Benchmarking Mendelian randomization methods for causal inference using genome-wide association study summary statistics.

Mendelian randomization (MR), which utilizes genetic variants as instrumental variables (IVs), has gained popularity as a method for causal inference between phenotypes using genetic data. While efforts have been made to relax IV assumptions and develop new methods for causal inference in the presence of invalid IVs due to confounding, the reliability of MR methods in real-world applications remains uncertain. Instead of using simulated datasets, we conducted a benchmark study evaluating 16 two-sample summary-level MR methods using real-world genetic datasets to provide guidelines for the best practices. Our study focused on the following crucial aspects: type I error control in the presence of various confounding scenarios (e.g., population stratification, pleiotropy, and family-level confounders like assortative mating), the accuracy of causal effect estimates, replicability, and power. By comprehensively evaluating the performance of compared methods over one thousand exposure-outcome trait pairs, our study not only provides valuable insights into the performance and limitations of the compared methods but also offers practical guidance for researchers to choose appropriate MR methods for causal inference.

The State of Use and Utility of Negative Controls in Pharmacoepidemiologic Studies.

Uses of real-world data in drug safety and effectiveness studies are often challenged by various sources of bias. We undertook a systematic search of the published literature through September 2020 to evaluate the state of use and utility of negative controls to address bias in pharmacoepidemiologic studies. Two reviewers independently evaluated study eligibility and abstracted data. Our search identified 184 eligible studies for inclusion. Cohort studies (115, 63%) and administrative data (114, 62%) were, respectively, the most common study design and data type used. Most studies used negative control outcomes (91, 50%), and for most studies the target source of bias was unmeasured confounding (93, 51%). We identified 4 utility domains of negative controls: 1) bias detection (149, 81%), 2) bias correction (16, 9%), 3) P-value calibration (8, 4%), and 4) performance assessment of different methods used in drug safety studies (31, 17%). The most popular methodologies used were the 95% confidence interval and P-value calibration. In addition, we identified 2 reference sets with structured steps to check the causality assumption of the negative control. While negative controls are powerful tools in bias detection, we found many studies lacked checking the underlying assumptions. This article is part of a Special Collection on Pharmacoepidemiology.

Effects and considerations of multiplexing ForenSeq Kintelligence libraries with a negative control.

The negative template control or negative amplification control has been an essential component of the forensic DNA analysis workflow that helps monitor contamination. As such, the inclusion of a negative control in forensic DNA analysis has been a requirement for all laboratories audited under the FBI's Quality Assurance Standards. As massively parallel sequencing (MPS) becomes more conventional in forensic laboratories, considerations for the inclusion of a negative control in every sequencing run can be evaluated. Although the inclusion of a negative control in library preparation and the first sequencing run has a practical function, there is less utility for its inclusion in all subsequent sequencing runs for that library preparation. Although this is universal to all MPS assays, it is most relevant for an assay that has a low sample multiplexing capacity, such as the ForenSeq Kintelligence Kit (Qiagen/Verogen, Inc.). The ForenSeq Kintelligence Kit is an investigative genetic genealogy (IGG) sequencing-based assay that targets 10,230 forensically relevant single-nucleotide polymorphisms. The manufacturer recommends multiplexing 3 libraries per sequencing run, which includes controls. The purpose of this study was to investigate the effect of the inclusion of a negative control in every Kintelligence sequencing run. We observed that the library generated from a negative amplification control will take 7%-14% of the run output. The loss of sequencing space taken by a negative control decreased the available output for DNA-containing samples, leading in some cases to allele or locus dropout and accompanying higher numbers of sixth to seventh order unknown associations in GEDmatch PRO.

The causal association between maternal depression, anxiety, and infection in pregnancy and neurodevelopmental disorders among 410 461 children: a population study using quasi-negative control cohorts and sibling analysis.

