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Simulation studies are widely used for evaluating the performance of statistical methods in psychology. However, the quality of simulation studies can vary widely in terms of their design, execution, and reporting. In order to assess the quality of typical simulation studies in psychology, we reviewed 321 articles published in Psychological Methods, Behavior Research Methods, and Multivariate Behavioral Research in 2021 and 2022, among which 100/321 = 31.2% report a simulation study. We find that many articles do not provide complete and transparent information about key aspects of the study, such as justifications for the number of simulation repetitions, Monte Carlo uncertainty estimates, or code and data to reproduce the simulation studies. To address this problem, we provide a summary of the ADEMP (aims, data-generating mechanism, estimands and other targets, methods, performance measures) design and reporting framework from Morris et al. (2019) adapted to simulation studies in psychology. Based on this framework, we provide ADEMP-PreReg, a step-by-step template for researchers to use when designing, potentially preregistering, and reporting their simulation studies. We give formulae for estimating common performance measures, their Monte Carlo standard errors, and for calculating the number of simulation repetitions to achieve a desired Monte Carlo standard error. Finally, we give a detailed tutorial on how to apply the ADEMP framework in practice using an example simulation study on the evaluation of methods for the analysis of pre-post measurement experiments. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Background: Bias from data missing not at random (MNAR) is a persistent concern in health-related research. A bias analysis quantitatively assesses how conclusions change under different assumptions about missingness using bias parameters that govern the magnitude and direction of the bias. Probabilistic bias analysis specifies a prior distribution for these parameters, explicitly incorporating available information and uncertainty about their true values. A Bayesian bias analysis combines the prior distribution with the data's likelihood function whilst a Monte Carlo bias analysis samples the bias parameters directly from the prior distribution. No study has compared a Monte Carlo bias analysis to a Bayesian bias analysis in the context of MNAR missingness., Methods: We illustrate an accessible probabilistic bias analysis using the Monte Carlo bias analysis approach and a well-known imputation method. We designed a simulation study based on a motivating example from the UK Biobank study, where a large proportion of the outcome was missing and missingness was suspected to be MNAR. We compared the performance of our Monte Carlo bias analysis to a principled Bayesian bias analysis, complete case analysis (CCA) and multiple imputation (MI) assuming missing at random., Results: As expected, given the simulation study design, CCA and MI estimates were substantially biased, with 95% confidence interval coverages of 7-48%. Including auxiliary variables (i.e., variables not included in the substantive analysis that are predictive of missingness and the missing data) in MI's imputation model amplified the bias due to assuming missing at random. With reasonably accurate and precise information about the bias parameter, the Monte Carlo bias analysis performed as well as the Bayesian bias analysis. However, when very limited information was provided about the bias parameter, only the Bayesian bias analysis was able to eliminate most of the bias due to MNAR whilst the Monte Carlo bias analysis performed no better than the CCA and MI., Conclusion: The Monte Carlo bias analysis we describe is easy to implement in standard software and, in the setting we explored, is a viable alternative to a Bayesian bias analysis. We caution careful consideration of choice of auxiliary variables when applying imputation where data may be MNAR., Competing Interests: Declarations Ethics approval and consent to participate For the simulation study, data were completely simulated, which did not require approval from an ethics committee or consent from participants. UKB received ethical approval from the UK National Health Service’s National Research Ethics Service (ref. 11/NW/0382). All participants provided written and informed consent for data collection, analysis, and record linkage. This research was conducted under UKB application number 16729. Consent for publication Not applicable. Competing interests TPM has received consultancy fees from: Bayer Healthcare Pharmaceuticals, Alliance Pharmaceuticals, Gilead Sciences, and Kite Pharmaceuticals. Since January 2023, ARC has been an employee of Novo Nordisk Research Centre Oxford, which is not related to the current work and had no involvement in the decision to publish. The remaining authors declare that they have no competing interests., (© 2024. The Author(s).)

Accurate frequentist performance of a method is desirable in confirmatory clinical trials, but is not sufficient on its own to justify the use of a missing data method. Reference-based conditional mean imputation, with variance estimation justified solely by its frequentist performance, has the surprising and undesirable property that the estimated variance becomes smaller the greater the number of missing observations; as explained under jump-to-reference it effectively forces the true treatment effect to be exactly zero for patients with missing data., (© 2024 John Wiley & Sons Ltd.)

To obtain valid inference following stratified randomisation, treatment effects should be estimated with adjustment for stratification variables. Stratification sometimes requires categorisation of a continuous prognostic variable (eg, age), which raises the question: should adjustment be based on randomisation categories or underlying continuous values? In practice, adjustment for randomisation categories is more common. We reviewed trials published in general medical journals and found none of the 32 trials that stratified randomisation based on a continuous variable adjusted for continuous values in the primary analysis. Using data simulation, this article evaluates the performance of different adjustment strategies for continuous and binary outcomes where the covariate-outcome relationship (via the link function) was either linear or non-linear. Given the utility of covariate adjustment for addressing missing data, we also considered settings with complete or missing outcome data. Analysis methods included linear or logistic regression with no adjustment for the stratification variable, adjustment for randomisation categories, or adjustment for continuous values assuming a linear covariate-outcome relationship or allowing for non-linearity using fractional polynomials or restricted cubic splines. Unadjusted analysis performed poorly throughout. Adjustment approaches that misspecified the underlying covariate-outcome relationship were less powerful and, alarmingly, biased in settings where the stratification variable predicted missing outcome data. Adjustment for randomisation categories tends to involve the highest degree of misspecification, and so should be avoided in practice. To guard against misspecification, we recommend use of flexible approaches such as fractional polynomials and restricted cubic splines when adjusting for continuous stratification variables in randomised trials., (© 2024 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Quantitative bias analysis (QBA) permits assessment of the expected impact of various imperfections of the available data on the results and conclusions of a particular real-world study. This article extends QBA methodology to multivariable time-to-event analyses with right-censored endpoints, possibly including time-varying exposures or covariates. The proposed approach employs data-driven simulations, which preserve important features of the data at hand while offering flexibility in controlling the parameters and assumptions that may affect the results. First, the steps required to perform data-driven simulations are described, and then two examples of real-world time-to-event analyses illustrate their implementation and the insights they may offer. The first example focuses on the omission of an important time-invariant predictor of the outcome in a prognostic study of cancer mortality, and permits separating the expected impact of confounding bias from non-collapsibility. The second example assesses how imprecise timing of an interval-censored event - ascertained only at sparse times of clinic visits - affects its estimated association with a time-varying drug exposure. The simulation results also provide a basis for comparing the performance of two alternative strategies for imputing the unknown event times in this setting. The R scripts that permit the reproduction of our examples are provided., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Simulation studies are powerful tools in epidemiology and biostatistics, but they can be hard to conduct successfully. Sometimes unexpected results are obtained. We offer advice on how to check a simulation study when this occurs, and how to design and conduct the study to give results that are easier to check. Simulation studies should be designed to include some settings in which answers are already known. They should be coded in stages, with data-generating mechanisms checked before simulated data are analysed. Results should be explored carefully, with scatterplots of standard error estimates against point estimates surprisingly powerful tools. Failed estimation and outlying estimates should be identified and dealt with by changing data-generating mechanisms or coding realistic hybrid analysis procedures. Finally, we give a series of ideas that have been useful to us in the past for checking unexpected results. Following our advice may help to prevent errors and to improve the quality of published simulation studies., (© The Author(s) 2023. Published by Oxford University Press on behalf of the International Epidemiological Association.)

