Unbiased Effect Estimates Research Articles

Latent Logistic Interaction Modeling: A Simulation and Empirical Illustration of Type D Personality

ABSTRACT This study focuses on three popular methods to model interactions between two constructs containing measurement error in predicting an observed binary outcome: logistic regression using (1) observed scores, (2) factor scores, and (3) Structural Equation Modeling (SEM). It is still unclear how they compare with respect to bias and precision in the estimated interaction when item scores underlying the interaction constructs are skewed and ordinal. In this article, we investigated this issue using both a Monte Carlo simulation and an empirical illustration of the effect of Type D personality on cardiac events. Our results indicated that the logistic regression using SEM performed best in terms of bias and confidence interval coverage, especially at sample sizes of 500 or larger. Although for most methods bias increased when item scores were skewed and ordinal, SEM produced relatively unbiased interaction effect estimates when items were modeled as ordered categorical.

PCN275 Network Meta-Analysis Design Considerations in a Complex and Rapidly Evolving Landscape: A Case Study in First-LINE (1L) Advanced NON-SMALL Cell LUNG Cancer (ANSCLC)

In 1L aNSCLC, the therapeutic landscape is complex and rapidly evolving. While the introduction of different immunotherapy-based treatments reflects advances in treatment efficacy and a shift toward more personalized medicine, it poses challenges in generating unbiased relative effect estimates via network meta-analysis (NMA). Our objective was to illustrate NMA design considerations in the 1L aNSCLC setting. A comprehensive set of NMA checklists was used for presenting NMA design choices in 1L aNSCLC. Using a systematically identified evidence base of 125 randomized controlled trials (RCTs), the following were identified as key design features: 1) proportional hazards assumption violations and differing lengths of follow-up; 2) effect modification, 3) lumping vs. splitting treatment nodes, and 4) study design heterogeneity including differences in blinding, chemotherapy arms, cross-over, and use of subsequent therapies. Methodological approaches to address the identified features were presented. Proportional hazards violations and differing lengths of follow-up were evident in RCTs comparing immunotherapies against chemotherapies. Several approaches were considered, including: constant hazard ratios for trials of similar follow-up; fractional polynomial/parametric NMAs; piecewise hazard ratios; restricted mean survival time; and survival at pre-defined times. Programmed death-ligand 1 expression level and histology were key effect modifying factors for some but not all comparisons in the network. Meta-regression was considered but was infeasible; instead, stratified networks were constructed. The choice to lump/split treatment nodes was endpoint-specific, with some chemotherapy combinations showing similar efficacy yet different safety profiles. Nine RCTs involved investigator’s choice control arms, adding complexity to defining treatment nodes. The cross-over design and use of subsequent therapy evolved over time and was evaluated alongside design heterogeneity using a study-by-study assessment of the potential impact on treatment effect size. We identified and presented approaches for handling multiple NMA design issues in 1L aNSCLC. These issues can be extrapolated and applied to other therapeutic settings.

Development of a fast and versatile method for genome‐wide association studies of longitudinal data

AbstractBackgroundApolipoprotein E ε4 shows a strong effect on the risk for developing Alzheimer’s disease (AD) but does not modulate the speed of cognitive decline after dementia onset. Accordingly, the influence of other genetic determinants might also change during the disease course of AD. To identify those determinants, methods are needed allowing for genome‐wide analysis of genetic effects using longitudinal data. Since the disease progression of AD, measured e.g as cognitive decline, may show a non‐linear trajectory over time, we developed a fast and flexible method for conducting genome‐wide association studies (GWAS).MethodWe extended the previously developed generalized least square approximation of linear mixed models (Rönnegard et al., 2016) to account for potential non‐linear trajectories. As GWAS studies usually combine results from different cohorts, this approach was combined with a partial derivative‐based meta‐analysis (Roshchupkin et al., 2016) that yields identical statistical power as pooled analysis but without the need of sharing individual participant data. To ensure suitability of our method, we conducted a Monte Carlo Simulation study generating data on 8000 participants with a non‐linear decline over 6 years of follow‐up and a 70% drop‐out rate. In each condition of the simulation study, we varied the number of cohorts providing the final sample size (1/5/40 studies), the minor allele frequency (MAF; 0.33/0.03) and the effect size of the genetic predictors on the longitudinal data. Thousand replications per condition were generated. Performance was compared to standard methods (i.e., full linear mixed models and invers‐variance‐weighted meta‐analysis).ResultCompared to a standard linear mixed model, our method was able to reduce, from several seconds to milliseconds, the computation time needed to calculate the association of one genetic variant with the longitudinal change. Our method producing unbiased effect estimates across all conditions. In case of less frequent variants (MAF = 0.03) and 40 studies, the standard invers‐variant weighted meta‐analysis showed higher type‐I‐error, but lower statistical power compared to the partial derivative‐based approach implemented in our method.ConclusionWe developed a fast and versatile method for longitudinal GWAS that maximizes power to detect genetic determinants of a wide range of different phenotypes in research on neurodegenerative diseases.