BACKGROUND: To address if the long-standing association between maternal infection, depression/anxiety in pregnancy, and offspring neurodevelopmental disorder (NDD) is causal, we conducted two negative-control studies. METHODS: Four primary care cohorts of UK children (pregnancy, 1 and 2 years prior to pregnancy, and siblings) born between 1 January 1990 and 31 December 2017 were constructed. NDD included autism/autism spectrum disorder, attention-deficit/hyperactivity disorder, intellectual disability, cerebral palsy, and epilepsy. Maternal exposures included depression/anxiety and/or infection. Maternal (age, smoking status, comorbidities, body mass index, NDD); child (gender, ethnicity, birth year); and area-level (region and level of deprivation) confounders were captured. The NDD incidence rate among (1) children exposed during or outside of pregnancy and (2) siblings discordant for exposure in pregnancy was compared using Cox-regression models, unadjusted and adjusted for confounders. RESULTS: The analysis included 410 461 children of 297 426 mothers and 2 793 018 person-years of follow-up with 8900 NDD cases (incidence rate = 3.2/1000 person years). After adjustments, depression and anxiety consistently associated with NDD (pregnancy-adjusted HR = 1.58, 95% CI 1.46-1.72; 1-year adj. HR = 1.49, 95% CI 1.39-1.60; 2-year adj. HR = 1.62, 95% CI 1.50-1.74); and to a lesser extent, of infection (pregnancy adj. HR = 1.16, 95% CI 1.10-1.22; 1-year adj. HR = 1.20, 95% CI 1.14-1.27; 2-year adj. HR = 1.19, 95% CI 1.12-1.25). NDD risk did not differ among siblings discordant for pregnancy exposure to mental illness HR = 0.97, 95% CI 0.77-1.21 or infection HR = 0.99, 95% CI 0.90-1.08. CONCLUSIONS: Maternal risk appears to be unspecific to pregnancy: our study provided no evidence of a specific, and therefore causal, link between in-utero exposure to infection, common mental illness, and later development of NDD.

Identification and estimation of causal effects in the presence of confounded principal strata.

Principal stratification has become a popular tool to address a broad class of causal inference questions, particularly in dealing with non-compliance and truncation by death problems. The causal effects within principal strata, which are determined by joint potential values of the intermediate variable, also known as the principal causal effects, are often of interest in these studies. The analysis of principal causal effects from observational studies mostly relies on the ignorability assumption of treatment assignment, which requires practitioners to accurately measure as many covariates as possible so that all potential sources of confounders are captured. However, in practice, collecting all potential confounding factors can be challenging and costly, rendering the ignorability assumption questionable. In this paper, we consider the identification and estimation of causal effects when treatment and principal stratification are confounded by unmeasured confounding. Specifically, we establish the nonparametric identification of principal causal effects using a pair of negative controls to mitigate unmeasured confounding, requiring they have no direct effect on the outcome variable. We also provide an estimation method for principal causal effects. Extensive simulations and a leukemia study are employed for illustration.

Identification and estimation of causal peer effects using double negative controls for unmeasured network confounding.

Identification and estimation of causal peer effects are challenging in observational studies for two reasons. The first is the identification challenge due to unmeasured network confounding, for example, homophily bias and contextual confounding. The second is network dependence of observations. We establish a framework that leverages a pair of negative control outcome and exposure variables (double negative controls) to non-parametrically identify causal peer effects in the presence of unmeasured network confounding. We then propose a generalised method of moments estimator and establish its consistency and asymptotic normality under an assumption about ψ-network dependence. Finally, we provide a consistent variance estimator.

Development of pENTR-NeCo-lacZα vectors for the preparation of negative control constructs in Gateway cloning.

Gateway cloning is a useful technology for the simple and reliable preparation of various construct in many organisms. However, there is a problem regarding the negative control construct in the Gateway cloning system. In this study, we developed the pENTR-NeCo-lacZα vector system to create an empty vector that can be used as a negative control construct in Gateway cloning.

Benchmarking MicrobIEM - a user-friendly tool for decontamination of microbiome sequencing data.

BACKGROUND: Microbiome analysis is becoming a standard component in many scientific studies, but also requires extensive quality control of the 16S rRNA gene sequencing data prior to analysis. In particular, when investigating low-biomass microbial environments such as human skin, contaminants distort the true microbiome sample composition and need to be removed bioinformatically. We introduce MicrobIEM, a novel tool to bioinformatically remove contaminants using negative controls. RESULTS: We benchmarked MicrobIEM against five established decontamination approaches in four 16S rRNA amplicon sequencing datasets: three serially diluted mock communities (108-103 cells, 0.4-80% contamination) with even or staggered taxon compositions and a skin microbiome dataset. Results depended strongly on user-selected algorithm parameters. Overall, sample-based algorithms separated mock and contaminant sequences best in the even mock, whereas control-based algorithms performed better in the two staggered mocks, particularly in low-biomass samples (≤ 106 cells). We show that a correct decontamination benchmarking requires realistic staggered mock communities and unbiased evaluation measures such as Youden's index. In the skin dataset, the Decontam prevalence filter and MicrobIEM's ratio filter effectively reduced common contaminants while keeping skin-associated genera. CONCLUSIONS: MicrobIEM's ratio filter for decontamination performs better or as good as established bioinformatic decontamination tools. In contrast to established tools, MicrobIEM additionally provides interactive plots and supports selecting appropriate filtering parameters via a user-friendly graphical user interface. Therefore, MicrobIEM is the first quality control tool for microbiome experts without coding experience.