Competing Interests: Competing interests: All authors have completed the ICMJE uniform disclosure form at https://www.icmje.org/disclosure-of-interest/ and declare: support from the UK Medical Research Council and the NIHR for the submitted work. BCK and SC declare grant funding (payable to employing institutions) from the MRC-NIHR Trials Methodology Research Partnership. BCK and ME declare grant funding (payable to employing institutions) from the NIHR for the FLO-ELA trial. TPM declares consultancy fees from Bayer Healthcare Pharmaceuticals, Alliance Pharmaceuticals, Gilead Sciences, and Kite Pharma; declares conference attendance and travel paid for as an invited speaker at the 2023 European Society for Blood and Marrow Transplantation conference; and is an independent member of the data and safety monitoring board for the FLO-ELA trial. All other authors declare no conflicts of interest.

Although new biostatistical methods are published at a very high rate, many of these developments are not trustworthy enough to be adopted by the scientific community. We propose a framework to think about how a piece of methodological work contributes to the evidence base for a method. Similar to the well-known phases of clinical research in drug development, we propose to define four phases of methodological research. These four phases cover (I) proposing a new methodological idea while providing, for example, logical reasoning or proofs, (II) providing empirical evidence, first in a narrow target setting, then (III) in an extended range of settings and for various outcomes, accompanied by appropriate application examples, and (IV) investigations that establish a method as sufficiently well-understood to know when it is preferred over others and when it is not; that is, its pitfalls. We suggest basic definitions of the four phases to provoke thought and discussion rather than devising an unambiguous classification of studies into phases. Too many methodological developments finish before phase III/IV, but we give two examples with references. Our concept rebalances the emphasis to studies in phases III and IV, that is, carefully planned method comparison studies and studies that explore the empirical properties of existing methods in a wider range of problems., (© 2023 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)

Background: Patient and public involvement (PPI) in trials aims to enhance research by improving its relevance and transparency. Planning for statistical analysis begins at the design stage of a trial within the protocol and is refined and detailed in a Statistical Analysis Plan (SAP). While PPI is common in design and protocol development it is less common within SAPs. This study aimed to reach consensus on the most important and relevant statistical analysis items within an SAP to involve patients and the public., Methods: We developed a UK-based, two-round Delphi survey through an iterative consultation with public partners, statisticians, and trialists. The consultation process started with 55 items from international guidance for statistical analysis plans. We aimed to recruit at least 20 participants per key stakeholder group for inclusion in the final analysis of the Delphi survey. Participants were asked to vote on each item using a Likert scale from 1 to 9, where a rating of 1 to 3 was labelled as having 'limited importance'; 4 to 6 as 'important but not critical' and 7 to 9 as 'critical' to involve patients and the public. Results from the second round determined consensus on critical items for PPI., Results: The consultation exercise led to the inclusion of 15 statistical items in the Delphi survey. We recruited 179 participants, of whom 72% (129: 36 statisticians, 29 patients or public partners, 25 clinical researchers or methodologists, 27 trial managers, and 12 PPI coordinators) completed both rounds. Participants were on average 48 years old, 60% were female, 84% were White, 64% were based in England and 84% had at least five years' experience in trials. Four items reached consensus regarding critical importance for patient and public involvement: presentation of results to trial participants; summary and presentation of harms; interpretation and presentation of findings in an academic setting; factors impacting how well a treatment works. No consensus was reached for the remaining 11 items. In general, the results were consistent across stakeholder groups., Discussion: We identified four critical items to involve patients and the public in statistical analysis plans. The remaining 11 items did not reach consensus and need to be considered in a case-by-case basis with most responders considering patient and public involvement important (but not critical). Our research provides a platform to enable focused future efforts to improve patient and public involvement in trials and enhance the relevance of statistical analyses to patients and the public., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Goulão et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Background: The population-level summary measure is a key component of the estimand for clinical trials with time-to-event outcomes. This is particularly the case for non-inferiority trials, because different summary measures imply different null hypotheses. Most trials are designed using the hazard ratio as summary measure, but recent studies suggested that the difference in restricted mean survival time might be more powerful, at least in certain situations. In a recent letter, we conjectured that differences between summary measures can be explained using the concept of the non-inferiority frontier and that for a fair simulation comparison of summary measures, the same analysis methods, making the same assumptions, should be used to estimate different summary measures. The aim of this article is to make such a comparison between three commonly used summary measures: hazard ratio, difference in restricted mean survival time and difference in survival at a fixed time point. In addition, we aim to investigate the impact of using an analysis method that assumes proportional hazards on the operating characteristics of a trial designed with any of the three summary measures., Methods: We conduct a simulation study in the proportional hazards setting. We estimate difference in restricted mean survival time and difference in survival non-parametrically, without assuming proportional hazards. We also estimate all three measures parametrically, using flexible survival regression, under the proportional hazards assumption., Results: Comparing the hazard ratio assuming proportional hazards with the other summary measures not assuming proportional hazards, relative performance varies substantially depending on the specific scenario. Fixing the summary measure, assuming proportional hazards always leads to substantial power gains compared to using non-parametric methods. Fixing the modelling approach to flexible parametric regression assuming proportional hazards, difference in restricted mean survival time is most often the most powerful summary measure among those considered., Conclusion: When the hazards are likely to be approximately proportional, reflecting this in the analysis can lead to large gains in power for difference in restricted mean survival time and difference in survival. The choice of summary measure for a non-inferiority trial with time-to-event outcomes should be made on clinical grounds; when any of the three summary measures discussed here is equally justifiable, difference in restricted mean survival time is most often associated with the most powerful test, on the condition that it is estimated under proportional hazards., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

The marginality principle guides analysts to avoid omitting lower-order terms from models in which higher-order terms are included as covariates. Lower-order terms are viewed as "marginal" to higher-order terms. We consider how this principle applies to three cases: regression models that may include the ratio of two measured variables; polynomial transformations of a measured variable; and factorial arrangements of defined interventions. For each case, we show that which terms or transformations are considered to be lower-order, and therefore marginal, depends on the scale of measurement, which is frequently arbitrary. Understanding the implications of this point leads to an intuitive understanding of the curse of dimensionality. We conclude that the marginality principle may be useful to analysts in some specific cases but caution against invoking it as a context-free recipe., (© 2023 The Authors. Biometrical Journal published by Wiley-VCH GmbH.)