Effect of immortal time bias on the association between atrial fibrillation ablation and incident stroke: a meta-analysis

Abstract Background/Introduction In the era of big data and large observational studies, identification and prevention of immortal time bias (ITB) is essential to attain unbiased effect estimates. Immortal time refers to a period of follow-up in a cohort when the outcome cannot occur. Typically, it results when the exposure is initiated after the start of follow-up. The misclassification of person-time results in a systematic overestimation of the treatment effect. ITB is a common methodological issue in epidemiology studies. We sought to assess the presence and magnitude of bias due to ITB in observational studies evaluating the effectiveness of catheter ablation (CA) for atrial fibrillation. Purpose To compare the association between CA and stroke in 1) observational studies that controlled for ITB, 2) observational studies that did not address ITB, and 3) randomized controlled trials (RCT). Methods The PUBMED database was screened from inception to January 15, 2020 for publications with the following string of search terms: (“ablation” or “catheter ablation” or “pulmonary vein isolation”) and “atrial fibrillation” and (“stroke” or “thromboembolism”). Observational studies and RCTs comparing CA to medical therapy were eligible. Studies were excluded if: 1) evaluation of the association was limited to a subgroup of AF patients, 2) cryoablation was performed, 3) strokes were not reported, and 4) HRs or 95% CI were not presented. Information on study characteristics, HRs, and the potential for ITB was extracted. Subsequently, articles were classified based on the type of study and whether ITB was addressed. For each group of articles, HRs were logarithmically transformed and pooled using the random effects model. Results A total of 10 observational studies and 1 randomized controlled trial were included in the present analysis. Of the 10 observational studies, only 2 studies were designed to prevent ITB. The pooled HR for observational studies without ITB prevention showed a statistically significant reduction in risk of stroke (HR 0.66 (95% CI 0.58–0.74); I2=27.3%) in CA patients compared to non-CA patients. However, pooling the two observational studies that prevented ITB indicated no difference in the incidence of stroke [HR 0.75 (95% CI 0.49–1.02); I2=4.5%] among patients with and without CA, a finding similar to CABANA trial [HR 0.42 (95% CI 0.11–1.21)]. Conclusion It is important to evaluate the effectiveness of procedures and medications using observational data to determine if the results from RCTs translate to the real-world. However, careful consideration needs to be taken in the design phase to avoid ITB and produce effect estimates that more accurately represent the true association between treatment and outcomes. Examples of design methods to prevent ITB include the use of a time-varying covariate or matching on pre-treatment exposure time. Funding Acknowledgement Type of funding source: None

Spline-based accelerated failure time model.

The accelerated failure time (AFT) model has been suggested as an alternative to the Cox proportional hazards model. However, a parametric AFT model requires the specification of an appropriate distribution for the event time, which is often difficult to identify in real-life studies and may limit applications. A semiparametric AFT model was developed by Komárek et al based on smoothed error distribution that does not require such specification. In this article, we develop a spline-based AFT model that also does not require specification of the parametric family of event time distribution. The baseline hazard function is modeled by regression B-splines, allowing for the estimation of a variety of smooth and flexible shapes. In comprehensive simulations, we validate the performance of our approach and compare with the results from parametric AFT models and the approach of Komárek. Both the proposed spline-based AFT model and the approach of Komárek provided unbiased estimates of covariate effects and survival curves for a variety of scenarios in which the event time followed different distributions, including both simple and complex cases. Spline-based estimates of the baseline hazard showed also a satisfactory numerical stability. As expected, the baseline hazard and survival probabilities estimated by the misspecified parametric AFT models deviated from the truth. We illustrated the application of the proposed model in a study of colon cancer.

