Data-Driven Simulations to Assess the Impact of Study Imperfections in Time-to-Event Analyses.

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.

Comments on 'standard and reference-based conditional mean imputation': Regulators and trial statisticians be aware!

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.

Genetic associations of risk behaviours and educational achievement.

Risk behaviours are common in adolescent and persist into adulthood, people who engage in more risk behaviours are more likely to have lower educational attainment. We applied genetic causal inference methods to explore the causal relationship between adolescent risk behaviours and educational achievement. Risk behaviours were phenotypically associated with educational achievement at age 16 after adjusting for confounders (-0.11, 95%CI: -0.11, -0.09). Genomic-based restricted maximum likelihood (GREML) results indicated that both traits were heritable and have a shared genetic architecture (Risk h 2 = 0.18, 95% CI: -0.11,0.47; education h 2 = 0.60, 95%CI: 0.50,0.70). Consistent with the phenotypic results, genetic variation associated with risk behaviour was negatively associated with education ( r g = -0.51, 95%CI: -1.04,0.02). Lastly, the bidirectional MR results indicate that educational achievement or a closely related trait is likely to affect risk behaviours PGI (ß=-1.04, 95% CI: -1.41, -0.67), but we found little evidence that the genetic variation associated with risk behaviours affected educational achievement (ß=0.00, 95% CI: -0.24,0.24). The results suggest engagement in risk behaviour may be partly driven by educational achievement or a closely related trait.

Local government spending and mental health: Untangling the impacts using a dynamic modelling approach.

This study investigated the impact of local government spending on mental health in England between 2013 and 2019. Guided by the "Health in All Policies" vision, which encourages the integration of health in all decision-making areas, we explored how healthcare and multiple nonmedical budgeting decisions related to population mental health. We used random curve general cross-lagged modelling to dynamically partition effects into the short-run (from t to t + 1) and long-run (from t to t + 2) impacts, account for unobserved area-level heterogeneity and reverse causality from health outcomes to financial investments, and comprehensive modelling of budget items as an interconnected system. Our findings revealed that spending in adult social care, healthcare, and law & order predicted long-term mental health gains (0.004-0.081 SDs increase for each additional 10% in expenditure). However, these sectors exhibited negative short-term impulses (0.012-0.077 SDs decrease for each additional 10% in expenditure), markedly offsetting the long-term gains. In turn, infrastructural and environmental spending related to short-run mental health gains (0.005-0.031 SDs increase for each additional 10% in expenditure), while the long-run effects were predominantly negative (0.005-0.028 SDs decrease for each additional 10% in expenditure). The frequent occurrence of short-run and long-run negative links suggested that government resources may not be effectively reaching the areas that are most in need. In the short-term, negative effects could also imply temporary disruptions to service delivery largely uncompensated by later mental health improvements. Nonetheless, some non-health spending policies, such as law & order and infrastructure, can be related to long-lasting positive mental health impacts.

Categorisation of continuous covariates for stratified randomisation: How should we adjust?

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.

Meta-regression of genome-wide association studies to estimate age-varying genetic effects.

Fixed-effect meta-analysis has been used to summarize genetic effects on a phenotype across multiple Genome-Wide Association Studies (GWAS) assuming a common underlying genetic effect. Genetic effects may vary with age (or other characteristics), and not allowing for this in a GWAS might lead to bias. Meta-regression models between study heterogeneity and allows effect modification of the genetic effects to be explored. The aim of this study was to explore the use of meta-analysis and meta-regression for estimating age-varying genetic effects on phenotypes. With simulations we compared the performance of meta-regression to fixed-effect and random -effects meta-analyses in estimating (i) main genetic effects and (ii) age-varying genetic effects (SNP by age interactions) from multiple GWAS studies under a range of scenarios. We applied meta-regression on publicly available summary data to estimate the main and age-varying genetic effects of the FTO SNP rs9939609 on Body Mass Index (BMI). Fixed-effect and random-effects meta-analyses accurately estimated genetic effects when these did not change with age. Meta-regression accurately estimated both main genetic effects and age-varying genetic effects. When the number of studies or the age-diversity between studies was low, meta-regression had limited power. In the applied example, each additional minor allele (A) of rs9939609 was inversely associated with BMI at ages 0 to 3, and positively associated at ages 5.5 to 13. Our findings challenge the assumption that genetic effects are consistent across all ages and provide a method for exploring this. GWAS consortia should be encouraged to use meta-regression to explore age-varying genetic effects.

Socio-economic differences in body mass index: the contribution of genetic factors.

BACKGROUND: Higher mean body mass index (BMI) among lower socioeconomic position (SEP) groups is well established in Western societies, but the influence of genetic factors on these differences is not well characterized. METHODS: We analyzed these associations using Finnish health surveys conducted between 1992 and 2017 (N = 33 523; 53% women) with information on measured weight and height, polygenic risk scores of BMI (PGS-BMI) and linked data from administrative registers to measure educational attainment, occupation-based social class and personal income. RESULTS: In linear regressions, largest adjusted BMI differences were found between basic and tertiary educated men (1.4 kg/m2, 95% confidence interval [CI] 1.2; 1.6) and women (2.5 kg/m2, 95% CI 2.3; 2.8), and inverse BMI gradients were also found for social class and income. These SEP differences arose partly because mean PGS-BMI was higher and partly because PGS-BMI predicted BMI more strongly in lower SEP groups. The inverse SEP gradients of BMI were steeper in women than in men, but sex differences were not found in the genetic contributions to these differences. CONCLUSIONS: Better understanding of the interplay between genes and environment provides insight into the mechanisms explaining SEP differences in BMI.