In network meta-analysis, studies evaluating multiple treatment comparisons are modeled simultaneously, and estimation is informed by a combination of direct and indirect evidence. Network meta-analysis relies on an assumption of consistency, meaning that direct and indirect evidence should agree for each treatment comparison. Here we propose new local and global tests for inconsistency and demonstrate their application to three example networks. Because inconsistency is a property of a loop of treatments in the network meta-analysis, we locate the local test in a loop. We define a model with one inconsistency parameter that can be interpreted as loop inconsistency. The model builds on the existing ideas of node-splitting and side-splitting in network meta-analysis. To provide a global test for inconsistency, we extend the model across multiple independent loops with one degree of freedom per loop. We develop a new algorithm for identifying independent loops within a network meta-analysis. Our proposed models handle treatments symmetrically, locate inconsistency in loops rather than in nodes or treatment comparisons, and are invariant to choice of reference treatment, making the results less dependent on model parameterization. For testing global inconsistency in network meta-analysis, our global model uses fewer degrees of freedom than the existing design-by-treatment interaction approach and has the potential to increase power. To illustrate our methods, we fit the models to three network meta-analyses varying in size and complexity. Local and global tests for inconsistency are performed and we demonstrate that the global model is invariant to choice of independent loops., (© 2023 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Individual participant data meta-analysis (IPDMA) projects obtain, check, harmonise and synthesise raw data from multiple studies. When undertaking the meta-analysis, researchers must decide between a two-stage or a one-stage approach. In a two-stage approach, the IPD are first analysed separately within each study to obtain aggregate data (e.g., treatment effect estimates and standard errors); then, in the second stage, these aggregate data are combined in a standard meta-analysis model (e.g., common-effect or random-effects). In a one-stage approach, the IPD from all studies are analysed in a single step using an appropriate model that accounts for clustering of participants within studies and, potentially, between-study heterogeneity (e.g., a general or generalised linear mixed model). The best approach to take is debated in the literature, and so here we provide clearer guidance for a broad audience. Both approaches are important tools for IPDMA researchers and neither are a panacea. If most studies in the IPDMA are small (few participants or events), a one-stage approach is recommended due to using a more exact likelihood. However, in other situations, researchers can choose either approach, carefully following best practice. Some previous claims recommending to always use a one-stage approach are misleading, and the two-stage approach will often suffice for most researchers. When differences do arise between the two approaches, often it is caused by researchers using different modelling assumptions or estimation methods, rather than using one or two stages per se., (© 2023 The Authors. Research Synthesis Methods published by John Wiley & Sons Ltd.)

Many trials use stratified randomisation, where participants are randomised within strata defined by one or more baseline covariates. While it is important to adjust for stratification variables in the analysis, the appropriate method of adjustment is unclear when stratification variables are affected by misclassification and hence some participants are randomised in the incorrect stratum. We conducted a simulation study to compare methods of adjusting for stratification variables affected by misclassification in the analysis of continuous outcomes when all or only some stratification errors are discovered, and when the treatment effect or treatment-by-covariate interaction effect is of interest. The data were analysed using linear regression with no adjustment, adjustment for the strata used to perform the randomisation (randomisation strata), adjustment for the strata if all errors are corrected (true strata), and adjustment for the strata after some errors are discovered and corrected (updated strata). The unadjusted model performed poorly in all settings. Adjusting for the true strata was optimal, while the relative performance of adjusting for the randomisation strata or the updated strata varied depending on the setting. As the true strata are unlikely to be known with certainty in practice, we recommend using the updated strata for adjustment and performing subgroup analyses, provided the discovery of errors is unlikely to depend on treatment group, as expected in blinded trials. Greater transparency is needed in the reporting of stratification errors and how they were addressed in the analysis., (© 2023 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

We describe a new command, artcat, that calculates sample size or power for a randomized controlled trial or similar experiment with an ordered categorical outcome, where analysis is by the proportional-odds model. artcat implements the method of Whitehead (1993, Statistics in Medicine 12: 2257-2271). We also propose and implement a new method that 1) allows the user to specify a treatment effect that does not obey the proportional-odds assumption, 2) offers greater accuracy for large treatment effects, and 3) allows for noninferiority trials. We illustrate the command and explore the value of an ordered categorical outcome over a binary outcome in various settings. We show by simulation that the methods perform well and that the new method is more accurate than Whitehead's method.

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., (© The Author(s) 2022. Published by Oxford University Press on behalf of the International Epidemiological Association.)

Factorial trials offer an efficient method to evaluate multiple interventions in a single trial, however the use of additional treatments can obscure research objectives, leading to inappropriate analytical methods and interpretation of results. We define a set of estimands for factorial trials, and describe a framework for applying these estimands, with the aim of clarifying trial objectives and ensuring appropriate primary and sensitivity analyses are chosen. This framework is intended for use in factorial trials where the intent is to conduct "two-trials-in-one" (ie, to separately evaluate the effects of treatments A and B), and is comprised of four steps: (i) specifying how additional treatment(s) (eg, treatment B) will be handled in the estimand, and how intercurrent events affecting the additional treatment(s) will be handled; (ii) designating the appropriate factorial estimator as the primary analysis strategy; (iii) evaluating the interaction to assess the plausibility of the assumptions underpinning the factorial estimator; and (iv) performing a sensitivity analysis using an appropriate multiarm estimator to evaluate to what extent departures from the underlying assumption of no interaction may affect results. We show that adjustment for other factors is necessary for noncollapsible effect measures (such as odds ratio), and through a trial re-analysis we find that failure to consider the estimand could lead to inappropriate interpretation of results. We conclude that careful use of the estimands framework clarifies research objectives and reduces the risk of misinterpretation of trial results, and should become a standard part of both the protocol and reporting of factorial trials., (© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

