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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 noncollapsibility. 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Membership of overlapping or intersecting sets may be recorded in a bundle of (0, 1) indicator variables. Annotated Euler or Venn diagrams may be used to show graphically the frequencies of subsets so defined, but beyond just a few sets such diagrams can be hard to draw and use effectively. This column presents two new commands for graphical alternatives: upsetplot and vennbar. Each command produces a bar chart by default, but there is scope to recast to different graphical forms. The differences between the new commands reflect the divide in Stata between twoway commands and other graph commands. They also provide some flexibility in graph design to match tastes and circumstances. The discussion includes many historical details and references. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

For simulation studies that evaluate methods of handling missing data, we argue that generating partially observed data by fixing the complete data and repeatedly simulating the missingness indicators is a superficially attractive idea but only rarely appropriate to use. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Background: The prevalence of genital chlamydia and gonorrhoea is higher in the 16-24 years age group than those in other age group. With users, we developed the theory-based safetxt intervention to reduce sexually transmitted infections. Objectives: To establish the effect of the safetxt intervention on the incidence of chlamydia/gonorrhoea infection at 1 year. Design: A parallel-group, individual-level, randomised superiority trial in which care providers and outcome assessors were blinded to allocation. Setting: Recruitment was from 92 UK sexual health clinics. Participants: Inclusion criteria were a positive chlamydia or gonorrhoea test result, diagnosis of non-specific urethritis or treatment started for chlamydia/gonorrhoea/non-specific urethritis in the last 2 weeks; owning a personal mobile phone; and being aged 16-24 years. Allocation: Remote computer-based randomisation with an automated link to the messaging system delivering intervention or control group messages. Intervention: The safetxt intervention was designed to reduce sexually transmitted infection by increasing partner notification, condom use and sexually transmitted infection testing before sex with new partners. It employed educational, enabling and incentivising content delivered by 42-79 text messages over 1 year, tailored according to type of infection, gender and sexuality. Comparator: A monthly message regarding trial participation. Main outcomes: The primary outcome was the incidence of chlamydia and gonorrhoea infection at 12 months, assessed using nucleic acid amplification tests. Secondary outcomes at 1 and 12 months included self-reported partner notification, condom use and sexually transmitted infection testing prior to sex with new partner(s). Results: Between 1 April 2016 and 23 November 2018, we assessed 20,476 people for eligibility and consented and randomised 6248 participants, allocating 3123 to the safetxt intervention and 3125 to the control. Primary outcome data were available for 4675 (74.8%) participants. The incidence of chlamydia/gonorrhoea infection was 22.2% (693/3123) in the intervention group and 20.3% (633/3125) in the control group (odds ratio 1.13, 95% confidence interval 0.98 to 1.31). There was no evidence of heterogeneity in any of the prespecified subgroups. Partner notification was 85.6% in the intervention group and 84.0% in the control group (odds ratio 1.14, 95% confidence interval 0.99 to 1.33). At 12 months, condom use at last sex was 33.8% in the intervention group and 31.2% in the control group (odds ratio 1.14, 95% confidence interval 1.01 to 1.28) and condom use at first sex with most recent new partner was 54.4% in the intervention group and 48.7% in the control group (odds ratio 1.27, 95% confidence interval 1.11 to 1.45). Testing before sex with a new partner was 39.5% in the intervention group and 40.9% in the control group (odds ratio 0.95, 95% confidence interval 0.82 to 1.10). Having two or more partners since joining the trial was 56.9% in the intervention group and 54.8% in the control group (odds ratio 1.11, 95% confidence interval 1.00 to 1.24) and having sex with someone new since joining the trial was 69.7% in the intervention group and 67.4% in the control group (odds ratio 1.13, 95% confidence interval 1.00 to 1.28). There were no differences in safety outcomes. Additional sensitivity and per-protocol analyses showed similar results. Limitations: Our understanding of the mechanism of action for the unanticipated effects is limited. Conclusions: The safetxt intervention did not reduce chlamydia and gonorrhoea infections, with slightly more infections in the intervention group. The intervention increased condom use but also increased the number of partners and new partners. Randomised controlled trials are essential for evaluating health communication interventions, which can have unanticipated effects. Future work: Randomised controlled trials evaluating novel interventions in this complex area are needed. Trial registration: This trial is registered as ISRCTN64390461. Funding: This project was funded by the National Institute for Health and Care Research (NIHR) Public Health Research programme and will be published in full in Public Health Research; Vol. 11, No. 1. See the NIHR Journals Library website for further project information. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. Author summary: When responding to epidemics of infectious diseases, it is essential to estimate how many cases are not being reported. Unfortunately reporting, the proportion of cases actually observed, is difficult to estimate during an outbreak, as it typically requires large surveys to be conducted on the affected populations. Here, we introduce a method for estimating reporting from case investigation data, using the proportion of cases with a known, reported infector. We used simulations to test the performance of our approach by mimicking features of a recent Ebola epidemic in the Democratic Republic of the Congo. We found that despite some uncertainty in smaller outbreaks, our approach can be used to obtain informative ballpark estimates of reporting under most settings. This method is simple and computationally inexpensive, and can be used to inform the response to any epidemic in which transmission events can be uncovered by case investigation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Aims/Hypothesis: Type 2 diabetes mellitus is associated with high levels of disease burden, including increased mortality risk and significant long-term morbidity. The prevalence of diabetes differs substantially among ethnic groups. We examined the prevalence of type 2 diabetes diagnoses in the UK primary care setting. Methods: We analysed data from 404,318 individuals in The Health Improvement Network database, aged 0–99 years and permanently registered with general practices in London. The association between ethnicity and the prevalence of type 2 diabetes diagnoses in 2013 was estimated using a logistic regression model, adjusting for effect of age group, sex, and social deprivation. A multiple imputation approach utilising population-level information about ethnicity from the UK census was used for imputing missing data. Results: Compared with those of White ethnicity (5.04%, 95% CI 4.95 to 5.13), the crude percentage prevalence of type 2 diabetes was higher in the Asian (7.69%, 95% CI 7.46 to 7.92) and Black (5.58%, 95% CI 5.35 to 5.81) ethnic groups, while lower in the Mixed/Other group (3.42%, 95% CI 3.19 to 3.66). After adjusting for differences in age group, sex, and social deprivation, all minority ethnic groups were more likely to have a diagnosis of type 2 diabetes compared with the White group (OR Asian versus White 2.36, 95% CI 2.26 to 2.47; OR Black versus White 1.65, 95% CI 1.56 to 1.73; OR Mixed/Other versus White 1.17, 95% CI 1.08 to 1.27). Conclusion: The prevalence of type 2 diabetes was higher in the Asian and Black ethnic groups, compared with the White group. Accurate estimates of ethnic prevalence of type 2 diabetes based on large datasets are important for facilitating appropriate allocation of public health resources, and for allowing population-level research to be undertaken examining disease trajectories among minority ethnic groups, that might help reduce inequalities. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Quantitative evidence synthesis through meta-analysis is central to evidence-based medicine. For well-documented reasons, the meta-analysis of individual patient data is held in higher regard than aggregate data. With access to individual patient data, the analysis is not restricted to a "two-stage" approach (combining estimates and standard errors) but can estimate parameters of interest by fitting a single model to all of the data, a so-called "one-stage" analysis. There has been debate about the merits of one- and two-stage analysis. Arguments for one-stage analysis have typically noted that a wider range of models can be fitted and overall estimates may be more precise. The two-stage side has emphasised that the models that can be fitted in two stages are sufficient to answer the relevant questions, with less scope for mistakes because there are fewer modelling choices to be made in the two-stage approach. For Gaussian data, we consider the statistical arguments for flexibility and precision in small-sample settings. Regarding flexibility, several of the models that can be fitted only in one stage may not be of serious interest to most meta-analysis practitioners. Regarding precision, we consider fixed- and random-effects meta-analysis and see that, for a model making certain assumptions, the number of stages used to fit this model is irrelevant; the precision will be approximately equal. Meta-analysts should choose modelling assumptions carefully. Sometimes relevant models can only be fitted in one stage. Otherwise, meta-analysts are free to use whichever procedure is most convenient to fit the identified model. [ABSTRACT FROM AUTHOR]

