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Collider bias occurs when conditioning on a common effect (collider) of two variables X , Y . In this article, we quantify the collider bias in the estimated association between exposure X and outcome Y induced by selecting on one value of a binary collider S of the exposure and the outcome. In the case of logistic regression, it is known that the magnitude of the collider bias in the exposure-outcome regression coefficient is proportional to the strength of interaction δ 3 between X and Y in a log-additive model for the collider: P ( S = 1 | X , Y ) = exp { δ 0 + δ 1 X + δ 2 Y + δ 3 X Y } . We show that this result also holds under a linear or Poisson regression model for the exposure-outcome association. We then illustrate numerically that even if a log-additive model with interactions is not the true model for the collider, the interaction term in such a model is still informative about the magnitude of collider bias. Finally, we discuss the implications of these findings for methods that attempt to adjust for collider bias, such as inverse probability weighting which is often implemented without including interactions between variables in the weighting model., Competing Interests: Declaration of conflicting interestsThe author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Background: Few studies have examined the risk of de novo hepatocellular carcinoma (HCC) among hepatitis C virus (HCV)-infected patients with cirrhosis who received interferon (IFN)-free direct-acting antiviral (DAA) therapy relative to patients who received IFN-containing therapy or remained untreated., Aims: To estimate the risk of de novo HCC with DAA treatment in cirrhotic HCV patients compared to no anti-HCV treatment and those treated with IFN-based therapy., Methods: We identified patients with chronic HCV infection and compensated cirrhosis in the US Department of Veterans Affairs healthcare system treated with IFN (2005 to 2013) or DAAs (2013 to 2017). We compared the risk of de novo HCC for patients treated with DAAs, IFN-containing regimens or no treatment after accounting for differences in demographics, alcohol and drug abuse, comorbidities, laboratory values, healthcare utilisation, prior HCV treatment and HCC surveillance., Results: A total of 53,847 patients contributed to untreated time, 27,147 patients contributed to DAA-treated time (15,641 contributed to both untreated and DAA-treated times) and 6809 patients contributed to IFN-treated time. HCC risk associated with DAA treatment was significantly lower than untreated [adjusted HR: 0.70 (95% CI: 0.65-0.74)]. The risk of HCC was not significantly different for patients treated with DAA compared with those treated with IFN [adjusted HR: 0.98 (95% CI: 0.87-1.10)]., Conclusions: The study shows a reduced risk of de novo HCC among patients with chronic HCV-related compensated cirrhosis who received DAA treatment compared to that of untreated patients. There were no differences in HCC risk between DAA-treated and IFN-treated patients., (Published 2025. This article is a U.S. Government work and is in the public domain in the USA.)

Mendelian randomization (MR) facilitates causal inference with observational data using publicly available genome-wide association study (GWAS) results. In a GWAS, one or more heritable covariates may be adjusted for to estimate the direct effects of SNPs on a focal trait or to improve statistical power, which may introduce collider bias in SNP-trait association estimates, thus affecting downstream MR analyses. Numerical studies suggested that using covariate-adjusted GWAS summary data might introduce bias in univariable Mendelian randomization (UVMR), which can be mitigated by multivariable Mendelian randomization (MVMR). However, it remains unclear and even mysterious why/how MVMR works; a rigorous theory is needed to explain and substantiate the above empirical observation. In this paper, we derive some analytical results when multiple covariates are adjusted for in the GWAS of exposure and/or the GWAS of outcome, thus supporting and explaining the empirical results. Our analytical results offer insights to how bias arises in UVMR and how it is avoided in MVMR, regardless of whether collider bias is present. We also consider applying UVMR or MVMR methods after collider-bias correction. We conducted extensive simulations to demonstrate that with covariate-adjusted GWAS summary data, MVMR had an advantage over UVMR by producing nearly unbiased causal estimates; however, in some situations it is advantageous to apply UVMR after bias correction. In real data analyses of the GWAS data with body mass index (BMI) being adjusted for metabolomic principal components, we examined the causal effect of BMI on blood pressure, confirming the above points., Competing Interests: Declaration of interests The authors declare no competing interests., (Copyright © 2025 The Author(s). Published by Elsevier Inc. All rights reserved.)

