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Background: With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation (population mean) may no longer be meaningful. In practice the typical approach is to continue defining the estimand this way or transform the outcome to obtain a more symmetric distribution, although neither approach may be entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate the causal difference in medians is limited. In this study we described and compared confounding-adjustment methods to address this gap., Methods: The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression (another form of IPW) and two little-known implementations of g-computation for this problem. Methods were evaluated within a simulation study under varying degrees of skewness in the outcome and applied to an empirical study using data from the Longitudinal Study of Australian Children., Results: Simulation results indicated the IPW estimator, weighted quantile regression and g-computation implementations minimised bias across all settings when the relevant models were correctly specified, with g-computation additionally minimising the variance. Multivariable quantile regression, which relies on a constant-effect assumption, consistently yielded biased results. Application to the empirical study illustrated the practical value of these methods., Conclusion: The presented methods provide appealing avenues for estimating the causal difference in medians., (© 2023. The Author(s).)

Introduction: Observational studies in health-related research often aim to answer causal questions. Missing data are common in these studies and often occur in multiple variables, such as the exposure, outcome and/or variables used to control for confounding. The standard classification of missing data as missing completely at random, missing at random (MAR) or missing not at random does not allow for a clear assessment of missingness assumptions when missingness arises in more than one variable. This presents challenges for selecting an analytic approach and determining when a sensitivity analysis under plausible alternative missing data assumptions is required. This is particularly pertinent with multiple imputation (MI), which is often justified by assuming data are MAR. The objective of this scoping review is to examine the use of MI in observational studies that address causal questions, with a focus on if and how (a) missingness assumptions are expressed and assessed, (b) missingness assumptions are used to justify the choice of a complete case analysis and/or MI for handling missing data and (c) sensitivity analyses under alternative plausible assumptions about the missingness mechanism are conducted., Methods and Analysis: We will review observational studies that aim to answer causal questions and use MI, published between January 2019 and December 2021 in five top general epidemiology journals. Studies will be identified using a full text search for the term 'multiple imputation' and then assessed for eligibility. Information extracted will include details about the study characteristics, missing data, missingness assumptions and MI implementation. Data will be summarised using descriptive statistics., Ethics and Dissemination: Ethics approval is not required for this review because data will be collected only from published studies. The results will be disseminated through a peer reviewed publication and conference presentations., Trial Registration Number: This protocol is registered on figshare (https://doi.org/10.6084/m9.figshare.20010497.v1)., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2023. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

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., (© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Joint modelling of longitudinal and time-to-event data has received much attention recently. Increasingly, extensions to standard joint modelling approaches are being proposed to handle complex data structures commonly encountered in applied research. In this paper, we propose a joint model for hierarchical longitudinal and time-to-event data. Our motivating application explores the association between tumor burden and progression-free survival in non-small cell lung cancer patients. We define tumor burden as a function of the sizes of target lesions clustered within a patient. Since a patient may have more than one lesion, and each lesion is tracked over time, the data have a three-level hierarchical structure: repeated measurements taken at time points (level 1) clustered within lesions (level 2) within patients (level 3). We jointly model the lesion-specific longitudinal trajectories and patient-specific risk of death or disease progression by specifying novel association structures that combine information across lower level clusters (e.g. lesions) into patient-level summaries (e.g. tumor burden). We provide user-friendly software for fitting the model under a Bayesian framework. Lastly, we discuss alternative situations in which additional clustering factor(s) occur at a level higher in the hierarchy than the patient-level, since this has implications for the model formulation.

