most educated mothers had larger BMI increases than children of the least educated mothers. At age 7 years, after controlling for trial arm and location,  children of university-educated mothers had higher BMIs than those born to secondary school-educated mothers by 0.11 z-score (95% CI: 0.03, 0.19) among girls and 0.18 (95% CI: 0.1, 0.27) among boys, equivalent to differences in BMI for a child of average height of 0.19 and 0.26 kg/m2, respectively. After further controlling for parental BMI, these differences attenuated to 0.08 z-score (95% CI: 0, 0.16) and 0.16 z-score (95% CI: 0.07, 0.24), respectively, but changed very little after additional adjustment for number of older siblings and mother's smoking status. Associations were similar when based on paternal educational attainment and highest household occupation. CONCLUSIONS: In Belarus, consistent with some middle-income countries, higher socioeconomic position was associated with greater BMI trajectories from age 3 onwards.

Interventions to support shared decision making for hypertension: A systematic review of controlled studies.

BACKGROUND: Hypertension (high blood pressure) is a common long-term health condition. Patient involvement in treating and monitoring hypertension is essential. Control of hypertension improves population cardiovascular outcomes. However, for an individual, potential benefits and harms of treatment are finely balanced. Shared decision making has the potential to align decisions with the preferences and values of patients. OBJECTIVE: Determine the effectiveness of interventions to support shared decision making in hypertension. SEARCH STRATEGY: Searches in MEDLINE, EMBASE, CINAHL, Web of Science and PsycINFO up to 30 September 2017. ELIGIBILITY CRITERIA: Controlled studies evaluating the effects of shared decision-making interventions for adults with hypertension compared with any comparator in any setting and reporting any outcome measures. RESULTS: Six studies (five randomized controlled trials) in European primary care were included. Main intervention components were as follows: training for health-care professionals, decision aids, patient coaching and a patient leaflet. Four studies, none at low risk of bias, reported a measure of shared decision making; the intervention increased shared decision making in one study. Four studies reported blood pressure between 6 months and 3 years after the intervention; there was no difference in blood pressure between intervention and control groups in any study. Lack of comparability between studies prevented meta-analysis. CONCLUSIONS: Despite widespread calls for shared decision making to be embedded in health care, there is little evidence to inform shared decision making for hypertension, one of the most common conditions managed in primary care.

Estimation of the linear mixed integrated Ornstein-Uhlenbeck model.

The linear mixed model with an added integrated Ornstein-Uhlenbeck (IOU) process (linear mixed IOU model) allows for serial correlation and estimation of the degree of derivative tracking. It is rarely used, partly due to the lack of available software. We implemented the linear mixed IOU model in Stata and using simulations we assessed the feasibility of fitting the model by restricted maximum likelihood when applied to balanced and unbalanced data. We compared different (1) optimization algorithms, (2) parameterizations of the IOU process, (3) data structures and (4) random-effects structures. Fitting the model was practical and feasible when applied to large and moderately sized balanced datasets (20,000 and 500 observations), and large unbalanced datasets with (non-informative) dropout and intermittent missingness. Analysis of a real dataset showed that the linear mixed IOU model was a better fit to the data than the standard linear mixed model (i.e. independent within-subject errors with constant variance).

Joint modelling rationale for chained equations.

BACKGROUND: Chained equations imputation is widely used in medical research. It uses a set of conditional models, so is more flexible than joint modelling imputation for the imputation of different types of variables (e.g. binary, ordinal or unordered categorical). However, chained equations imputation does not correspond to drawing from a joint distribution when the conditional models are incompatible. Concurrently with our work, other authors have shown the equivalence of the two imputation methods in finite samples. METHODS: Taking a different approach, we prove, in finite samples, sufficient conditions for chained equations and joint modelling to yield imputations from the same predictive distribution. Further, we apply this proof in four specific cases and conduct a simulation study which explores the consequences when the conditional models are compatible but the conditions otherwise are not satisfied. RESULTS: We provide an additional "non-informative margins" condition which, together with compatibility, is sufficient. We show that the non-informative margins condition is not satisfied, despite compatible conditional models, in a situation as simple as two continuous variables and one binary variable. Our simulation study demonstrates that as a consequence of this violation order effects can occur; that is, systematic differences depending upon the ordering of the variables in the chained equations algorithm. However, the order effects appear to be small, especially when associations between variables are weak. CONCLUSIONS: Since chained equations is typically used in medical research for datasets with different types of variables, researchers must be aware that order effects are likely to be ubiquitous, but our results suggest they may be small enough to be negligible.