Estimating indirect parental genetic effects on offspring phenotypes using virtual parental genotypes derived from sibling and half sibling pairs.

Indirect parental genetic effects may be defined as the influence of parental genotypes on offspring phenotypes over and above that which results from the transmission of genes from parents to their children. However, given the relative paucity of large-scale family-based cohorts around the world, it is difficult to demonstrate parental genetic effects on human traits, particularly at individual loci. In this manuscript, we illustrate how parental genetic effects on offspring phenotypes, including late onset conditions, can be estimated at individual loci in principle using large-scale genome-wide association study (GWAS) data, even in the absence of parental genotypes. Our strategy involves creating “virtual” mothers and fathers by estimating the genotypic dosages of parental genotypes using physically genotyped data from relative pairs. We then utilize the expected dosages of the parents, and the actual genotypes of the offspring relative pairs, to perform conditional genetic association analyses to obtain asymptotically unbiased estimates of maternal, paternal and offspring genetic effects. We apply our approach to 19066 sibling pairs from the UK Biobank and show that a polygenic score consisting of imputed parental educational attainment SNP dosages is strongly related to offspring educational attainment even after correcting for offspring genotype at the same loci. We develop a freely available web application that quantifies the power of our approach using closed form asymptotic solutions. We implement our methods in a user-friendly software package IMPISH (IMputing Parental genotypes In Siblings and Half Siblings) which allows users to quickly and efficiently impute parental genotypes across the genome in large genome-wide datasets, and then use these estimated dosages in downstream linear mixed model association analyses. We conclude that imputing parental genotypes from relative pairs may provide a useful adjunct to existing large-scale genetic studies of parents and their offspring.

Epistemic Uncertainty in Site Response as Derived from One-Dimensional Ground Response Analyses

One-dimensional ground response analyses (GRAs) are often used with an expectation that they provide unbiased estimates of site effects. Under that hypothesis, epistemic uncertainty in site response arises mainly from uncertain soil properties. This approach has dominated practice for projects where site-specific site response is estimated for use in probabilistic seismic hazard analyses. We extend the uncertainty framework to also consider modeling errors (i.e., inability of GRAs to model site response for some sites). We quantify this epistemic uncertainty using vertical array data in which the downhole motion is input to GRAs to predict ground motions at the surface. Residuals (i.e., difference between observed and predicted ground motion intensity measures in natural log units) are partitioned into between- and within-site components. After correcting for overprediction bias near the site period, we quantify epistemic uncertainty using between-site standard deviation, which ranges from 0.2 to 0.35 using California data. A Japan data set analyzed in the literature provides similar results. This dispersion is only modestly smaller than the site-to-site variability from ergodic models for active tectonic regions, which limits the apparent benefits of site-specific GRAs. Dispersion results are not appreciably affected by varying damping models, although a model informed by site-specific observations minimizes bias relative to alternative models based on geotechnical laboratory tests and seismological crustal attenuation studies.

Adding Measurement Error to Location Data to Protect Subject Confidentiality While Allowing for Consistent Estimation of Exposure Effects

Summary In public use data sets, it is desirable not to report a respondent's location precisely to protect subject confidentiality. However, the direct use of perturbed location data to construct explanatory exposure variables for regression models will generally make naive estimates of all parameters biased and inconsistent. We propose an approach where a perturbation vector, consisting of a random distance at a random angle, is added to a respondent's reported geographic co-ordinates. We show that, as long as the distribution of the perturbation is public and there is an underlying prior population density map, external researchers can construct unbiased and consistent estimates of location-dependent exposure effects by using numerical integration techniques over all possible actual locations, although coefficient confidence intervals are wider than if the true location data were known. We examine our method by using a Monte Carlo simulation exercise and apply it to a real world example using data on perceived and actual distance to a health facility in Tanzania.