Maternal prenatal cholesterol levels predict offspring weight trajectories during childhood in the Norwegian Mother, Father and Child Cohort Study.

BACKGROUND: Numerous intrauterine factors may affect the offspring's growth during childhood. We aimed to explore if maternal and paternal prenatal lipid, apolipoprotein (apo)B and apoA1 levels are associated with offspring weight, length, and body mass index from 6 weeks to eight years of age. This has previously been studied to a limited extent. METHODS: This parental negative control study is based on the Norwegian Mother, Father and Child Cohort Study and uses data from the Medical Birth Registry of Norway. We included 713 mothers and fathers with or without self-reported hypercholesterolemia and their offspring. Seven parental metabolites were measured by nuclear magnetic resonance spectroscopy, and offspring weight and length were measured at 12 time points. Data were analyzed by linear spline mixed models, and the results are presented as the interaction between parental metabolite levels and offspring spline (age). RESULTS: Higher maternal total cholesterol (TC) level was associated with a larger increase in offspring body weight up to 8 years of age (0.03 ≤ Pinteraction ≤ 0.04). Paternal TC level was not associated with change in offspring body weight (0.17 ≤ Pinteraction ≤ 0.25). Higher maternal high-density lipoprotein cholesterol (HDL-C) and apoA1 levels were associated with a lower increase in offspring body weight up to 8 years of age (0.001 ≤ Pinteraction ≤ 0.005). Higher paternal HDL-C and apoA1 levels were associated with a lower increase in offspring body weight up to 5 years of age but a larger increase in offspring body weight from 5 to 8 years of age (0.01 ≤ Pinteraction ≤ 0.03). Parental metabolites were not associated with change in offspring height or body mass index up to 8 years of age (0.07 ≤ Pinteraction ≤ 0.99). CONCLUSIONS: Maternal compared to paternal TC, HDL-C, and apoA1 levels were more strongly and consistently associated with offspring body weight during childhood, supporting a direct intrauterine effect.

Increasing efficiency and reducing bias when assessing HPV vaccination efficacy by using nontargeted HPV strains.

Studies of vaccine efficacy often record both the incidence of vaccine-targeted virus strains (primary outcome) and the incidence of nontargeted strains (secondary outcome). However, standard estimates of vaccine efficacy on targeted strains ignore the data on nontargeted strains. Assuming nontargeted strains are unaffected by vaccination, we regard the secondary outcome as a negative control outcome and show how using such data can (i) increase the precision of the estimated vaccine efficacy against targeted strains in randomized trials and (ii) reduce confounding bias of that same estimate in observational studies. For objective (i), we augment the primary outcome estimating equation with a function of the secondary outcome that is unbiased for zero. For objective (ii), we jointly estimate the treatment effects on the primary and secondary outcomes. If the bias induced by the unmeasured confounders is similar for both types of outcomes, as is plausible for factors that influence the general risk of infection, then we can use the estimated efficacy against the secondary outcomes to remove the bias from estimated efficacy against the primary outcome. We demonstrate the utility of these approaches in studies of HPV vaccines that only target a few highly carcinogenic strains. In this example, using nontargeted strains increased precision in randomized trials modestly but reduced bias in observational studies substantially.

Pragmatic considerations for negative control outcome studies to guide non-randomized comparative analyses: A narrative review.