Modelling childhood growth using fractional polynomials and linear splines.

BACKGROUND: There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). METHODS: We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. RESULTS: Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. CONCLUSIONS: Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures.

Sample-constrained partial identification with application to selection bias.

Many partial identification problems can be characterized by the optimal value of a function over a set where both the function and set need to be estimated by empirical data. Despite some progress for convex problems, statistical inference in this general setting remains to be developed. To address this, we derive an asymptotically valid confidence interval for the optimal value through an appropriate relaxation of the estimated set. We then apply this general result to the problem of selection bias in population-based cohort studies. We show that existing sensitivity analyses, which are often conservative and difficult to implement, can be formulated in our framework and made significantly more informative via auxiliary information on the population. We conduct a simulation study to evaluate the finite sample performance of our inference procedure, and conclude with a substantive motivating example on the causal effect of education on income in the highly selected UK Biobank cohort. We demonstrate that our method can produce informative bounds using plausible population-level auxiliary constraints. We implement this method in the [Formula: see text] package [Formula: see text].

Exploring the impact of selection bias in observational studies of COVID-19: a simulation study.

BACKGROUND: Non-random selection of analytic subsamples could introduce selection bias in observational studies. We explored the potential presence and impact of selection in studies of SARS-CoV-2 infection and COVID-19 prognosis. METHODS: We tested the association of a broad range of characteristics with selection into COVID-19 analytic subsamples in the Avon Longitudinal Study of Parents and Children (ALSPAC) and UK Biobank (UKB). We then conducted empirical analyses and simulations to explore the potential presence, direction and magnitude of bias due to this selection (relative to our defined UK-based adult target populations) when estimating the association of body mass index (BMI) with SARS-CoV-2 infection and death-with-COVID-19. RESULTS: In both cohorts, a broad range of characteristics was related to selection, sometimes in opposite directions (e.g. more-educated people were more likely to have data on SARS-CoV-2 infection in ALSPAC, but less likely in UKB). Higher BMI was associated with higher odds of SARS-CoV-2 infection and death-with-COVID-19. We found non-negligible bias in many simulated scenarios. CONCLUSIONS: Analyses using COVID-19 self-reported or national registry data may be biased due to selection. The magnitude and direction of this bias depend on the outcome definition, the true effect of the risk factor and the assumed selection mechanism; these are likely to differ between studies with different target populations. Bias due to sample selection is a key concern in COVID-19 research based on national registry data, especially as countries end free mass testing. The framework we have used can be applied by other researchers assessing the extent to which their results may be biased for their research question of interest.

Reducing smoking in adolescents: cost-effectiveness results from the cluster randomized ASSIST (A Stop Smoking In Schools Trial).

INTRODUCTION: School-based smoking prevention programmes can be effective, but evidence on cost-effectiveness is lacking. We conducted a cost-effectiveness analysis of a school-based "peer-led" intervention. METHODS: We evaluated the ASSIST (A Stop Smoking In Schools Trial) programme in a cluster randomized controlled trial. The ASSIST programme trained students to act as peer supporters during informal interactions to encourage their peers not to smoke. Fifty-nine secondary schools in England and Wales were randomized to receive the ASSIST programme or usual smoking education. Ten thousand seven hundred and thirty students aged 12-13 years attended participating schools. Previous work has demonstrated that the ASSIST programme achieved a 2.1% (95% CI = 0%-4.2%) reduction in smoking prevalence. We evaluated the public sector cost, prevalence of weekly smoking, and cost per additional student not smoking at 24 months. RESULTS: The ASSIST programme cost of £32 (95% CI = £29.70-£33.80) per student. The incremental cost per student not smoking at 2 years was £1,500 (95% CI = £669-£9,947). Students in intervention schools were less likely to believe that they would be a smoker at age 16 years (odds ratio [OR] = 0.80; 95% CI = 0.66-0.96). CONCLUSIONS: A peer-led intervention reduced smoking among adolescents at a modest cost. The intervention is cost-effective under realistic assumptions regarding the extent to which reductions in adolescent smoking lead to lower smoking prevalence and/or earlier smoking cessation in adulthood. The annual cost of extending the intervention to Year 8 students in all U.K. schools would be in the region of £38 million and could result in 20,400 fewer adolescent smokers.