Spatial spillover effects of global forest product trade

Spatial spillover is widespread in forest product trade. We employ a spatial autoregressive (SAR) interaction model to analyze spatial spillover effects of global forest product trade in 2004 and 2014 and their underlying determinants. The SAR interaction model, specified with three types of spatial dependence (origin-to-origin, destination-to-destination and origin-to-destination) can account for the complex spatial interconnection of forest product trade, leading to unbiased and consistent estimates of effects of determinants on trade flows. Although all the spatial dependence parameters are statistically significant, the spatial interconnectivity was much stronger among destination countries than across origin countries. The identified spatial dependence reflects a core-periphery structure of the trade network. The effect decomposition shows that changes in the principal explanatory variables in the SAR interaction model had a greater total effect (TE) on trade flows in 2014 than in 2004. This attributes to a substantial increase of the origin effect (OE), destination effect (DE) and network effect (NE) from 2004 to 2014. Especially, NE rose by a big margin during this period and accounted for approximately 45% of TE in 2014 for each determinant. Based on the magnitude of NE that represents the spatial spillover effect, gross domestic product (GDP) ranked first, followed by gross national income (GNI) per capita, roundwood production per capita and tariffs. Besides the strong evidence of spatial spillover effects, we also find that countries tended to mimic their neighbors in forest product trade engagements. Our findings shed new light on the spatial interconnection of global forest product trade and offer implications for future trade and forest conservation policy design.

A fair comparison of tree-based and parametric methods in multiple imputation by chained equations.

Multiple imputation by chained equations (MICE) has emerged as a leading strategy for imputing missing epidemiological data due to its ease of implementation and ability to maintain unbiased effect estimates and valid inference. Within the MICE algorithm, imputation can be performed using a variety of parametric or nonparametric methods. Literature has suggested that nonparametric tree-based imputation methods outperform parametric methods in terms of bias and coverage when there are interactions or other nonlinear effects among the variables. However, these studies fail to provide a fair comparison as they do not follow the well-established recommendation that any effects in the final analysis model (including interactions) should be included in the parametric imputation model. We show via simulation that properly incorporating interactions in the parametric imputation model leads to much better performance. In fact, correctly specified parametric imputation and tree-based random forest imputation perform similarly when estimating the interaction effect. Parametric imputation leads to slightly higher coverage for the interaction effect, but it has wider confidence intervals than random forest imputation and requires correct specification of the imputation model. Epidemiologists should take care in specifying MICE imputation models, and this paper assists in that task by providing a fair comparison of parametric and tree-based imputation in MICE.

Causal Inference with Bipartite Designs

Bipartite experiments are a recent object of study in causal inference, whereby treatment is applied to one set of units and outcomes of interest are measured on a different set of units. These experiments are particularly useful in settings where strong interference effects occur between units of a bipartite graph. In market experiments, for example, assigning treatment at the seller-level and measuring outcomes at the buyer-level (or vice-versa) may lead to causal models that better account for the interference that naturally occurs between buyers and sellers. While bipartite experiments have been shown to improve the estimation of causal effects in certain settings, the analysis must be done carefully so as to not introduce unnecessary bias. We leverage the generalized propensity score literature to show that we can obtain unbiased estimates of causal effects for bipartite experiments under a standard set of assumptions. We also discuss the construction of confidence sets with proper coverage probabilities. We evaluate these methods using a bipartite graph from a publicly available dataset studied in previous work on bipartite experiments, showing through simulations a significant bias reduction and improved coverage.

Powerful rare variant association testing in a copula-based joint analysis of multiple phenotypes.

In genetic association studies of rare variants, the low power of association tests is one of the main challenges. In this study, we propose a new single-marker association test called C-JAMP (Copula-based Joint Analysis of Multiple Phenotypes), which is based on a joint model of multiple phenotypes given genetic markers and other covariates. We evaluated its performance and compared its empirical type I error and power with existing univariate and multivariate single-marker and multi-marker rare-variant tests in extensive simulation studies. C-JAMP yielded unbiased genetic effect estimates and valid type I errors with an adjusted test statistic. When strongly dependent traits were jointly analyzed, C-JAMP had the highest power in all scenarios except when a high percentage of variants were causal with moderate/small effect sizes. When traits with weak or moderate dependence were analyzed, whether C-JAMP or competing approaches had higher power depended on the effect size. When C-JAMP was applied with a misspecified copula function, it still achieved high power in some of the scenarios considered. In a real-data application, we analyzed sequencing data using C-JAMP and performed the first genome-wide association studies of high-molecular-weight and medium-molecular-weight adiponectin plasma concentrations. C-JAMP identified 20 rare variants with p-values smaller than 10-5 , while all other tests resulted in the identification of fewer variants with higher p-values. In summary, the results indicate that C-JAMP is a powerful, flexible, and robust method for association studies, and we identified novel candidate markers for adiponectin. C-JAMP is implemented as an R package and freely available from https://cran.r-project.org/package=CJAMP.