Background: Internet-accessed sexually transmitted infection testing (e-STI testing) is increasingly available as an alternative to testing in clinics. Typically this testing modality enables users to order a test kit from a virtual service (via a website or app), collect their own samples, return test samples to a laboratory, and be notified of their results by short message service (SMS) or telephone. e-STI testing is assumed to increase access to testing in comparison with face-to-face services, but the evidence is unclear. We conducted a randomised controlled trial to assess the effectiveness of an e-STI testing and results service (chlamydia, gonorrhoea, HIV, and syphilis) on STI testing uptake and STI cases diagnosed.Methods and Findings: The study took place in the London boroughs of Lambeth and Southwark. Between 24 November 2014 and 31 August 2015, we recruited 2,072 participants, aged 16-30 years, who were resident in these boroughs, had at least 1 sexual partner in the last 12 months, stated willingness to take an STI test, and had access to the internet. Those unable to provide consent and unable to read English were excluded. Participants were randomly allocated to receive 1 text message with the web link of an e-STI testing and results service (intervention group) or to receive 1 text message with the web link of a bespoke website listing the locations, contact details, and websites of 7 local sexual health clinics (control group). Participants were free to use any other services or interventions during the study period. The primary outcomes were self-reported STI testing at 6 weeks, verified by patient record checks, and self-reported STI diagnosis at 6 weeks, verified by patient record checks. Secondary outcomes were the proportion of participants prescribed treatment for an STI, time from randomisation to completion of an STI test, and time from randomisation to treatment of an STI. Participants were sent a £10 cash incentive on submission of self-reported data. We completed all follow-up, including patient record checks, by 17 June 2016. Uptake of STI testing was increased in the intervention group at 6 weeks (50.0% versus 26.6%, relative risk [RR] 1.87, 95% CI 1.63 to 2.15, P < 0.001). The proportion of participants diagnosed was 2.8% in the intervention group versus 1.4% in the control group (RR 2.10, 95% CI 0.94 to 4.70, P = 0.079). No evidence of heterogeneity was observed for any of the pre-specified subgroup analyses. The proportion of participants treated was 1.1% in the intervention group versus 0.7% in the control group (RR 1.72, 95% CI 0.71 to 4.16, P = 0.231). Time to test, was shorter in the intervention group compared to the control group (28.8 days versus 36.5 days, P < 0.001, test for difference in restricted mean survival time [RMST]), but no differences were observed for time to treatment (83.2 days versus 83.5 days, P = 0.51, test for difference in RMST). We were unable to recruit the planned 3,000 participants and therefore lacked power for the analyses of STI diagnoses and STI cases treated.Conclusions: The e-STI testing service increased uptake of STI testing for all groups including high-risk groups. The intervention required people to attend clinic for treatment and did not reduce time to treatment. Service innovations to improve treatment rates for those diagnosed online are required and could include e-treatment and postal treatment services. e-STI testing services require long-term monitoring and evaluation.Trial Registration: ISRCTN Registry ISRCTN13354298. [ABSTRACT FROM AUTHOR]

How should we approach trial design when we can get some, but not all, of the way to the numbers required for a randomised phase III trial? We present an ordered framework for designing randomised trials to address the problem when the ideal sample size is considered larger than the number of participants that can be recruited in a reasonable time frame. Staying with the frequentist approach that is well accepted and understood in large trials, we propose a framework that includes small alterations to the design parameters. These aim to increase the numbers achievable and also potentially reduce the sample size target. The first step should always be to attempt to extend collaborations, consider broadening eligibility criteria and increase the accrual time or follow-up time. The second set of ordered considerations are the choice of research arm, outcome measures, power and target effect. If the revised design is still not feasible, in the third step we propose moving from two- to one-sided significance tests, changing the type I error rate, using covariate information at the design stage, re-randomising patients and borrowing external information. We discuss the benefits of some of these possible changes and warn against others. We illustrate, with a worked example based on the Euramos-1 trial, the application of this framework in designing a trial that is feasible, while still providing a good evidence base to evaluate a research treatment. This framework would allow appropriate evaluation of treatments when large-scale phase III trials are not possible, but where the need for high-quality randomised data is as pressing as it is for common diseases. [ABSTRACT FROM AUTHOR]

Background: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy.Methods: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets.Results: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall.Conclusions: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt. [ABSTRACT FROM AUTHOR]

