Estimation of causal effects of a time-varying exposure at multiple time points through multivariable mendelian randomization.

Mendelian Randomisation (MR) is a powerful tool in epidemiology that can be used to estimate the causal effect of an exposure on an outcome in the presence of unobserved confounding, by utilising genetic variants as instrumental variables (IVs) for the exposure. The effect estimates obtained from MR studies are often interpreted as the lifetime effect of the exposure in question. However, the causal effects of some exposures are thought to vary throughout an individual's lifetime with periods during which an exposure has a greater effect on a particular outcome. Multivariable MR (MVMR) is an extension of MR that allows for multiple, potentially highly related, exposures to be included in an MR estimation. MVMR estimates the direct effect of each exposure on the outcome conditional on all the other exposures included in the estimation. We explore the use of MVMR to estimate the direct effect of a single exposure at different time points in an individual's lifetime on an outcome. We use simulations to illustrate the interpretation of the results from such analyses and the key assumptions required. We show that causal effects at different time periods can be estimated through MVMR when the association between the genetic variants used as instruments and the exposure measured at those time periods varies. However, this estimation will not necessarily identify exact time periods over which an exposure has the most effect on the outcome. Prior knowledge regarding the biological basis of exposure trajectories can help interpretation. We illustrate the method through estimation of the causal effects of childhood and adult BMI on C-Reactive protein and smoking behaviour.

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.

Robust genetic nurture effects on education: A systematic review and meta-analysis based on 38,654 families across 8 cohorts.

Similarities between parents and offspring arise from nature and nurture. Beyond this simple dichotomy, recent genomic studies have uncovered "genetic nurture" effects, whereby parental genotypes influence offspring outcomes via environmental pathways rather than genetic transmission. Such genetic nurture effects also need to be accounted for to accurately estimate "direct" genetic effects (i.e., genetic effects on a trait originating in the offspring). Empirical studies have indicated that genetic nurture effects are particularly relevant to the intergenerational transmission of risk for child educational outcomes, which are, in turn, associated with major psychological and health milestones throughout the life course. These findings have yet to be systematically appraised across contexts. We conducted a systematic review and meta-analysis to quantify genetic nurture effects on educational outcomes. A total of 12 studies comprising 38,654 distinct parent(s)-offspring pairs or trios from 8 cohorts reported 22 estimates of genetic nurture effects. Genetic nurture effects on offspring's educational outcomes (ßgenetic nurture = 0.08, 95% CI [0.07, 0.09]) were smaller than direct genetic effects (ßdirect genetic = 0.17, 95% CI [0.13, 0.20]). Findings were largely consistent across studies. Genetic nurture effects originating from mothers and fathers were of similar magnitude, highlighting the need for a greater inclusion of fathers in educational research. Genetic nurture effects were largely explained by observed parental education and socioeconomic status, pointing to their role in environmental pathways shaping child educational outcomes. Findings provide consistent evidence that environmentally mediated parental genetic influences contribute to the intergenerational transmission of educational outcomes, in addition to effects due to genetic transmission.

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.

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.

Assortative mating and within-spouse pair comparisons.

Spousal comparisons have been proposed as a design that can both reduce confounding and estimate effects of the shared adulthood environment. However, assortative mating, the process by which individuals select phenotypically (dis)similar mates, could distort associations when comparing spouses. We evaluated the use of spousal comparisons, as in the within-spouse pair (WSP) model, for aetiological research such as genetic association studies. We demonstrated that the WSP model can reduce confounding but may be susceptible to collider bias arising from conditioning on assorted spouse pairs. Analyses using UK Biobank spouse pairs found that WSP genetic association estimates were smaller than estimates from random pairs for height, educational attainment, and BMI variants. Within-sibling pair estimates, robust to demographic and parental effects, were also smaller than random pair estimates for height and educational attainment, but not for BMI. WSP models, like other within-family models, may reduce confounding from demographic factors in genetic association estimates, and so could be useful for triangulating evidence across study designs to assess the robustness of findings. However, WSP estimates should be interpreted with caution due to potential collider bias.

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.

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.

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.

Measuring the unknown: An estimator and simulation study for assessing case reporting during epidemics.

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.

Handling misclassified stratification variables in the analysis of randomised trials with continuous outcomes.

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.

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.

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 comparison of different population-level summary measures for randomised trials with time-to-event outcomes, with a focus on non-inferiority trials.

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.

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.

artcat: Sample-size calculation for an ordered categorical outcome.

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.

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.

Estimands for factorial trials.

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.

Marital status and genetic liability independently predict coronary heart disease incidence.

AIMS: Married individuals have a lower coronary heart disease (CHD) risk than non-married, but the mechanisms behind this are not fully understood. We analyzed whether genetic liability to CHD may affect these associations. METHODS: Marital status, a polygenic score of CHD (PGS-CHD), and other risk factors for CHD were measured from 35,444 participants (53% female) in Finnish population-based surveys conducted between 1992 and 2012. During the register-based follow-up until 2020, there were 2439 fatal and non-fatal incident CHD cases. The data were analyzed using linear and Cox regression models. RESULTS: Divorced and cohabiting men and women had a higher genetic risk of CHD than married individuals, but the difference was very small (0.023-0.058 standard deviation of PGS-CHD, p-values 0.011-0.429). Both marital status and PGS-CHD were associated with CHD incidence, but the associations were largely independent. Adjusting for behavioral and metabolic risk factors for CHD explained part of these associations (11-20%). No interaction was found between marital status and PGS-CHD for CHD incidence. CONCLUSIONS: We showed minor differences between the marital status categories in PGS-CHD and demonstrated that marital status and genetic liability predicted CHD incidence largely independently. This emphasizes the need to measure multiple risk factors when predicting CHD risk.