Sensitivity analysis for the generalized shared-parameter model framework

ABSTRACTIn this paper, we assess the effect of tuberculosis pericarditis treatment (prednisolone) on CD4 count changes over time and draw inferences in the presence of missing data. We accounted for the missing data and performed sensitivity analyses to assess robustness of inferences, from a model that assumes that the data are missing at random, to models that assume that the data are not missing at random. Our sensitivity approaches are within the shared-parameter model framework. We implemented the approach by Creemers and colleagues to the CD4 count data and performed simulation studies to evaluate the performance of this approach. We also assessed the influence of potentially influential subjects, on parameter estimates, via the global influence approach. Our results revealed that inferences from missing at random analysis model are robust to not missing at random models and influential subjects did not overturn the study conclusions about prednisolone effect and missing data mechanism. Prednisolone was found to have no significant effect on CD4 count changes over time and also did not interact with anti-retroviral therapy. The simulation studies produced unbiased estimates of prednisolone effect with lower mean square errors and coverage probabilities approximately equal the nominal coverage probability.

Within study comparisons and risk of bias in international development: Systematic review and critical appraisal.

Many systematic reviews incorporate nonrandomised studies of effects, sometimes called quasi-experiments or natural experiments. However, the extent to which nonrandomised studies produce unbiased effect estimates is unclear in expectation or in practice. The usual way that systematic reviews quantify bias is through "risk of bias assessment" and indirect comparison of findings across studies using meta-analysis. A more direct, practical way to quantify the bias in nonrandomised studies is through "internal replication research", which compares the findings from nonrandomised studies with estimates from a benchmark randomised controlled trial conducted in the same population. Despite the existence of many risks of bias tools, none are conceptualised to assess comprehensively nonrandomised approaches with selection on unobservables, such as regression discontinuity designs (RDDs). The few that are conceptualised with these studies in mind do not draw on the extensive literature on internal replications (within-study comparisons) of randomised trials. Our research objectives were as follows:Objective 1: to undertake a systematic review of nonrandomised internal study replications of international development interventions.Objective 2: to develop a risk of bias tool for RDDs, an increasingly common method used in social and economic programme evaluation. We used the following methods to achieve our objectives.Objective 1: we searched systematically for nonrandomised internal study replications of benchmark randomised experiments of social and economic interventions in low- and middle-income countries (L&MICs). We assessed the risk of bias in benchmark randomised experiments and synthesised evidence on the relative bias effect sizes produced by benchmark and nonrandomised comparison arms.Objective 2: We used document review and expert consultation to develop further a risk of bias tool for quasi-experimental studies of interventions (ROBINS-I) for RDDs. Objective 1: we located 10 nonrandomised internal study replications of randomised trials in L&MICs, six of which are of RDDs and the remaining use a combination of statistical matching and regression techniques. We found that benchmark experiments used in internal replications in international development are in the main well-conducted but have "some concerns" about threats to validity, usually arising due to the methods of outcomes data collection. Most internal replication studies report on a range of different specifications for both the benchmark estimate and the nonrandomised replication estimate. We extracted and standardised 604 bias coefficient effect sizes from these studies, and present average results narratively.Objective 2: RDDs are characterised by prospective assignment of participants based on a threshold variable. Our review of the literature indicated there are two main types of RDD. The most common type of RDD is designed retrospectively in which the researcher identifies post-hoc the relationship between outcomes and a threshold variable which determines assignment to intervention at pretest. These designs usually draw on routine data collection such as administrative records or household surveys. The other, less common, type is a prospective design where the researcher is also involved in allocating participants to treatment groups from the outset. We developed a risk of bias tool for RDDs. Internal study replications provide the grounds on which bias assessment tools can be evidenced. We conclude that existing risk of bias tools needs to be further developed for use by Campbell collaboration authors, and there is a wide range of risk of bias tools and internal study replications to draw on in better designing these tools. We have suggested the development of a promising approach for RDD. Further work is needed on common methodologies in programme evaluation, for example on statistical matching approaches. We also highlight that broader efforts to identify all existing internal replication studies should consider more specialised systematic search strategies within particular literatures; so as to overcome a lack of systematic indexing of this evidence.