PURPOSE: This narrative review describes the application of negative control outcome (NCO) methods to assess potential bias due to unmeasured or mismeasured confounders in non-randomized comparisons of drug effectiveness and safety. An NCO is assumed to have no causal relationship with a treatment under study while subject to the same confounding structure as the treatment and outcome of interest; an association between treatment and NCO then reflects the potential for uncontrolled confounding between treatment and outcome. METHODS: We focus on two recently completed NCO studies that assessed the comparability of outcome risk for patients initiating different osteoporosis medications and lipid-lowering therapies, illustrating several ways in which confounding may result. In these studies, NCO methods were implemented in claims-based data sources, with the results used to guide the decision to proceed with comparative effectiveness or safety analyses. RESULTS: Based on this research, we provide recommendations for future NCO studies, including considerations for the identification of confounding mechanisms in the target patient population, the selection of NCOs expected to satisfy required assumptions, the interpretation of NCO effect estimates, and the mitigation of uncontrolled confounding detected in NCO analyses. We propose the use of NCO studies prior to initiating comparative effectiveness or safety research, providing information on the potential presence of uncontrolled confounding in those comparative analyses. CONCLUSIONS: Given the increasing use of non-randomized designs for regulatory decision-making, the application of NCO methods will strengthen study design, analysis, and interpretation of real-world data and the credibility of the resulting real-world evidence.

Using Negative Control Outcomes and Difference-in-Differences Analysis to Estimate Treatment Effects in an Entirely Treated Cohort: The Effect of Ivacaftor in Cystic Fibrosis.

When an entire cohort of patients receives a treatment, it is difficult to estimate the treatment effect in the treated because there are no directly comparable untreated patients. Attempts can be made to find a suitable control group (e.g., historical controls), but underlying differences between the treated and untreated can result in bias. Here we show how negative control outcomes combined with difference-in-differences analysis can be used to assess bias in treatment effect estimates and obtain unbiased estimates under certain assumptions. Causal diagrams and potential outcomes are used to explain the methods and assumptions. We apply the methods to UK Cystic Fibrosis Registry data to investigate the effect of ivacaftor, introduced in 2012 for a subset of the cystic fibrosis population with a particular genotype, on lung function and annual rate (days/year) of receiving intravenous (IV) antibiotics (i.e., IV days). We consider 2 negative control outcomes: outcomes measured in the pre-ivacaftor period and outcomes among persons ineligible for ivacaftor because of their genotype. Ivacaftor was found to improve lung function in year 1 (an approximately 6.5-percentage-point increase in ppFEV1), was associated with reduced lung function decline (an approximately 0.5-percentage-point decrease in annual ppFEV1 decline, though confidence intervals included 0), and reduced the annual rate of IV days (approximately 60% over 3 years).

Regression-based negative control of homophily in dyadic peer effect analysis.

A prominent threat to causal inference about peer effects in social science studies is the presence of homophily bias , that is, social influence between friends and families is entangled with common characteristics or underlying similarities that form close connections. Analysis of social study data has suggested that certain health conditions such as obesity and psychological states including happiness and loneliness can spread between friends and relatives. However, such analyses of peer effects or contagion effects have come under criticism because homophily bias may compromise the causal statement. We develop a regression-based approach which leverages a negative control exposure for identification and estimation of contagion effects on additive or multiplicative scales, in the presence of homophily bias. We apply our methods to evaluate the peer effect of obesity in Framingham Offspring Study.

Handling unobserved confounding in the relation between prenatal risk factors and child outcomes: a latent variable strategy.

BACKGROUND: Several studies have examined maternal health behavior during pregnancy and child outcomes. Negative control variables have been used to address unobserved confounding in such studies. This approach assumes that confounders affect the exposure and the negative control to the same degree. The current study introduces a novel latent variable approach that relaxes this assumption by accommodating repeated measures of maternal health behavior during pregnancy. METHODS: Monte Carlo simulations were used to examine the performance of the latent variable approach. A real-life example is also provided, using data from the Norwegian Mother, Father, and Child Study (MoBa). RESULTS: Simulations: Regular regression analyses without a negative control variable worked poorly in the presence of unobserved confounding. Including a negative control variable improved result substantially. The latent variable approach provided unbiased results in several situations where the other analysis models worked poorly. Real-life data: Maternal alcohol use in the first trimester was associated with increased ADHD symptoms in the child in the standard regression model. This association was not present in the latent variable approach. CONCLUSION: The current study showed that a latent variable approach with a negative control provided unbiased estimates of causal associations between repeated measures of maternal health behavior during pregnancy and child outcomes, even when the effect of the confounder differed in magnitude between the negative control and the exposures. The real-life example showed that inferences from the latent variable approach were incompatible with those from the standard regression approach. Limitations of the approach are discussed.

Use of negative control outcomes to assess the comparability of patients initiating lipid-lowering therapies.