Genome-wide association studies (GWASs) are often performed on ratios composed of a numerator trait divided by a denominator trait. Examples include body mass index (BMI) and the waist-to-hip ratio, among many others. Explicitly or implicitly, the goal of forming the ratio is typically to adjust for an association between the numerator and denominator. While forming ratios may be clinically expedient, there are several important issues with performing GWAS on ratios. Forming a ratio does not "adjust" for the denominator in the sense of conditioning on it, and it is unclear whether associations with ratios are attributable to the numerator, the denominator, or both. Here we demonstrate that associations arising in ratio GWAS can be entirely denominator driven, implying that at least some associations uncovered by ratio GWAS may be due solely to a putative adjustment variable. In a survey of 10 common ratio traits, we find that the ratio model disagrees with the adjusted model (performing GWAS on the numerator while conditioning on the denominator) at around 1/3 of loci. Using BMI as an example, we show that variants detected by only the ratio model are more strongly associated with the denominator (height), while variants detected by only the adjusted model are more strongly associated with the numerator (weight). Although the adjusted model provides effect sizes with a clearer interpretation, it is susceptible to collider bias. We propose and validate a simple method of correcting for the genetic component of collider bias via leave-one-chromosome-out polygenic scoring., Competing Interests: Declaration of interests Z.R.M., R.D., H.S., D.A., S.M., K.S., members of the insitro Research Team, T.K., D.K., C.O., and T.W.S. are current or former employees and shareholders of Insitro. G.D.S. and D.M. are advisors to Insitro., (Copyright © 2025. Published by Elsevier Inc.)

Objectives: Small-for-gestational age (SGA) is a causal factor for malnutrition (undernutrition). The available evidence on this causal relationship is based on observational studies and suffers from confounding and collider biases. This study aimed to construct a theoretical causal model to estimate the effect of SGA on malnutrition in children aged less than 5 years., Methods: For the causal model, we designated term-SGA status as the exposure variable and malnutrition at 6 months to 5 years of age (diagnosed by World Health Organization criteria) as the outcome variable. Causal estimands were formulated for three stakeholders. A "rapid narrative review" methodology was adopted for literature synthesis. Studies (observational and randomized) listing the causal factors of malnutrition in children aged less than 5 years from the Indian subcontinent were eligible. Four databases (PubMed, Scopus, Web of Science, and ProQuest) were searched and restricted to the last 10 years (search date: December 15, 2023). Information about the causal factors (covariates) of malnutrition and study characteristics was extracted from the article abstracts. Next, a causal model in the form of a directed acyclic graph (DAG) (DAGitty software) was constructed by connecting exposure, outcome, and covariate nodes using the sequential causal criteria of temporality, face validity, recourse to theory, and counterfactual thought experiments., Results: The search yielded 4818 records, of which 342 abstracts were included. Most of the studies were conducted in India (39%) and Bangladesh (27%). The literature synthesis identified 81 factors that were grouped into 17 nodes, referring to 5 domains: socioeconomic, parental, child-related, environmental, and political. The DAG identified 12 different minimal sufficient adjustment sets (conditioning sets for regression analysis) to estimate the total effect of SGA on malnutrition., Conclusion: We offer an evidence-based causal diagram that will minimize bias due to improper selection of factors in studies focusing on malnutrition in term-SGA infants. The DAG and adjustment sets will facilitate the design and data analysis of future studies., Competing Interests: Declaration of competing interest The authors declare no conflict of interest related to this work., (Copyright © 2024 Elsevier Inc. All rights reserved.)