Background: Longitudinal categorical variables are sometimes restricted in terms of how individuals transition between categories over time. For example, with a time-dependent measure of smoking categorised as never-smoker, ex-smoker, and current-smoker, current-smokers or ex-smokers cannot transition to a never-smoker at a subsequent wave. These longitudinal variables often contain missing values, however, there is little guidance on whether these restrictions need to be accommodated when using multiple imputation methods. Multiply imputing such missing values, ignoring the restrictions, could lead to implausible transitions., Methods: We designed a simulation study based on the Longitudinal Study of Australian Children, where the target analysis was the association between (incomplete) maternal smoking and childhood obesity. We set varying proportions of data on maternal smoking to missing completely at random or missing at random. We compared the performance of fully conditional specification with multinomial and ordinal logistic imputation, and predictive mean matching, two-fold fully conditional specification, indicator based imputation under multivariate normal imputation with projected distance-based rounding, and continuous imputation under multivariate normal imputation with calibration, where each of these multiple imputation methods were applied, accounting for the restrictions using a semi-deterministic imputation procedure., Results: Overall, we observed reduced bias when applying multiple imputation methods with restrictions, and fully conditional specification with predictive mean matching performed the best. Applying fully conditional specification and two-fold fully conditional specification for imputing nominal variables based on multinomial logistic regression had severe convergence issues. Both imputation methods under multivariate normal imputation produced biased estimates when restrictions were not accommodated, however, we observed substantial reductions in bias when restrictions were applied with continuous imputation under multivariate normal imputation with calibration., Conclusion: In a similar longitudinal setting we recommend the use of fully conditional specification with predictive mean matching, with restrictions applied during the imputation stage.

Modern epidemiological studies collect data on time-varying individual-specific characteristics, such as body mass index and blood pressure. Incorporation of such time-dependent covariates in time-to-event models is of great interest, but raises some challenges. Of specific concern are measurement error, and the non-synchronous updating of covariates across individuals, due for example to missing data. It is well known that in the presence of either of these issues the last observation carried forward (LOCF) approach traditionally used leads to bias. Joint models of longitudinal and time-to-event outcomes, developed recently, address these complexities by specifying a model for the joint distribution of all processes and are commonly fitted by maximum likelihood or Bayesian approaches. However, the adequate specification of the full joint distribution can be a challenging modeling task, especially with multiple longitudinal markers. In fact, most available software packages are unable to handle more than one marker and offer a restricted choice of survival models. We propose a two-stage approach, Multiple Imputation for Joint Modeling (MIJM), to incorporate multiple time-dependent continuous covariates in the semi-parametric Cox and additive hazard models. Assuming a primary focus on the time-to-event model, the MIJM approach handles the joint distribution of the markers using multiple imputation by chained equations, a computationally convenient procedure that is widely available in mainstream statistical software. We developed an R package "survtd" that allows MIJM and other approaches in this manuscript to be applied easily, with just one call to its main function. A simulation study showed that MIJM performs well across a wide range of scenarios in terms of bias and coverage probability, particularly compared with LOCF, simpler two-stage approaches, and a Bayesian joint model. The Framingham Heart Study is used to illustrate the approach.

Statistics on mortality related to each disease are usually based on the so-called underlying cause of death, which is selected from the diseases declared on the standardized death certificate using international rules. However, the assumption that each death is caused by exactly one disease is debatable, particularly with an aging population in an era where infectious diseases are replaced by chronic and degenerative diseases. The need to consider multiple causes of death has been acknowledged in epidemiologic research, with a growing body of literature producing statistics based on any mention of a disease on the death certificate. Yet there has not been a formal framework proposed for the statistical modeling of death arising from multiple causes. We propose a model for multiple cause of death data grounded on an empirical approach that assigns weights to each cause on the death certificate. We describe how this model for multiple-cause mortality, which extends the usual competing risks model used to conceptualize single-cause mortality, can serve to study the burden and etiology of mortality related to each disease, particularly using Cox regression methodology. We discuss how the multiple-cause, single-cause, and "any-mention" approaches compare in this regard. A simulation study and an application to a study of socioeconomic inequalities in mortality show the value of the proposed methods for exploiting this precious source of data to gain new insights, especially for certain diseases. See video abstract at, http://links.lww.com/EDE/B84.

Competing risks arise when patients may fail from several causes. Strategies for modeling event-specific quantities often assume that the cause of failure is known for all patients, but this is seldom the case. Several authors have addressed the problem of modeling the cause-specific hazard rates with missing causes of failure. In contrast, direct modeling of the cumulative incidence function has received little attention.We provide a general framework for regression modeling of this function in the missing cause setting, encompassing key models such as the Fine and Gray and additive models, by considering two extensions of the Andersen–Klein pseudo-value approach. The first extension is a novel inverse probability weighting method, whereas the second extension is based on a previously proposed multiple imputation procedure.We evaluated the gain in using these approaches with small samples in an extensive simulation study. We analyzed the data from an Eastern Cooperative Oncology Group breast cancer treatment clinical trial to illustrate the practical value and ease of implementation of the proposed methods.