The Sensitivity of Spatial Regression Models to Network Misspecification

Spatial econometric models become increasingly popular in various subfields of political science. However, the necessity to specify the underlying network of dependencies, denoted by $\boldsymbol{W}$, prior to estimation is a prevalent source of criticism since the true dependence structure is rarely known and theories mostly provide insufficient guidance. The present study investigates the effects of thisnetwork uncertaintywhich is a special case of model uncertainty that arises from uncertainty about the correct specification of $\boldsymbol{W}$. It advocates Bayesian model averaging (BMA) as a superior approach to this problem, located at the intersection of theory and empirics. Conducting Monte Carlo experiments, I demonstrate that, while the effect estimates are robust toward a misspecification in the functional form of $\boldsymbol{W}$, uncertainty in the neighborhood definition can bias the effect estimates derived from spatial autoregressive models. In contrast to alternative techniques, BMA directly addresses network uncertainty, correctly identifies the true network structure in the set of feasible alternatives, and provides unbiased effect estimates. Two replication studies from different subfields of the discipline illustrate the benefits of this approach for applied research.

Average Effects Based on Regressions with a Logarithmic Link Function: A New Approach with Stochastic Covariates.

Researchers often use regressions with a logarithmic link function to evaluate the effects of a treatment on a count variable. In order to judge the average effectiveness of the treatment on the original count scale, they compute average treatment effects, which are defined as the average difference between the expected outcomes under treatment and under control. Current practice is to evaluate the expected differences at every observation and use the sample mean of these differences as a point estimate of the average effect. The standard error for this average effect estimate is based on the implicit assumption that covariate values are fixed, i.e., do not vary across different samples. In this paper, we present a new way of analytically computing average effects based on regressions with log link using stochastic covariates and develop new formulas to obtain standard errors for the average effect. In a simulation study, we evaluate the statistical performance of our new estimator and compare it with the traditional approach. Our findings suggest that the new approach gives unbiased effect estimates and standard errors and outperforms the traditional approach when strong interaction and/or a skewed covariate is present.

Characterization of circadian blood pressure patterns using non-linear mixed effects modeling.

Characterizing the time course of baseline or pre-drug blood pressure is important in acquiring unbiased estimates of antihypertensive drug effect. In this study, we recruited 23 healthy male volunteers and measured systolic (SBP) and diastolic blood pressure (DBP) over 24 hours on an hourly basis. Using a non-linear mixed effects model, circadian rhythm observed in blood pressure measurements was described by incorporating two cosine functions with periods 24 and 12 hours. A mixture model was applied to identify subgroups exhibiting qualitatively different circadian rhythms. Our results suggested that 78% of the study population, defined as ‘dippers’, demonstrated a typical circadian profile with a morning rise and a nocturnal dip. The remaining 22% of the subjects defined as ‘non-dippers’, however, were not adequately described using the typical profile and demonstrated an elevation of blood pressure during night-time. Covariate search identified weight as being positively correlated with mesor of SBP. Visual predictive checks using 1,000 simulated datasets were performed for model validation. Observations were in agreement with predicted values in ‘dippers’, but deviated slightly in ‘non-dippers’. Our work is expected to serve as a useful reference in assessing systematic intra-day blood pressure fluctuations and antihypertensive effects as well as assessing drug safety of incrementally modified drugs.

Appropriate statistical methods for analysing partially nested randomised controlled trials with continuous outcomes: a simulation study