Randomized controlled trials provide essential evidence for the evaluation of new and existing medical treatments. Unfortunately, the statistical analysis is often complicated by the occurrence of protocol deviations, which mean we cannot always measure the intended outcomes for individuals who deviate, resulting in a missing-data problem. In such settings, however one approaches the analysis, an untestable assumption about the distribution of the unobserved data must be made. To understand how far the results depend on these assumptions, the primary analysis should be supplemented by a range of sensitivity analyses, which explore how the conclusions vary over a range of different credible assumptions for the missing data. In this article, we describe a new command, mimix, that can be used to perform reference-based sensitivity analyses for randomized controlled trials with longitudinal quantitative outcome data, using the approach proposed by Carpenter, Roger, and Kenward (2013, Journal of Biopharmaceutical Statistics 23: 1352-1371). Under this approach, we make qualitative assumptions about how individuals' missing outcomes relate to those observed in relevant groups in the trial, based on plausible clinical scenarios. Statistical analysis then proceeds using the method of multiple imputation. [ABSTRACT FROM AUTHOR]

A major factor in the uptake of new statistical methods is the availability of user-friendly software implementations. One attractive feature of Stata is that users can write their own commands and release them to other users via Statistical Software Components at Boston College. Authors of statistical programs do not always get adequate credit, because programs are rarely cited properly. There is no obvious measure of a program's impact, but researchers are under increasing pressure to demonstrate the impact of their work to funders. In addition to encouraging proper citation of software, the number of downloads of a user-written package can be regarded as a measure of impact over time. In this article, we explain how such information can be accessed for any month from July 2007 and summarized using the new ssccount command. [ABSTRACT FROM AUTHOR]

Multivariable fractional polynomial (MFP) models are commonly used in medical research. The datasets in which MFP models are applied often contain covariates with missing values. To handle the missing values, we describe methods for combining multiple imputation with MFP modelling, considering in turn three issues: first, how to impute so that the imputation model does not favour certain fractional polynomial (FP) models over others; second, how to estimate the FP exponents in multiply imputed data; and third, how to choose between models of differing complexity. Two imputation methods are outlined for different settings. For model selection, methods based on Wald-type statistics and weighted likelihood-ratio tests are proposed and evaluated in simulation studies. The Wald-based method is very slightly better at estimating FP exponents. Type I error rates are very similar for both methods, although slightly less well controlled than analysis of complete records; however, there is potential for substantial gains in power over the analysis of complete records. We illustrate the two methods in a dataset from five trauma registries for which a prognostic model has previously been published, contrasting the selected models with that obtained by analysing the complete records only. [ABSTRACT FROM AUTHOR]

Background: Recruitment to clinical trials is often problematic, with many trials failing to recruit to their target sample size. As a result, patient care may be based on suboptimal evidence from underpowered trials or non-randomised studies.Methods: For many conditions patients will require treatment on several occasions, for example, to treat symptoms of an underlying chronic condition (such as migraines, where treatment is required each time a new episode occurs), or until they achieve treatment success (such as fertility, where patients undergo treatment on multiple occasions until they become pregnant). We describe a re-randomisation design for these scenarios, which allows each patient to be independently randomised on multiple occasions. We discuss the circumstances in which this design can be used.Results: The re-randomisation design will give asymptotically unbiased estimates of treatment effect and correct type I error rates under the following conditions: (a) patients are only re-randomised after the follow-up period from their previous randomisation is complete; (b) randomisations for the same patient are performed independently; and (c) the treatment effect is constant across all randomisations. Provided the analysis accounts for correlation between observations from the same patient, this design will typically have higher power than a parallel group trial with an equivalent number of observations.Conclusions: If used appropriately, the re-randomisation design can increase the recruitment rate for clinical trials while still providing an unbiased estimate of treatment effect and correct type I error rates. In many situations, it can increase the power compared to a parallel group design with an equivalent number of observations. [ABSTRACT FROM AUTHOR]

Multiple imputation is a practical, principled approach to handling missing data. When used to impute missing values in covariates of regression models, imputation models may be misspecified if they are not compatible with the substantive model of interest for the outcome. In this article, we introduce the smcfcs command, which imputes covariates by substantive-model compatible fully conditional specification. This modifies the popular fully conditional specification or chained-equations approach to multiple imputation by imputing each covariate compatibly with a user-specified substantive model. We compare the smcfcs command with standard fully conditional specification imputation using mi impute chained in a simulation study and illustrative analysis of data from a study investigating time to tumor recurrence in breast cancer. [ABSTRACT FROM AUTHOR]