Tumor progression is driven by the accumulation of genetic alterations, including both point mutations and copy number changes. Understanding the temporal sequence of these events is crucial for comprehending the disease but is not directly discernible from cross-sectional genomic data. Cancer progression models, including Mutual Hazard Networks (MHNs), aim to reconstruct the dynamics of tumor progression by learning the causal interactions between genetic events based on their co-occurrence patterns in cross-sectional data. Here, we highlight a commonly overlooked bias in cross-sectional datasets that can distort progression modeling. Tumors become clinically detectable when they cause symptoms or are identified through imaging or tests. Detection factors, such as size, inflammation (fever, fatigue), and elevated biochemical markers, are influenced by genomic alterations. Ignoring these effects leads to "conditioning on a collider" bias, where events making the tumor more observable appear anticorrelated, creating false suppressive effects or masking promoting effects among genetic events. We enhance MHNs by incorporating the effects of genetic progression events on the inclusion of a tumor in a dataset, thus correcting for collider bias. We derive an efficient tensor formula for the likelihood function and apply it to two datasets from the MSK-IMPACT study. In colon adenocarcinoma, we observe a significantly higher rate of clinical detection for TP53-positive tumors, while in lung adenocarcinoma, the same is true for EGFR-positive tumors. Compared to classical MHNs, this approach eliminates several spurious suppressive interactions and uncovers multiple promoting effects.

The test-negative design (TND) is a popular method for evaluating vaccine effectiveness (VE). A "classical" TND study includes symptomatic individuals tested for the disease targeted by the vaccine to estimate VE against symptomatic infection. However, recent applications of the TND have attempted to estimate VE against infection by including all tested individuals, regardless of their symptoms. In this article, we use directed acyclic graphs and simulations to investigate potential biases in TND studies of COVID-19 VE arising from the use of this "alternative" approach, particularly when applied during periods of widespread testing. We show that the inclusion of asymptomatic individuals can potentially lead to collider stratification bias, uncontrolled confounding by health and healthcare-seeking behaviors (HSBs), and differential outcome misclassification. While our focus is on the COVID-19 setting, the issues discussed here may also be relevant in the context of other infectious diseases. This may be particularly true in scenarios where there is either a high baseline prevalence of infection, a strong correlation between HSBs and vaccination, different testing practices for vaccinated and unvaccinated individuals, or settings where both the vaccine under study attenuates symptoms of infection and diagnostic accuracy is modified by the presence of symptoms., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.)

Background: Published analyses of prostate cancer nested case-control and survival data in the Alpha-Tocopherol, Beta-Carotene Cancer Prevention (ATBC) Study cohort suggested that men with higher baseline vitamin D [25(OH)D] concentrations have both (i) increased prostate cancer risk and (ii) decreased prostate cancer-specific fatality., Methods: To investigate possible factors responsible for a spurious association with prostate cancer fatality, we reanalysed baseline serum vitamin D associations with prostate cancer risk and prostate cancer-specific fatality in case-control data nested within the ATBC Study (1000 controls and 1000 incident prostate cancer cases). Conditional logistic regression and Cox proportion hazard models were used, respectively, to estimate odds ratios for risk and hazard ratios for prostate cancer-specific fatality, overall and by disease aggressiveness. We replicated these case-control analyses using baseline serum measurements of alpha-tocopherol (vitamin E), beta-carotene and retinol (vitamin A), and used the entire ATBC Study cohort (n = 29 085) to estimate marginal associations between these baseline vitamins and prostate cancer incidence and fatality following blood collection., Results: Vitamin D analyses agreed closely with those originally published, with opposite risk and fatality associations. By contrast, the analyses of alpha-tocopherol, beta-carotene and retinol yielded concordant associations for prostate cancer incidence and prostate cancer-specific fatality., Conclusions: We found evidence of neither artefacts in the nested prostate cancer case-control data set nor detection or collider biases in the fatality analyses. The present findings therefore support a valid inverse (i.e. beneficial) association between vitamin D and prostate cancer-specific survival that warrants further evaluation, including possibly in controlled trials., (Published by Oxford University Press on behalf of the International Epidemiological Association 2024.)