PURPOSE: Clinical trials have demonstrated efficacy of proprotein convertase subtilisin/kexin type 9 inhibitors (PCSK9i) in reducing risk of cardiovascular disease events, but effectiveness in routine clinical care has not been well-studied. We used negative control outcomes to assess potential confounding in an observational study of PCSK9i versus ezetimibe or high-intensity statin. METHODS: Using commercial claims, we identified U.S. adults initiating PCSK9i, ezetimibe, or high-intensity statin in 2015-2018, with other lipid-lowering therapy (LLT) use in the year prior (LLT cohort) or atherosclerotic cardiovascular disease (ASCVD) in the past 90 days (ASCVD cohort). We compared initiators of PCSK9i to ezetimibe and high-intensity statin by estimating one-year risks of negative control outcomes influenced by frailty or health-seeking behaviors. Inverse probability of treatment and censoring weighted estimators of risk differences (RDs) were used to evaluate residual confounding after controlling for covariates. RESULTS: PCSK9i initiators had lower one-year risks of negative control outcomes associated with frailty, such as decubitus ulcer in the ASCVD cohort (PCSK9i vs. high-intensity statin RD = -3.5%, 95% confidence interval (CI): -4.6%, -2.5%; PCSK9i vs. ezetimibe RD = -1.3%, 95% CI: -2.1%, -0.6%), with similar but attenuated associations in the LLT cohort. Lower risks of accidents and fractures were also observed for PCSK9i, varying by cohort. Risks were similar for outcomes associated with health-seeking behaviors, although trended higher for PCSK9i in the ASCVD cohort. CONCLUSIONS: Observed associations suggest lower frailty and potentially greater health-seeking behaviors among PCSK9i initiators, particularly those with a recent ASCVD diagnosis, with the potential to bias real-world analyses of treatment effectiveness.

The effects of modifiable maternal pregnancy exposures on offspring molar-incisor hypomineralisation: A negative control study.

OBJECTIVES: Explore associations between modifiable maternal pregnancy exposures: pre-pregnancy body mass index (BMI), pregnancy smoking and alcohol consumption with offspring molar-incisor hypomineralisation (MIH) and use negative control analyses to explore for the presence of confounding. METHOD: Using data from a prospective UK birth cohort, Avon Longitudinal Study of Parents and Children, we performed logistic regression to explore confounder adjusted associations between maternal pre-pregnancy BMI and smoking and alcohol consumption during pregnancy with MIH. We compared these with negative control exposure (paternal BMI, smoking and alcohol) and outcome (offspring dental trauma) analyses. RESULTS: 5,536 mother/offspring pairs were included (297 (5.4%) MIH cases). We found a weak, positive association between maternal mean BMI and offspring MIH (Odds Ratio (OR) per 1-kg/m2 difference in BMI: 1.04, 95% confidence interval (CI): 1.00, 1.08). Results of subsequent analyses suggested this effect was non-linear and being driven by women in the highest BMI quintile (OR for women in the highest BMI quintile versus the lowest: 1.61 95%CI: 1.02, 2.60). Negative control analyses showed no evidence of an association between paternal BMI and offspring MIH (OR: 0.94, 95%CI: 0.89,1.00) and maternal BMI and offspring dental trauma (OR: 0.99, 95%CI: 0.96, 1.02). There was no clear evidence of an association for maternal smoking (OR: 0.76, 95%CI: 0.46,1.22) or alcohol consumption (OR: 0.79, 95%CI: 0.56, 1.21) with offspring MIH with results imprecisely estimated. CONCLUSION: We found a possible intrauterine effect for high maternal pre-pregnancy BMI on offspring MIH, but no robust evidence of an intrauterine effect for maternal pregnancy smoking or alcohol consumption. A key limitation includes possible misclassification of MIH. Replication of these results is warranted.

Identification and Estimation of Causal Effects Using a Negative-Control Exposure in Time-Series Studies With Applications to Environmental Epidemiology.

The initial aim of environmental epidemiology is to estimate the causal effects of environmental exposures on health outcomes. However, due to lack of enough covariates in most environmental data sets, current methods without enough adjustments for confounders inevitably lead to residual confounding. We propose a negative-control exposure based on a time-series studies (NCE-TS) model to effectively eliminate unobserved confounders using an after-outcome exposure as a negative-control exposure. We show that the causal effect is identifiable and can be estimated by the NCE-TS for continuous and categorical outcomes. Simulation studies indicate unbiased estimation by the NCE-TS model. The potential of NCE-TS is illustrated by 2 challenging applications: We found that living in areas with higher levels of surrounding greenness over 6 months was associated with less risk of stroke-specific mortality, based on the Shandong Ecological Health Cohort during January 1, 2010, to December 31, 2018. In addition, we found that the widely established negative association between temperature and cancer risks was actually caused by numbers of unobserved confounders, according to the Global Open Database from 2003-2012. The proposed NCE-TS model is implemented in an R package (R Foundation for Statistical Computing, Vienna, Austria) called NCETS, freely available on GitHub.