The quantitative analysis of research data is a core element of empirical research. The performance of statistical methods that are used for analyzing empirical data can be evaluated and compared using computer simulations. A single simulation study can influence the analyses of thousands of empirical studies to follow. With great power comes great responsibility. Here, we argue that this responsibility includes replication of simulation studies to ensure a sound foundation for data analytical decisions. Furthermore, being designed, run, and reported by humans, simulation studies face challenges similar to other experimental empirical research and hence should not be exempt from replication attempts. We highlight that the potential replicability of simulation studies is an opportunity quantitative methodology as a field should pay more attention to., Competing Interests: Most researchers are genuinely interested in the progress of science and happy to understand the limitations of their theories, hypotheses, or methods in order to refine and evolve them [for a commendable example see (9)]. Yet the feeling of ownership and pride in the context of one's own scientific contributions make us prone to engaging in questionable research practices like HARKING, cherry picking, or p-hacking [see, e.g., (10) for an explanation of these terms]. We have no reason to believe that quantitative methodologists are an exception, as they may be biased toward their own methods just as empirical researchers are biased toward their theories. Even the slightest perceived threat of reputation or citation loss might make authors of simulation studies conflicted when deciding about, for example, which methods to compare, which scenarios to study, which performance measures to compare the methods on, and how to present and interpret the results (3). Confirmation bias makes it furthermore less likely for errors to be detected whenever the simulation code yielded a “favorable” result. In recent years, the Replication/Reproducibility crisis has made evident that pressures outside of the process of scientific discovery can play an overdue role in the design, reporting, and publication of results. When the primary directive of academics is to publish diligently and copiously, it should not come as a surprise if lapses in quality and attention, whether intentional or not, become common over time and the conclusions of published papers become suspect. For the case of simulation research, this could take any number of forms, such as highlighting the aspects of a simulation study where one's preferred method outperforms others, or selectively choosing or reporting specific simulation conditions aimed at guiding the conclusions intended by the researchers. Salami slicing, the practice of obtaining multiple publications from a single dataset (11), is another aspect where simulation research could follow the current academic incentive structure. A simulation study could easily be broken into smaller parts or “mini-simulations” with the aim of maximizing the number of publications that can be produced from a single simulation study.Author TM declares that he consults for Kite Pharma, Inc. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The handling editor AS declared a shared affiliation with the author TM at the time of review., (Copyright © 2022 Lohmann, Astivia, Morris and Groenwold.)

The fraction of cases reported, known as 'reporting', is a key performance indicator in an outbreak response, and an essential factor to consider when modelling epidemics and assessing their impact on populations. Unfortunately, its estimation is inherently difficult, as it relates to the part of an epidemic which is, by definition, not observed. We introduce a simple statistical method for estimating reporting, initially developed for the response to Ebola in Eastern Democratic Republic of the Congo (DRC), 2018-2020. This approach uses transmission chain data typically gathered through case investigation and contact tracing, and uses the proportion of investigated cases with a known, reported infector as a proxy for reporting. Using simulated epidemics, we study how this method performs for different outbreak sizes and reporting levels. Results suggest that our method has low bias, reasonable precision, and despite sub-optimal coverage, usually provides estimates within close range (5-10%) of the true value. Being fast and simple, this method could be useful for estimating reporting in real-time in settings where person-to-person transmission is the main driver of the epidemic, and where case investigation is routinely performed as part of surveillance and contact tracing activities., Competing Interests: The authors have declared that no competing interests exist.

Objective: To improve communication of harm in publications of randomised controlled trials via the development of recommendations for visually presenting harm outcomes., Design: Consensus study., Setting: 15 clinical trials units registered with the UK Clinical Research Collaboration, an academic population health department, Roche Products, and The BMJ ., Participants: Experts in clinical trials: 20 academic statisticians, one industry statistician, one academic health economist, one data graphics designer, and two clinicians., Main Outcome: measures A methodological review of statistical methods identified visualisations along with those recommended by consensus group members. Consensus on visual recommendations was achieved (at least 60% of the available votes) over a series of three meetings with participants. The participants reviewed and critically appraised candidate visualisations against an agreed framework and voted on whether to endorse each visualisation. Scores marginally below this threshold (50-60%) were revisited for further discussions and votes retaken until consensus was reached., Results: 28 visualisations were considered, of which 10 are recommended for researchers to consider in publications of main research findings. The choice of visualisations to present will depend on outcome type (eg, binary, count, time-to-event, or continuous), and the scenario (eg, summarising multiple emerging events or one event of interest). A decision tree is presented to assist trialists in deciding which visualisations to use. Examples are provided of each endorsed visualisation, along with an example interpretation, potential limitations, and signposting to code for implementation across a range of standard statistical software. Clinician feedback was incorporated into the explanatory information provided in the recommendations to aid understanding and interpretation., Conclusions: Visualisations provide a powerful tool to communicate harms in clinical trials, offering an alternative perspective to the traditional frequency tables. Increasing the use of visualisations for harm outcomes in clinical trial manuscripts and reports will provide clearer presentation of information and enable more informative interpretations. The limitations of each visualisation are discussed and examples of where their use would be inappropriate are given. Although the decision tree aids the choice of visualisation, the statistician and clinical trial team must ultimately decide the most appropriate visualisations for their data and objectives. Trialists should continue to examine crude numbers alongside visualisations to fully understand harm profiles., Competing Interests: Competing interests: All authors have completed the ICMJE uniform disclosure form at www.icmje.org/disclosure-of-interest/ and declare: no support from any organisation for the submitted work; no financial relationships with any organisations that might have an interest in the submitted work in the previous three years; no other relationships or activities that could appear to have influenced the submitted work., (© Author(s) (or their employer(s)) 2019. Re-use permitted under CC BY. No commercial re-use. See rights and permissions. Published by BMJ.)

Background: It has long been advised to account for baseline covariates in the analysis of confirmatory randomised trials, with the main statistical justifications being that this increases power and, when a randomisation scheme balanced covariates, permits a valid estimate of experimental error. There are various methods available to account for covariates but it is not clear how to choose among them., Methods: Taking the perspective of writing a statistical analysis plan, we consider how to choose between the three most promising broad approaches: direct adjustment, standardisation and inverse-probability-of-treatment weighting., Results: The three approaches are similar in being asymptotically efficient, in losing efficiency with mis-specified covariate functions and in handling designed balance. If a marginal estimand is targeted (for example, a risk difference or survival difference), then direct adjustment should be avoided because it involves fitting non-standard models that are subject to convergence issues. Convergence is most likely with IPTW. Robust standard errors used by IPTW are anti-conservative at small sample sizes. All approaches can use similar methods to handle missing covariate data. With missing outcome data, each method has its own way to estimate a treatment effect in the all-randomised population. We illustrate some issues in a reanalysis of GetTested, a randomised trial designed to assess the effectiveness of an electonic sexually transmitted infection testing and results service., Conclusions: No single approach is always best: the choice will depend on the trial context. We encourage trialists to consider all three methods more routinely., (© 2022. The Author(s).)