Phases of methodological research in biostatistics-Building the evidence base for new methods.

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.

How to check a simulation study.

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.

Comment on Oberman & Vink: Should we fix or simulate the complete data in simulation studies evaluating missing data methods?

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.

Maternal depressive symptoms and young people's higher education participation and choice of university: Evidence from a longitudinal cohort study.

BACKGROUND: Participation in higher education has significant and long-lasting consequences for people's socioeconomic trajectories. Maternal depression is linked to poorer educational achievement for children in school, but its impact on university attendance is unclear. METHODS: In an English longitudinal cohort study (N = 8952), we explore whether young people whose mothers experienced elevated depressive symptoms are less likely to attend university, and the role of potential mediators in the young person: educational achievement in school, depressive symptoms, and locus of control. We also examine whether maternal depressive symptoms influence young people's choice of university, and non-attendees' reasons for not participating in higher education. RESULTS: Young people whose mothers experienced more recurrent depressive symptoms were less likely to attend university (OR = 0.88, CI = 0.82,0.94, p < 0.001) per occasion of elevated maternal depressive symptoms) after adjusting for confounders. Mediation analysis indicated this was largely explained by educational achievement in school (e.g., 82.7 % mediated by age 16 achievement) and locus of control at 16. There was mixed evidence for an impact on choice of university. For participants who did not study at university, maternal depressive symptoms were linked to stating as a reason having had other priorities to do with family or children (OR: 1.17, CI = 1.02,1.35). LIMITATIONS: Lack of data on the other parent's depression, loss to follow-up, possibly selective non-response. CONCLUSIONS: Young people whose mothers experience elevated depressive symptoms on multiple occasions are less likely to participate in higher education; educational achievement in secondary school, but not the young people's own depressive symptoms, substantially mediated the effect.

Involving patients and the public In sTatistIcal Analysis pLans (INITIAL): A delphi survey.

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.

Methodological approaches, challenges, and opportunities in the application of Mendelian randomisation to lifecourse epidemiology: A systematic literature review.

Diseases diagnosed in adulthood may have antecedents throughout (including prenatal) life. Gaining a better understanding of how exposures at different stages in the lifecourse influence health outcomes is key to elucidating the potential benefits of disease prevention strategies. Mendelian randomisation (MR) is increasingly used to estimate causal effects of exposures across the lifecourse on later life outcomes. This systematic literature review explores MR methods used to perform lifecourse investigations and reviews previous work that has utilised MR to elucidate the effects of factors acting at different stages of the lifecourse. We conducted searches in PubMed, Embase, Medline and MedRXiv databases. Thirteen methodological studies were identified. Four studies focused on the impact of time-varying exposures in the interpretation of "standard" MR techniques, five presented methods for repeat measures of the same exposure, and four described methodological approaches to handling multigenerational exposures. A further 127 studies presented the results of an applied research question. Over half of these estimated effects in a single generation and were largely confined to the exploration of questions regarding body composition. The remaining mostly estimated maternal effects. There is a growing body of research focused on the development and application of MR methods to address lifecourse research questions. The underlying assumptions require careful consideration and the interpretation of results rely on select conditions. Whilst we do not advocate for a particular strategy, we encourage practitioners to make informed decisions on how to approach a research question in this field with a solid understanding of the limitations present and how these may be affected by the research question, modelling approach, instrument selection, and data availability.

A new approach to evaluating loop inconsistency in network meta-analysis.

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.

The marginality principle revisited: Should "higher-order" terms always be accompanied by "lower-order" terms in regression analyses?

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.

Polygenic Prediction of Education and Its Role in the Intergenerational Transmission of Education: Cohort Changes Among Finnish Men and Women Born in 1925-1989.

Major changes in the educational distribution of the population and in institutions over the past century have affected the societal barriers to educational attainment. These changes can possibly result in stronger genetic associations. Using genetically informed, population-representative Finnish surveys linked to administrative registers, we investigated the polygenic associations and intergenerational transmission of education for those born between 1925 and 1989. First, we found that a polygenic index (PGI) designed to capture genetic predisposition to education strongly increased the predictiveness of educational attainment in pre-1950s cohorts, particularly among women. When decomposing the total contribution of PGI across different educational transitions, the transition between the basic and academic secondary tracks was the most important. This transition accounted for 60-80% of the total PGI-education association among most cohorts. The transition between academic secondary and higher tertiary levels increased its contribution across cohorts. Second, for cohorts born between 1955 and 1984, we observed that one eighth of the association between parental and one's own education is explained by the PGI. There was also an increase in the intergenerational correlation of education among these cohorts, which was partly explained by an increasing association between family education of origin and the PGI.

Two-stage or not two-stage? That is the question for IPD meta-analysis projects.

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.