Associations Between Prenatal Exposure to Air Pollution and Congenital Hypothyroidism.

Adequate thyroid hormone availability is required for normal brain development. Studies have found associations between prenatal exposure to air pollutants and thyroid hormones in pregnant women and newborns. We aimed to examine associations of trimester-specific residential exposure to common air pollutants with congenital hypothyroidism (CHT). All term infants born in Israel during 2009-2015 were eligible for inclusion. We used data on CHT from the national neonatal screening lab of Israel, and exposure data from spatiotemporal air pollution models. We used multivariable logistic regression models to estimate associations of exposures with CHT, adjusting for ethnicity, socioeconomic status, geographical area, conception season, conception year, gestational age, birth weight, and child sex. To assess residual confounding, we used postnatal exposures to the same pollutants as negative controls. The study population included 696,461 neonates. We found a positive association between third-trimester nitrogen oxide exposure and CHT (per interquartile-range change, odds ratio = 1.23, 95% confidence interval: 1.08, 1.41) and a similar association for nitrogen dioxide. There was no evidence of residual confounding or bias by correlation among exposure periods for these associations.

Spotlight influenza: Estimation of influenza vaccine effectiveness in elderly people with assessment of residual confounding by negative control outcomes, Finland, 2012/13 to 2019/20.

BackgroundCohort studies on vaccine effectiveness are prone to confounding bias if the distribution of risk factors is unbalanced between vaccinated and unvaccinated study subjects.AimWe aimed to estimate influenza vaccine effectiveness in the elderly population in Finland by controlling for a sufficient set of confounders based on routinely available register data.MethodsFor each of the eight consecutive influenza seasons from 2012/13 through 2019/20, we conducted a cohort study comparing the hazards of laboratory-confirmed influenza in vaccinated and unvaccinated people aged 65-100 years using individual-level medical and demographic data. Vaccine effectiveness was estimated as 1 minus the hazard ratio adjusted for the confounders age, sex, vaccination history, nights hospitalised in the past and presence of underlying chronic conditions. To assess the adequacy of the selected set of confounders, we estimated hazard ratios of off-season hospitalisation for acute respiratory infection as a negative control outcome.ResultsEach analysed cohort comprised around 1 million subjects, of whom 37% to 49% were vaccinated. Vaccine effectiveness against laboratory-confirmed influenza ranged from 16% (95% confidence interval (CI): 12-19) to 48% (95% CI: 41-54). More than 80% of the laboratory-confirmed cases were hospitalised. The adjusted off-season hazard ratio estimates varied between 1.00 (95% CI: 0.94-1.05) and 1.08 (95% CI: 1.01-1.15), indicating that residual confounding was absent or negligible.ConclusionSeasonal influenza vaccination reduces the hazard of severe influenza disease in vaccinated elderly people. Data about age, sex, vaccination history and utilisation of hospital care proved sufficient to control confounding.

UNIFYING AND GENERALIZING METHODS FOR REMOVING UNWANTED VARIATION BASED ON NEGATIVE CONTROLS.

Unwanted variation, including hidden confounding, is a well-known problem in many fields, but particularly in large-scale gene expression studies. Recent proposals to use control genes, genes assumed to be unassociated with the covariates of interest, have led to new methods to deal with this problem. Several versions of these removing unwanted variation (RUV) methods have been proposed, including RUV1, RUV2, RUV4, RUVinv, RUVrinv, and RUVfun. Here, we introduce a general framework, RUV*, that both unites and generalizes these approaches. This unifying framework helps clarify the connections between existing methods. In particular, we provide conditions under which RUV2 and RUV4 are equivalent. The RUV* framework preserves an advantage of the RUV approaches, namely, their modularity, which facilitates the development of novel methods based on existing matrix imputation algorithms. We illustrate this by implementing RUVB, a version of RUV* based on Bayesian factor analysis. In realistic simulations based on real data, we found RUVB to be competitive with existing methods in terms of both power and calibration. However, providing a consistently reliable calibration among the data sets remains challenging.