Competing Interests: Declaration of interest None

Simulation studies allow us to explore the properties of statistical methods. They provide a powerful tool with a multiplicity of aims; among others: evaluating and comparing new or existing statistical methods, assessing violations of modelling assumptions, helping with the understanding of statistical concepts, and supporting the design of clinical trials. The increased availability of powerful computational tools and usable software has contributed to the rise of simulation studies in the current literature. However, simulation studies involve increasingly complex designs, making it difficult to provide all relevant results clearly. Dissemination of results plays a focal role in simulation studies: it can drive applied analysts to use methods that have been shown to perform well in their settings, guide researchers to develop new methods in a promising direction, and provide insights into less established methods. It is crucial that we can digest relevant results of simulation studies. Therefore, we developed INTEREST : an INteractive Tool for Exploring REsults from Simulation sTudies . The tool has been developed using the Shiny framework in R and is available as a web app or as a standalone package. It requires uploading a tidy format dataset with the results of a simulation study in R, Stata, SAS, SPSS, or comma-separated format. A variety of performance measures are estimated automatically along with Monte Carlo standard errors; results and performance summaries are displayed both in tabular and graphical fashion, with a wide variety of available plots. Consequently, the reader can focus on simulation parameters and estimands of most interest. In conclusion, INTEREST can facilitate the investigation of results from simulation studies and supplement the reporting of results, allowing researchers to share detailed results from their simulations, readers to explore them freely.

Composite endpoints are commonly used to define primary outcomes in randomized controlled trials. A participant may be classified as meeting the endpoint if they experience an event in one or several components (eg, a favorable outcome based on a composite of being alive and attaining negative culture results in trials assessing tuberculosis treatments). Partially observed components that are not missing simultaneously complicate the analysis of the composite endpoint. An intuitive strategy frequently used in practice for handling missing values in the components is to derive the values of the composite endpoint from observed components when possible, and exclude from analysis participants whose composite endpoint cannot be derived. Alternatively, complete record analysis (CRA) (excluding participants with any missing components) or multiple imputation (MI) can be used. We compare a set of methods for analyzing a composite endpoint with partially observed components mathematically and by simulation, and apply these methods in a reanalysis of a published trial (TOPPS). We show that the derived composite endpoint can be missing not at random even when the components are missing completely at random. Consequently, the treatment effect estimated from the derived endpoint is biased while CRA results without the derived endpoint are valid. Missing at random mechanisms require MI of the components. We conclude that, although superficially attractive, deriving the composite endpoint from observed components should generally be avoided. Despite the potential risk of imputation model mis-specification, MI of missing components is the preferred approach in this study setting., (© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Background: An estimand is a precise description of the treatment effect to be estimated from a trial (the question) and is distinct from the methods of statistical analysis (how the question is to be answered). The potential use of estimands to improve trial research and reporting has been underpinned by the recent publication of the ICH E9(R1) Addendum on the use of estimands in clinical trials in 2019. We set out to assess how well estimands are described in published trial protocols., Methods: We reviewed 50 trial protocols published in October 2020 in Trials and BMJ Open. For each protocol, we determined whether the estimand for the primary outcome was explicitly stated, not stated but inferable (i.e. could be constructed from the information given), or not inferable., Results: None of the 50 trials explicitly described the estimand for the primary outcome, and in 74% of trials, it was impossible to infer the estimand from the information included in the protocol. The population attribute of the estimand could not be inferred in 36% of trials, the treatment condition attribute in 20%, the population-level summary measure in 34%, and the handling of intercurrent events in 60% (the strategy for handling non-adherence was not inferable in 32% of protocols, and the strategy for handling mortality was not inferable in 80% of the protocols for which it was applicable). Conversely, the outcome attribute was stated for all trials. In 28% of trials, three or more of the five estimand attributes could not be inferred., Conclusions: The description of estimands in published trial protocols is poor, and in most trials, it is impossible to understand exactly what treatment effect is being estimated. Given the utility of estimands to improve clinical research and reporting, this urgently needs to change., (© 2021. The Author(s).)

Objective: Missing data can produce biased estimates in interrupted time series (ITS) analyses. We reviewed recent ITS investigations on health topics for determining 1) the data management strategies and statistical analysis performed, 2) how often missing data were considered and, if so, how they were evaluated, reported and handled., Study Design and Setting: This was a scoping review following standard recommendations from the PRISMA Extension for Scoping Reviews. We included a random sample of all ITS studies that assessed any intervention relevant to health care (eg, policies or programmes) with individual-level data, published in 2019, with abstracts indexed on MEDLINE., Results: From 732 studies identified, we finally reviewed 60. Reporting of missing data was rare. Data aggregation, statistical tools for modelling population-level data and complete case analyses were preferred, but these can lead to bias when data are missing at random. Seasonality and other time-dependent confounders were rarely accounted for and, when they were, missing data implications were typically ignored. Very few studies reflected on the consequences of missing data., Conclusion: Handling and reporting of missing data in recent ITS studies performed for health research have many shortcomings compared with best practice., Competing Interests: Dr Tim P Morris reports personal fees from Kite Pharma, Inc., outside the submitted work. Professor James Carpenter reports grants from MRC Clinical Trials Unit, during the conduct of the study; and personal fees from Novartis, outside the submitted work. The authors report no other potential conflicts of interest for this work., (© 2021 Bazo-Alvarez et al.)

In health research, statistical methods are frequently used to address a wide variety of research questions. For almost every analytical challenge, different methods are available. But how do we choose between different methods and how do we judge whether the chosen method is appropriate for our specific study? Like in any science, in statistics, experiments can be run to find out which methods should be used under which circumstances. The main objective of this paper is to demonstrate that simulation studies, that is, experiments investigating synthetic data with known properties, are an invaluable tool for addressing these questions. We aim to provide a first introduction to simulation studies for data analysts or, more generally, for researchers involved at different levels in the analyses of health data, who (1) may rely on simulation studies published in statistical literature to choose their statistical methods and who, thus, need to understand the criteria of assessing the validity and relevance of simulation results and their interpretation; and/or (2) need to understand the basic principles of designing statistical simulations in order to efficiently collaborate with more experienced colleagues or start learning to conduct their own simulations. We illustrate the implementation of a simulation study and the interpretation of its results through a simple example inspired by recent literature, which is completely reproducible using the R-script available from online supplemental file 1., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2020. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