Selection bias has long been central in methodological discussions across epidemiology and other fields. In epidemiology, the concept of selection bias has been continually evolving over time. In this issue of the Journal, Mathur and Shpitser (Am J Epidemiol. XXXX;XXX(XX):XXXX-XXXX) present simple graphical rules for using a Single World Intervention Graph (SWIG) to assess the presence of selection bias when estimating treatment effects in both the general population and a selected sample. Notably, the authors examine the setting in which the treatment affects selection, an issue not well-addressed in the existing literature on selection bias. To place the work by Mathur and Shpitser in context, we review the evolution of the concept of selection bias in epidemiology, with a primary focus on the developments in the last 20-30 years since the introduction of causal directed acyclic graphs (DAGs) to epidemiologic research., (© The Author(s) 2024. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: Throughout the Covid-19 pandemic, researchers have made use of electronic health records to research this disease in a rapidly evolving environment of questions and discoveries. These studies are prone to collider bias as they restrict the population of Covid-19 patients to only those with severe disease. Inverse probability weighting is typically used to correct for this bias but requires information from the unrestricted population. Using electronic health records from a South London NHS trust, this work demonstrates a method to correct for collider bias using externally sourced data while examining the relationship between minority ethnicities and poor Covid-19 outcomes., Methods: The probability of inclusion within the observed hospitalised cohort was modelled based on estimates from published national data. The model described the relationship between patient ethnicity, hospitalisation, and death due to Covid-19 - a relationship suggested to be susceptible to collider bias. The obtained probabilities (as applied to the observed patient cohort) were used as inverse probability weights in survival analysis examining ethnicity (and covariates) as a risk factor for death due to Covid-19., Results: Within the observed cohort, unweighted analysis of survival suggested a reduced risk of death in those of Black ethnicity - differing from the published literature. Applying inverse probability weights to this analysis amended this aberrant result to one more compatible with the literature. This effect was consistent when the analysis was applied to patients within only the first wave of Covid-19 and across two waves of Covid-19 and was robust against adjustments to the modelled relationship between hospitalisation, patient ethnicity, and death due to Covid-19 made as part of a sensitivity analysis., Conclusions: In conclusion, this analysis demonstrates the feasibility of using external publications to correct for collider bias (or other forms of selection bias) induced by the restriction of a population to a hospitalised cohort using an example from the recent Covid-19 pandemic., (© 2024. The Author(s).)

Type 2 diabetes (T2D) is a major risk factor for heart failure (HF) and has elevated incidence among individuals with HF. Since genetics and HF can independently influence T2D, collider bias may occur when T2D (i.e., collider) is controlled for by design or analysis. Thus, we conducted a genome-wide association study (GWAS) of diabetes-related HF with correction for collider bias. We first performed a GWAS of HF to identify genetic instrumental variables (GIVs) for HF and to enable bidirectional Mendelian randomization (MR) analysis between T2D and HF. We identified 61 genomic loci, significantly associated with all-cause HF in 114,275 individuals with HF and over 1.5 million controls of European ancestry. Using a two-sample bidirectional MR approach with 59 and 82 GIVs for HF and T2D, respectively, we estimated that T2D increased HF risk (odds ratio [OR] 1.07, 95% confidence interval [CI] 1.04-1.10), while HF also increased T2D risk (OR 1.60, 95% CI 1.36-1.88). Then we performed a GWAS of diabetes-related HF corrected for collider bias due to the study design of index cases. After removing the spurious association of TCF7L2 locus due to collider bias, we identified two genome-wide significant loci close to PITX2 (chromosome 4) and CDKN2B-AS1 (chromosome 9) associated with diabetes-related HF in the Million Veteran Program and replicated the associations in the UK Biobank. Our MR findings provide strong evidence that HF increases T2D risk. As a result, collider bias leads to spurious genetic associations of diabetes-related HF, which can be effectively corrected to identify true positive loci., Competing Interests: Declaration of interests J.J. reports research funding from Amgen, Kowa, Alnylam, Department of Veterans Affairs and National Institutes of Health. Within the past several years, L.S.P. has served on Scientific Advisory Boards for Boehringer Ingelheim and Janssen and has or had research support from Merck, Pfizer, Eli Lilly, Novo Nordisk, Sanofi, PhaseBio, Roche, Abbvie, Vascular Pharmaceuticals, Janssen, Glaxo SmithKline, and the Cystic Fibrosis Foundation and is also a cofounder, officer, board member, and stockholder of a company, Diasyst, Inc., which markets software aimed to help improve diabetes management., (Published by Elsevier Inc.)