Bootstrap inference for multiple imputation under uncongeniality and misspecification.

Multiple imputation has become one of the most popular approaches for handling missing data in statistical analyses. Part of this success is due to Rubin's simple combination rules. These give frequentist valid inferences when the imputation and analysis procedures are so-called congenial and the embedding model is correctly specified, but otherwise may not. Roughly speaking, congeniality corresponds to whether the imputation and analysis models make different assumptions about the data. In practice, imputation models and analysis procedures are often not congenial, such that tests may not have the correct size, and confidence interval coverage deviates from the advertised level. We examine a number of recent proposals which combine bootstrapping with multiple imputation and determine which are valid under uncongeniality and model misspecification. Imputation followed by bootstrapping generally does not result in valid variance estimates under uncongeniality or misspecification, whereas certain bootstrap followed by imputation methods do. We recommend a particular computationally efficient variant of bootstrapping followed by imputation.

Accounting for missing data in statistical analyses: multiple imputation is not always the answer.

BACKGROUND: Missing data are unavoidable in epidemiological research, potentially leading to bias and loss of precision. Multiple imputation (MI) is widely advocated as an improvement over complete case analysis (CCA). However, contrary to widespread belief, CCA is preferable to MI in some situations. METHODS: We provide guidance on choice of analysis when data are incomplete. Using causal diagrams to depict missingness mechanisms, we describe when CCA will not be biased by missing data and compare MI and CCA, with respect to bias and efficiency, in a range of missing data situations. We illustrate selection of an appropriate method in practice. RESULTS: For most regression models, CCA gives unbiased results when the chance of being a complete case does not depend on the outcome after taking the covariates into consideration, which includes situations where data are missing not at random. Consequently, there are situations in which CCA analyses are unbiased while MI analyses, assuming missing at random (MAR), are biased. By contrast MI, unlike CCA, is valid for all MAR situations and has the potential to use information contained in the incomplete cases and auxiliary variables to reduce bias and/or improve precision. For this reason, MI was preferred over CCA in our real data example. CONCLUSIONS: Choice of method for dealing with missing data is crucial for validity of conclusions, and should be based on careful consideration of the reasons for the missing data, missing data patterns and the availability of auxiliary information.

Relative efficiency of joint-model and full-conditional-specification multiple imputation when conditional models are compatible: The general location model.

Estimating the parameters of a regression model of interest is complicated by missing data on the variables in that model. Multiple imputation is commonly used to handle these missing data. Joint model multiple imputation and full-conditional specification multiple imputation are known to yield imputed data with the same asymptotic distribution when the conditional models of full-conditional specification are compatible with that joint model. We show that this asymptotic equivalence of imputation distributions does not imply that joint model multiple imputation and full-conditional specification multiple imputation will also yield asymptotically equally efficient inference about the parameters of the model of interest, nor that they will be equally robust to misspecification of the joint model. When the conditional models used by full-conditional specification multiple imputation are linear, logistic and multinomial regressions, these are compatible with a restricted general location joint model. We show that multiple imputation using the restricted general location joint model can be substantially more asymptotically efficient than full-conditional specification multiple imputation, but this typically requires very strong associations between variables. When associations are weaker, the efficiency gain is small. Moreover, full-conditional specification multiple imputation is shown to be potentially much more robust than joint model multiple imputation using the restricted general location model to mispecification of that model when there is substantial missingness in the outcome variable.