Introduction: In a five-arm randomized clinical trial (RCT) with stratified randomization across 54 sites, we encountered low primary outcome event proportions, resulting in multiple sites with zero events either overall or in one or more study arms. In this paper, we systematically evaluated different statistical methods of accounting for center in settings with low outcome event proportions., Methods: We conducted a simulation study and a reanalysis of a completed RCT to compare five popular methods of estimating an odds ratio for multicenter trials with stratified randomization by center: (i) no center adjustment, (ii) random intercept model, (iii) Mantel-Haenszel model, (iv) generalized estimating equation (GEE) with an exchangeable correlation structure, and (v) GEE with small sample correction (GEE-small sample correction). We varied the number of total participants (200, 500, 1000, 5000), number of centers (5, 50, 100), control group outcome percentage (2%, 5%, 10%), true odds ratio (1, > 1), intra-class correlation coefficient (ICC) (0.025, 0.075), and distribution of participants across the centers (balanced, skewed)., Results: Mantel-Haenszel methods generally performed poorly in terms of power and bias and led to the exclusion of participants from the analysis because some centers had no events. Failure to account for center in the analysis generally led to lower power and type I error rates than other methods, particularly with ICC = 0.075. GEE had an inflated type I error rate except in some settings with a large number of centers. GEE-small sample correction maintained the type I error rate at the nominal level but suffered from reduced power and convergence issues in some settings when the number of centers was small. Random intercept models generally performed well in most scenarios, except with a low event rate (i.e., 2% scenario) and small total sample size (n ≤ 500), when all methods had issues., Discussion: Random intercept models generally performed best across most scenarios. GEE-small sample correction performed well when the number of centers was large. We do not recommend the use of Mantel-Haenszel, GEE, or models that do not account for center. When the expected event rate is low, we suggest that the statistical analysis plan specify an alternative method in the case of non-convergence of the primary method.

Background: In the interrupted time series (ITS) approach, it is common to average the outcome of interest at each time point and then perform a segmented regression (SR) analysis. In this study, we illustrate that such 'aggregate-level' analysis is biased when data are missing at random (MAR) and provide alternative analysis methods., Methods: Using electronic health records from the UK, we evaluated weight change over time induced by the initiation of antipsychotic treatment. We contrasted estimates from aggregate-level SR analysis against estimates from mixed models with and without multiple imputation of missing covariates, using individual-level data. Then, we conducted a simulation study for insight about the different results in a controlled environment., Results: Aggregate-level SR analysis suggested a substantial weight gain after initiation of treatment (average short-term weight change: 0.799kg/week) compared to mixed models (0.412kg/week). Simulation studies confirmed that aggregate-level SR analysis was biased when data were MAR. In simulations, mixed models gave less biased estimates than SR analysis and, in combination with multilevel multiple imputation, provided unbiased estimates. Mixed models with multiple imputation can be used with other types of ITS outcomes (eg, proportions). Other standard methods applied in ITS do not help to correct this bias problem., Conclusion: Aggregate-level SR analysis can bias the ITS estimates when individual-level data are MAR, because taking averages of individual-level data before SR means that data at the cluster level are missing not at random. Avoiding the averaging-step and using mixed models with or without multilevel multiple imputation of covariates is recommended., Competing Interests: Dr Tra My Pham reports grants from Medical Research Council, grants from National Institute for Health Research (NIHR) School for Primary Care Research, grants from Awards to establish the Farr Institute of Health Informatics Research, London, outside the submitted work. Professor James Carpenter reports grants from UK Medical Research Council, during the conduct of the study; personal fees from Novartis, grants from AstraZeneca, outside the submitted work. The authors report no other potential conflicts of interest for this work., (© 2020 Bazo-Alvarez et al.)

Missing data due to loss to follow-up or intercurrent events are unintended, but unfortunately inevitable in clinical trials. Since the true values of missing data are never known, it is necessary to assess the impact of untestable and unavoidable assumptions about any unobserved data in sensitivity analysis. This tutorial provides an overview of controlled multiple imputation (MI) techniques and a practical guide to their use for sensitivity analysis of trials with missing continuous outcome data. These include δ- and reference-based MI procedures. In δ-based imputation, an offset term, δ, is typically added to the expected value of the missing data to assess the impact of unobserved participants having a worse or better response than those observed. Reference-based imputation draws imputed values with some reference to observed data in other groups of the trial, typically in other treatment arms. We illustrate the accessibility of these methods using data from a pediatric eczema trial and a chronic headache trial and provide Stata code to facilitate adoption. We discuss issues surrounding the choice of δ in δ-based sensitivity analysis. We also review the debate on variance estimation within reference-based analysis and justify the use of Rubin's variance estimator in this setting, since as we further elaborate on within, it provides information anchored inference., (© 2020 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

When designing a clinical trial, explicitly defining the treatment estimands of interest (that which is to be estimated) can help to clarify trial objectives and ensure the questions being addressed by the trial are clinically meaningful. There are several challenges when defining estimands. Here, we discuss a number of these in the context of trials of treatments for patients hospitalised with COVID-19 and make suggestions for how estimands should be defined for key outcomes. We suggest that treatment effects should usually be measured as differences in proportions (or risk or odds ratios) for outcomes such as death and requirement for ventilation, and differences in means for outcomes such as the number of days ventilated. We further recommend that truncation due to death should be handled differently depending on whether a patient- or resource-focused perspective is taken; for the former, a composite approach should be used, while for the latter, a while-alive approach is preferred. Finally, we suggest that discontinuation of randomised treatment should be handled from a treatment policy perspective, where non-adherence is ignored in the analysis (i.e. intention to treat).

A one-stage individual participant data (IPD) meta-analysis synthesizes IPD from multiple studies using a general or generalized linear mixed model. This produces summary results (eg, about treatment effect) in a single step, whilst accounting for clustering of participants within studies (via a stratified study intercept, or random study intercepts) and between-study heterogeneity (via random treatment effects). We use simulation to evaluate the performance of restricted maximum likelihood (REML) and maximum likelihood (ML) estimation of one-stage IPD meta-analysis models for synthesizing randomized trials with continuous or binary outcomes. Three key findings are identified. First, for ML or REML estimation of stratified intercept or random intercepts models, a t-distribution based approach generally improves coverage of confidence intervals for the summary treatment effect, compared with a z-based approach. Second, when using ML estimation of a one-stage model with a stratified intercept, the treatment variable should be coded using "study-specific centering" (ie, 1/0 minus the study-specific proportion of participants in the treatment group), as this reduces the bias in the between-study variance estimate (compared with 1/0 and other coding options). Third, REML estimation reduces downward bias in between-study variance estimates compared with ML estimation, and does not depend on the treatment variable coding; for binary outcomes, this requires REML estimation of the pseudo-likelihood, although this may not be stable in some situations (eg, when data are sparse). Two applied examples are used to illustrate the findings., (© 2020 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