Background: Biobanks typically rely on volunteer-based sampling. This results in large samples (power) at the cost of representativeness (bias). The problem of volunteer bias is debated. Here, we (i) show that volunteering biases associations in UK Biobank (UKB) and (ii) estimate inverse probability (IP) weights that correct for volunteer bias in UKB., Methods: Drawing on UK Census data, we constructed a subsample representative of UKB's target population, which consists of all individuals invited to participate. Based on demographic variables shared between the UK Census and UKB, we estimated IP weights (IPWs) for each UKB participant. We compared 21 weighted and unweighted bivariate associations between these demographic variables to assess volunteer bias., Results: Volunteer bias in all associations, as naively estimated in UKB, was substantial-in some cases so severe that unweighted estimates had the opposite sign of the association in the target population. For example, older individuals in UKB reported being in better health, in contrast to evidence from the UK Census. Using IPWs in weighted regressions reduced 87% of volunteer bias on average. Volunteer-based sampling reduced the effective sample size of UKB substantially, to 32% of its original size., Conclusions: Estimates from large-scale biobanks may be misleading due to volunteer bias. We recommend IP weighting to correct for such bias. To aid in the construction of the next generation of biobanks, we provide suggestions on how to best ensure representativeness in a volunteer-based design. For UKB, IPWs have been made available., (© The Author(s) 2024. Published by Oxford University Press on behalf of the International Epidemiological Association.)

Background: Mortality data obtained from death certificates have been studied to explore causal associations between diseases. However, these analyses are subject to collider and reporting biases (selection and information biases, respectively). We aimed to assess to what extent associations of causes of death estimated from individual mortality data can be extrapolated as associations of disease states in the general population., Methods: We used a multistate model to generate populations of individuals and simulate their health states up to death from national health statistics and artificially replicate collider bias. Associations between health states can then be estimated from such simulated deaths by logistic regression and the magnitude of collider bias assessed. Reporting bias can be approximated by comparing the estimates obtained from the observed death certificates (subject to collider and reporting biases) with those obtained from the simulated deaths (subject to collider bias only). As an illustrative example, we estimated the association between cancer and suicide in French death certificates and found that cancer was negatively associated with suicide. Collider bias, due to conditioning inclusion in the study population on death, increasingly downwarded the associations with cancer site lethality. Reporting bias was much stronger than collider bias and depended on the cancer site, but not prognosis., Results: The magnitude of the biases ranged from 1.7 to 9.3 for collider bias, and from 4.7 to 64 for reporting bias., Conclusions: These results argue for an assessment of the magnitude of both collider and reporting biases before performing analyses of cause of death associations exclusively from mortality data. If these biases cannot be corrected, results from these analyses should not be extrapolated to the general population., (© 2023. The Author(s).)

In their seminal 2002 paper, "Causal Knowledge as a Prerequisite for Confounding Evaluation: An Application to Birth Defects Epidemiology," Hernán et al. (Am J Epidemiol. 2002;155(2):176-184) emphasized the importance of using theory rather than data to guide confounding control, focusing on colliders as variables that share characteristics with confounders but whose control may actually introduce bias into analyses. In this commentary, we propose that the importance of this paper stems from the connection the authors made between nonexchangeability as the ultimate source of bias and structural representations of bias using directed acyclic graphs. This provided both a unified approach to conceptualizing bias and a means of distinguishing between different sources of bias, particularly confounding and selection bias. Drawing on examples from the paper, we also highlight unresolved questions about the relationship between collider bias, selection bias, and generalizability and argue that causal knowledge is a prerequisite not only for identifying confounders but also for developing any hypothesis about potential sources of bias., (© The Author(s) 2022. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