BackgroundIn individually randomised trials we might expect interventions delivered in groups or by care providers to result in clustering of outcomes for participants treated in the same group or by the same care provider. In partially nested randomised controlled trials (pnRCTs) this clustering only occurs in one trial arm, commonly the intervention arm. It is important to measure and account for between-cluster variability in trial design and analysis. We compare analysis approaches for pnRCTs with continuous outcomes, investigating the impact on statistical inference of cluster sizes, coding of the non-clustered arm, intracluster correlation coefficient (ICCs), and differential variance between intervention and control arm, and provide recommendations for analysis.MethodsWe performed a simulation study assessing the performance of six analysis approaches for a two-arm pnRCT with a continuous outcome. These include: linear regression model; fully clustered mixed-effects model with singleton clusters in control arm; fully clustered mixed-effects model with one large cluster in control arm; fully clustered mixed-effects model with pseudo clusters in control arm; partially nested homoscedastic mixed effects model, and partially nested heteroscedastic mixed effects model. We varied the cluster size, number of clusters, ICC, and individual variance between the two trial arms.ResultsAll models provided unbiased intervention effect estimates. In the partially nested mixed-effects models, methods for classifying the non-clustered control arm had negligible impact. Failure to account for even small ICCs resulted in inflated Type I error rates and over-coverage of confidence intervals. Fully clustered mixed effects models provided poor control of the Type I error rates and biased ICC estimates. The heteroscedastic partially nested mixed-effects model maintained relatively good control of Type I error rates, unbiased ICC estimation, and did not noticeably reduce power even with homoscedastic individual variances across arms.ConclusionsIn general, we recommend the use of a heteroscedastic partially nested mixed-effects model, which models the clustering in only one arm, for continuous outcomes similar to those generated under the scenarios of our simulations study. However, with few clusters (3–6), small cluster sizes (5–10), and small ICC (≤0.05) this model underestimates Type I error rates and there is no optimal model.

Robust analysis of stepped wedge trials using cluster-level summaries within periods.

In stepped‐wedge trials (SWTs), the intervention is rolled out in a random order over more than 1 time‐period. SWTs are often analysed using mixed‐effects models that require strong assumptions and may be inappropriate when the number of clusters is small.We propose a non‐parametric within‐period method to analyse SWTs. This method estimates the intervention effect by comparing intervention and control conditions in a given period using cluster‐level data corresponding to exposure. The within‐period intervention effects are combined with an inverse‐variance‐weighted average, and permutation tests are used. We present an example and, using simulated data, compared the method to (1) a parametric cluster‐level within‐period method, (2) the most commonly used mixed‐effects model, and (3) a more flexible mixed‐effects model. We simulated scenarios where period effects were common to all clusters, and when they varied according to a distribution informed by routinely collected health data.The non‐parametric within‐period method provided unbiased intervention effect estimates with correct confidence‐interval coverage for all scenarios. The parametric within‐period method produced confidence intervals with low coverage for most scenarios. The mixed‐effects models' confidence intervals had low coverage when period effects varied between clusters but had greater power than the non‐parametric within‐period method when period effects were common to all clusters.The non‐parametric within‐period method is a robust method for analysing SWT. The method could be used by trial statisticians who want to emphasise that the SWT is a randomised trial, in the common position of being uncertain about whether data will meet the assumptions necessary for mixed‐effect models.

A sibling method for identifying vQTLs.

The propensity of a trait to vary within a population may have evolutionary, ecological, or clinical significance. In the present study we deploy sibling models to offer a novel and unbiased way to ascertain loci associated with the extent to which phenotypes vary (variance-controlling quantitative trait loci, or vQTLs). Previous methods for vQTL-mapping either exclude genetically related individuals or treat genetic relatedness among individuals as a complicating factor addressed by adjusting estimates for non-independence in phenotypes. The present method uses genetic relatedness as a tool to obtain unbiased estimates of variance effects rather than as a nuisance. The family-based approach, which utilizes random variation between siblings in minor allele counts at a locus, also allows controls for parental genotype, mean effects, and non-linear (dominance) effects that may spuriously appear to generate variation. Simulations show that the approach performs equally well as two existing methods (squared Z-score and DGLM) in controlling type I error rates when there is no unobserved confounding, and performs significantly better than these methods in the presence of small degrees of confounding. Using height and BMI as empirical applications, we investigate SNPs that alter within-family variation in height and BMI, as well as pathways that appear to be enriched. One significant SNP for BMI variability, in the MAST4 gene, replicated. Pathway analysis revealed one gene set, encoding members of several signaling pathways related to gap junction function, which appears significantly enriched for associations with within-family height variation in both datasets (while not enriched in analysis of mean levels). We recommend approximating laboratory random assignment of genotype using family data and more careful attention to the possible conflation of mean and variance effects.