Background: The coronavirus pandemic (Covid-19) presents a variety of challenges for ongoing clinical trials, including an inevitably higher rate of missing outcome data, with new and non-standard reasons for missingness. International drug trial guidelines recommend trialists review plans for handling missing data in the conduct and statistical analysis, but clear recommendations are lacking., Methods: We present a four-step strategy for handling missing outcome data in the analysis of randomised trials that are ongoing during a pandemic. We consider handling missing data arising due to (i) participant infection, (ii) treatment disruptions and (iii) loss to follow-up. We consider both settings where treatment effects for a 'pandemic-free world' and 'world including a pandemic' are of interest., Results: In any trial, investigators should; (1) Clarify the treatment estimand of interest with respect to the occurrence of the pandemic; (2) Establish what data are missing for the chosen estimand; (3) Perform primary analysis under the most plausible missing data assumptions followed by; (4) Sensitivity analysis under alternative plausible assumptions. To obtain an estimate of the treatment effect in a 'pandemic-free world', participant data that are clinically affected by the pandemic (directly due to infection or indirectly via treatment disruptions) are not relevant and can be set to missing. For primary analysis, a missing-at-random assumption that conditions on all observed data that are expected to be associated with both the outcome and missingness may be most plausible. For the treatment effect in the 'world including a pandemic', all participant data is relevant and should be included in the analysis. For primary analysis, a missing-at-random assumption - potentially incorporating a pandemic time-period indicator and participant infection status - or a missing-not-at-random assumption with a poorer response may be most relevant, depending on the setting. In all scenarios, sensitivity analysis under credible missing-not-at-random assumptions should be used to evaluate the robustness of results. We highlight controlled multiple imputation as an accessible tool for conducting sensitivity analyses., Conclusions: Missing data problems will be exacerbated for trials active during the Covid-19 pandemic. This four-step strategy will facilitate clear thinking about the appropriate analysis for relevant questions of interest.

In this paper we study approaches for dealing with treatment when developing a clinical prediction model. Analogous to the estimand framework recently proposed by the European Medicines Agency for clinical trials, we propose a 'predictimand' framework of different questions that may be of interest when predicting risk in relation to treatment started after baseline. We provide a formal definition of the estimands matching these questions, give examples of settings in which each is useful and discuss appropriate estimators including their assumptions. We illustrate the impact of the predictimand choice in a dataset of patients with end-stage kidney disease. We argue that clearly defining the estimand is equally important in prediction research as in causal inference.

Background: Missing data in covariates can result in biased estimates and loss of power to detect associations. It can also lead to other challenges in time-to-event analyses including the handling of time-varying effects of covariates, selection of covariates and their flexible modelling. This review aims to describe how researchers approach time-to-event analyses with missing data., Methods: Medline and Embase were searched for observational time-to-event studies in oncology published from January 2012 to January 2018. The review focused on proportional hazards models or extended Cox models. We investigated the extent and reporting of missing data and how it was addressed in the analysis. Covariate modelling and selection, and assessment of the proportional hazards assumption were also investigated, alongside the treatment of missing data in these procedures., Results: 148 studies were included. The mean proportion of individuals with missingness in any covariate was 32%. 53% of studies used complete-case analysis, and 22% used multiple imputation. In total, 14% of studies stated an assumption concerning missing data and only 34% stated missingness as a limitation. The proportional hazards assumption was checked in 28% of studies, of which, 17% did not state the assessment method. 58% of 144 multivariable models stated their covariate selection procedure with use of a pre-selected set of covariates being the most popular followed by stepwise methods and univariable analyses. Of 69 studies that included continuous covariates, 81% did not assess the appropriateness of the functional form., Conclusion: While guidelines for handling missing data in epidemiological studies are in place, this review indicates that few report implementing recommendations in practice. Although missing data are present in many studies, we found that few state clearly how they handled it or the assumptions they have made. Easy-to-implement but potentially biased approaches such as complete-case analysis are most commonly used despite these relying on strong assumptions and where often more appropriate methods should be employed. Authors should be encouraged to follow existing guidelines to address missing data, and increased levels of expectation from journals and editors could be used to improve practice.

Background: Antipsychotics are often prescribed for long-term periods, however, most evidence of their impact on body weight comes from short-term clinical trials. Particularly, impact associated with dosage has been barely studied., Aims: The aim of this study was to describe the short- and long-term change in body weight of people initiated on high or low doses of the three most commonly prescribed second-generation antipsychotics., Methods: Retrospective cohorts of individuals with a diagnosed psychotic disorder observed from 2005 to 2015 in the UK primary care. The exposure was the first prescription of olanzapine, quetiapine or risperidone. The main outcome was change in body weight four years before and four years after initiation of antipsychotic treatment, stratified on sex and 'low' or 'high' dose., Results: In total, 22,306 women and 16,559 men were observed. Olanzapine treatment was associated with the highest change in weight, with higher doses resulting in more weight gain. After 4 years, given a high dose of olanzapine (> 5 mg), women gained on average +6.1 kg; whereas given a low dose (⩽ 5 mg), they gained +4.4 kg. During the first six weeks of olanzapine treatment, they gained on average +3.2 kg on high dose and +1.9 kg on low dose. The trends were similar for men. Individuals prescribed risperidone and quetiapine experienced less weight gain in both the short- and long-term., Conclusions: Olanzapine treatment was associated with the highest increase in weight. Higher doses were associated with more weight gain. Doctors should prescribe the lowest effective dose to balance mental-health benefits, weight gain and other adverse effects.

Objectives: To examine reactions to the proposed improvements to standard Kaplan-Meier plots, the standard way to present time-to-event data, and to understand which (if any) facilitated better depiction of (1) the state of patients over time, and (2) uncertainty over time in the estimates of survival., Design: A survey of stakeholders' opinions on the proposals., Setting: A web-based survey, open to international participation, for those with an interest in visualisation of time-to-event data., Participants: 1174 people participated in the survey over a 6-week period. Participation was global (although primarily Europe and North America) and represented a wide range of researchers (primarily statisticians and clinicians)., Main Outcome Measures: Two outcome measures were of principal importance: (1) participants' opinions of each proposal compared with a 'standard' Kaplan-Meier plot; and (2) participants' overall ranking of the proposals (including the standard)., Results: Most proposals were more popular than the standard Kaplan-Meier plot. The most popular proposals in the two categories, respectively, were an extended table beneath the plot depicting the numbers at risk, censored and having experienced an event at periodic timepoints, and CIs around each Kaplan-Meier curve., Conclusions: This study produced a high response number, reflecting the importance of graphics for time-to-event data. Those producing and publishing Kaplan-Meier plots-both authors and journals-should, as a starting point, consider using the combination of the two favoured proposals., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2019. Re-use permitted under CC BY. Published by BMJ.)