Background: Alpha-1 adrenergic receptor antagonists prevent cytokine storm in mouse sepsis models. This led to the hypothesis that alpha-1 blockers may prevent severe coronavirus disease 2019 (COVID-19), which is characterized by hypercytokinemia and progressive respiratory failure., Methods: We performed an observational case-control study in male Medicare beneficiaries aged 65 years or older, with or without benign prostatic hyperplasia (BPH), and treated with alpha-1 receptor blockers or 5-alpha reductase inhibitors. Adjusted odds ratios (aOR) and 95% confidence intervals (CI) were estimated for outcomes of uncomplicated and severe COVID-19 hospitalization (intensive care unit admission, invasive mechanical ventilation, or death)., Results: There were 20,963 cases of hospitalized COVID-19 matched to 101,161 controls on calendar date and neighborhood of residence. In the primary analysis (males with BPH), there was no difference in risk of uncomplicated COVID-19 hospitalization (aOR 1.08, 95% CI 0.996-1.17) or hospitalization with severe complications (aOR 0.97, 95% CI 0.88-1.08). In the secondary analysis (males with or without BPH), the corresponding aORs were 1.02 (95% CI, 0.96-1.09) (uncomplicated) and 0.99 (95% CI, 0.91-1.07) (complicated), respectively. Subgroup and sensitivity analyses yielded similar results. Of note, there was no difference in risk of severe COVID-19 hospitalization when comparing non-selective vs selective alpha-1 blocker use (aOR 0.98, 95% CI 0.86-1.10), higher- vs lower-dose alpha-1 blocker use (aOR 0.96, 95% CI 0.86-1.08), or current vs remote alpha-1 blocker use (aOR 1.04, 95% CI 0.91-1.18)., Conclusions: Prevalent use of alpha-1 receptor blockers was not associated with a protective or harmful effect on risk of uncomplicated or severe hospitalized COVID-19., (Published by Elsevier Inc.)

Epidemiological studies often have missing data, which are commonly handled by multiple imputation (MI). In MI, in addition to those required for the substantive analysis, imputation models often include other variables ("auxiliary variables"). Auxiliary variables that predict the partially observed variables can reduce the standard error (SE) of the MI estimator and, if they also predict the probability that data are missing, reduce bias due to data being missing not at random. However, guidance for choosing auxiliary variables is lacking. We examine the consequences of a poorly chosen auxiliary variable: if it shares a common cause with the partially observed variable and the probability that it is missing (i.e., it is a "collider"), its inclusion can induce bias in the MI estimator and may increase the SE. We quantify, both algebraically and by simulation, the magnitude of bias and SE when either the exposure or outcome is incomplete. When the substantive analysis outcome is partially observed, the bias can be substantial, relative to the magnitude of the exposure coefficient. In settings in which a complete records analysis is valid, the bias is smaller when the exposure is partially observed. However, bias can be larger if the outcome also causes missingness in the exposure. When using MI, it is important to examine, through a combination of data exploration and considering plausible casual diagrams and missingness mechanisms, whether potential auxiliary variables are colliders., Competing Interests: Conflict of interest The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Objectives: Studies from the first waves of the coronavirus disease 2019 (COVID-19) pandemic suggest that individuals from minority ethnicities are at an increased risk of worse outcomes. Concerns exist that this relationship is potentially driven by bias from analyzing hospitalized patients only. We investigate this relationship and the possible presence of bias., Study Design and Setting: Using data from South London hospitals across two COVID-19 waves (February 2020 - May 2021), the relationship between ethnicity and COVID-19 outcomes was examined using regression models. Three iterations of each model were completed: 1) an unadjusted analysis, 2) adjusting for covariates (medical history and deprivation), and 3) adjusting for covariates and bias induced by conditioning on hospitalization., Results: Among 3,133 patients, those who were Asian had a two-fold increased risk of death during the hospital stay that was consistent across the two COVID-19 waves and was not affected by correcting for conditioning on hospitalization. However, wave-specific effects demonstrate significant differences between ethnic groups until bias from using a hospitalized cohort was corrected for., Conclusion: Worsened COVID-19 outcomes in minority ethnicities may be minimized by correcting for bias induced by conditioning on hospitalization. Consideration of this bias should be a key component of study design., Competing Interests: Declaration of competing interest There are no conflicts of interest to declare., (Copyright © 2023 The Author(s). Published by Elsevier Inc. All rights reserved.)

Female sex in patients with atrial fibrillation (AF) is a controversial and paradoxical risk factor for stroke-controversial because it increases the risk of stroke only among older women of some ethnicities and paradoxical because it appears to contradict male predominance in cardiovascular diseases. However, the underlying mechanism remains unclear. We conducted simulations to examine the hypothesis that this sex difference is generated non-causally through left truncation due to competing risks (CR) such as coronary artery diseases, which occur more frequently among men than among women and share common unobserved causes with stroke. We modeled the hazards of stroke and CR with correlated heterogeneous risk. We assumed that some people died of CR before AF diagnosis and calculated the hazard ratio of female sex in the left-truncated AF population. In this situation, female sex became a risk factor for stroke in the absence of causal roles. The hazard ratio was attenuated in young populations without left truncation and in populations with low CR and high stroke incidence, which is consistent with real-world observations. This study demonstrated that spurious risk factors can be identified through left truncation due to correlated CR. Female sex in patients with AF may be a paradoxical risk factor for stroke.

Objectives: Collider bias is a common threat to internal validity in clinical research but is rarely mentioned in informatics education or literature. Conditioning on a collider, which is a variable that is the shared causal descendant of an exposure and outcome, may result in spurious associations between the exposure and outcome. Our objective is to introduce readers to collider bias and its corollaries in the retrospective analysis of electronic health record (EHR) data., Target Audience: Collider bias is likely to arise in the reuse of EHR data, due to data-generating mechanisms and the nature of healthcare access and utilization in the United States. Therefore, this tutorial is aimed at informaticians and other EHR data consumers without a background in epidemiological methods or causal inference., Scope: We focus specifically on problems that may arise from conditioning on forms of healthcare utilization, a common collider that is an implicit selection criterion when one reuses EHR data. Directed acyclic graphs (DAGs) are introduced as a tool for identifying potential sources of bias during study design and planning. References for additional resources on causal inference and DAG construction are provided., (© The Author(s) 2023. Published by Oxford University Press on behalf of the American Medical Informatics Association.)

Objectives: We provide a brief overview of collider bias and its implications for criminological research., Methods: Owing to the nature of the topics studied, as well as the common data sources used to carry out much of this research, work in the field may often become vulnerable to a specific methodological problem known as collider bias. Collider bias occurs when exposure variables and outcomes independently cause a third variable, and this variable is included in statistical models. Colliders represent somewhat of a paradox in that there is scholarship discussing the issue, yet it has managed to remain a relatively cryptic threat compared to other sources of bias., Results: We argue that, far from being an obscure concern, colliders almost certainly have pervasive impact in criminal justice and criminology., Conclusion: We close by offering a general set of strategies for addressing the challenges posed by collider bias. While there is no panacea, there are better practices, many of which are underutilized in the disciplines that study crime and its attendant topics., (© The Author(s), under exclusive licence to Springer Nature B.V. 2023.)