Simulation studies are computer experiments that involve creating data by pseudo-random sampling. A key strength of simulation studies is the ability to understand the behavior of statistical methods because some "truth" (usually some parameter/s of interest) is known from the process of generating the data. This allows us to consider properties of methods, such as bias. While widely used, simulation studies are often poorly designed, analyzed, and reported. This tutorial outlines the rationale for using simulation studies and offers guidance for design, execution, analysis, reporting, and presentation. In particular, this tutorial provides a structured approach for planning and reporting simulation studies, which involves defining aims, data-generating mechanisms, estimands, methods, and performance measures ("ADEMP"); coherent terminology for simulation studies; guidance on coding simulation studies; a critical discussion of key performance measures and their estimation; guidance on structuring tabular and graphical presentation of results; and new graphical presentations. With a view to describing recent practice, we review 100 articles taken from Volume 34 of Statistics in Medicine, which included at least one simulation study and identify areas for improvement., (© 2019 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

Multiple imputation (MI) has become popular for analyses with missing data in medical research. The standard implementation of MI is based on the assumption of data being missing at random (MAR). However, for missing data generated by missing not at random mechanisms, MI performed assuming MAR might not be satisfactory. For an incomplete variable in a given data set, its corresponding population marginal distribution might also be available in an external data source. We show how this information can be readily utilised in the imputation model to calibrate inference to the population by incorporating an appropriately calculated offset termed the "calibrated-δ adjustment." We describe the derivation of this offset from the population distribution of the incomplete variable and show how, in applications, it can be used to closely (and often exactly) match the post-imputation distribution to the population level. Through analytic and simulation studies, we show that our proposed calibrated-δ adjustment MI method can give the same inference as standard MI when data are MAR, and can produce more accurate inference under two general missing not at random missingness mechanisms. The method is used to impute missing ethnicity data in a type 2 diabetes prevalence case study using UK primary care electronic health records, where it results in scientifically relevant changes in inference for non-White ethnic groups compared with standard MI. Calibrated-δ adjustment MI represents a pragmatic approach for utilising available population-level information in a sensitivity analysis to explore potential departures from the MAR assumption., (© 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)

Background: Clinical databases are increasingly used for health research; many of them capture information on common health indicators including height, weight, blood pressure, cholesterol level, smoking status, and alcohol consumption. However, these are often not recorded on a regular basis; missing data are ubiquitous. We described the recording of health indicators in UK primary care and evaluated key implications for handling missing data., Methods: We examined the recording of health indicators in The Health Improvement Network (THIN) UK primary care database over time, by demographic variables (age and sex) and chronic diseases (diabetes, myocardial infarction, and stroke). Using weight as an example, we fitted linear and logistic regression models to examine the associations of weight measurements and the probability of having weight recorded with individuals' demographic characteristics and chronic diseases., Results: In total, 6,345,851 individuals aged 18-99 years contributed data to THIN between 2000 and 2015. Women aged 18-65 years were more likely than men of the same age to have health indicators recorded; this gap narrowed after age 65. About 60-80% of individuals had their height, weight, blood pressure, smoking status, and alcohol consumption recorded during the first year of registration. In the years following registration, these proportions fell to 10%-40%. Individuals with chronic diseases were more likely to have health indicators recorded, particularly after the introduction of a General Practitioner incentive scheme. Individuals' demographic characteristics and chronic diseases were associated with both observed weight measurements and missingness in weight., Conclusion: Missing data in common health indicators will affect statistical analysis in health research studies. A single analysis of primary care data using the available information alone may be misleading. Multiple imputation of missing values accounting for demographic characteristics and disease status is recommended but should be considered and implemented carefully. Sensitivity analysis exploring alternative assumptions for missing data should also be evaluated., Competing Interests: Disclosure The authors report no conflicts of interest in this work.

One-stage individual participant data meta-analysis models should account for within-trial clustering, but it is currently debated how to do this. For continuous outcomes modeled using a linear regression framework, two competing approaches are a stratified intercept or a random intercept. The stratified approach involves estimating a separate intercept term for each trial, whereas the random intercept approach assumes that trial intercepts are drawn from a normal distribution. Here, through an extensive simulation study for continuous outcomes, we evaluate the impact of using the stratified and random intercept approaches on statistical properties of the summary treatment effect estimate. Further aims are to compare (i) competing estimation options for the one-stage models, including maximum likelihood and restricted maximum likelihood, and (ii) competing options for deriving confidence intervals (CI) for the summary treatment effect, including the standard normal-based 95% CI, and more conservative approaches of Kenward-Roger and Satterthwaite, which inflate CIs to account for uncertainty in variance estimates. The findings reveal that, for an individual participant data meta-analysis of randomized trials with a 1:1 treatment:control allocation ratio and heterogeneity in the treatment effect, (i) bias and coverage of the summary treatment effect estimate are very similar when using stratified or random intercept models with restricted maximum likelihood, and thus either approach could be taken in practice, (ii) CIs are generally best derived using either a Kenward-Roger or Satterthwaite correction, although occasionally overly conservative, and (iii) if maximum likelihood is required, a random intercept performs better than a stratified intercept model. An illustrative example is provided., (© 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons, Ltd.)

In Cox regression, it is important to test the proportional hazards assumption and sometimes of interest in itself to study time-varying effects (TVEs) of covariates. TVEs can be investigated with log hazard ratios modelled as a function of time. Missing data on covariates are common and multiple imputation is a popular approach to handling this to avoid the potential bias and efficiency loss resulting from a "complete-case" analysis. Two multiple imputation methods have been proposed for when the substantive model is a Cox proportional hazards regression: an approximate method (Imputing missing covariate values for the Cox model in Statistics in Medicine (2009) by White and Royston) and a substantive-model-compatible method (Multiple imputation of covariates by fully conditional specification: accommodating the substantive model in Statistical Methods in Medical Research (2015) by Bartlett et al). At present, neither accommodates TVEs of covariates. We extend them to do so for a general form for the TVEs and give specific details for TVEs modelled using restricted cubic splines. Simulation studies assess the performance of the methods under several underlying shapes for TVEs. Our proposed methods give approximately unbiased TVE estimates for binary covariates with missing data, but for continuous covariates, the substantive-model-compatible method performs better. The methods also give approximately correct type I errors in the test for proportional hazards when there is no TVE and gain power to detect TVEs relative to complete-case analysis. Ignoring TVEs at the imputation stage results in biased TVE estimates, incorrect type I errors, and substantial loss of power in detecting TVEs. We also propose a multivariable TVE model selection algorithm. The methods are illustrated using data from the Rotterdam Breast Cancer Study. R code is provided., (© 2018 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.)