Ecologists often rely on randomized control trials (RCTs) to quantify causal relationships in nature. Many of our foundational insights of ecological phenomena can be traced back to well-designed experiments, and RCTs continue to provide valuable insights today. Although RCTs are often regarded as the "gold standard" for causal inference, it is important to recognize that they too rely on a set of causal assumptions that must be justified and met by the researcher to draw valid causal conclusions. We use key ecological examples to show how biases such as confounding, overcontrol, and collider bias can occur in experimental setups. In tandem, we highlight how such biases can be removed through the application of the structural causal model (SCM) framework. The SCM framework visualizes the causal structure of a system or process under study using directed acyclic graphs (DAGs) and subsequently applies a set of graphical rules to remove bias from both observational and experimental data. We show how DAGs can be applied across ecological experimental studies to ensure proper study design and statistical analysis, leading to more accurate causal estimates drawn from experimental data. Although causal conclusions drawn from RCTs are often taken at face value, ecologists are increasingly becoming aware that experimental approaches must be carefully designed and analyzed to avoid potential biases. By applying DAGs as a visual and conceptual tool, experimental ecologists can increasingly meet the causal assumptions required for valid causal inference., Competing Interests: There is no conflict of interest to declare., (© 2023 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.)

Occupancy models are a vital tool for ecologists studying the patterns and drivers of species occurrence, but their use often involves selecting among models with different sets of occupancy and detection covariates. The information-theoretic approach, which employs information criteria such as Akaike's information criterion (AIC) is arguably the most popular approach for model selection in ecology and is often used for selecting occupancy models. However, the information-theoretic approach risks selecting models that produce inaccurate parameter estimates due to a phenomenon called collider bias, a type of confounding that can arise when adding explanatory variables to a model. Using simulations, we investigated the consequences of collider bias (using an illustrative example called M-bias) in the occupancy and detection processes of an occupancy model, and explored the implications for model selection using AIC and a common alternative, the Schwarz criterion (or Bayesian information criterion, BIC). We found that when M-bias was present in the occupancy process, AIC and BIC selected models that inaccurately estimated the effect of the focal occupancy covariate, while simultaneously producing more accurate predictions of the site-level occupancy probability than other models in the candidate set. In contrast, M-bias in the detection process did not impact the focal estimate; all models made accurate inferences, while the site-level predictions of the AIC/BIC-best model were slightly more accurate. Our results show that information criteria can be used to select occupancy covariates if the sole purpose of the model is prediction, but must be treated with more caution if the purpose is to understand how environmental variables affect occupancy. By contrast, detection covariates can usually be selected using information criteria regardless of the model's purpose. These findings illustrate the importance of distinguishing between the tasks of parameter inference and prediction in ecological modeling. Furthermore, our results underline concerns about the use of information criteria to compare different biological hypotheses in observational studies., (© 2022 The Authors. Ecology published by Wiley Periodicals LLC on behalf of The Ecological Society of America.)

Background: When quantifying differences in health outcomes between immigrants and non-immigrants, it is common practice to adjust for observed differences in outcome risk factors between the groups being compared. However, as some of these outcome risk factors may act as mediators on the causal path between the exposure and outcome, adjusting for these may remove effects of factors that characterize the immigrants rather than removing a bias between immigrants and non-immigrants., Methods: This study investigates the underlying conditions for which adjusting for outcome risk factors in regression models can lead to the estimation of either total or direct effect for the difference in health outcomes between immigrants and non-immigrants. For this investigation, we use modern tools in causal inference to construct causal models that we believe are highly relevant in an immigrant dataset. In these models, the outcome risk factor is modeled either as a mediator, a selection factor, or a combined mediator/selection factor. Unlike mediators, selection factors are variables that affect the probability of being in the immigrant dataset and may contribute to a bias when comparing immigrants and non-immigrants., Results: When the outcome risk factor acts both as a mediator and selection factor, the adjustment for the risk factor in regression models leads to the estimation of what is known as a "controlled" direct effect. When the outcome risk factor is either a selection factor or a mediator alone, the adjustment for the risk factor in regression models leads to the estimation of a total effect or a controlled direct effect, respectively. In all regression analyses, also adjusting for various confounding paths, including mediator-outcome confounding, may be necessary to obtain valid controlled direct effects or total effects., Conclusions: Depending on the causal role of the outcome risk factors in immigrant datasets, regression adjustment for these may result in the estimation of either total effects or controlled direct effects for the difference in outcomes between immigrants and non-immigrants. Because total and controlled direct effects are interpreted differently, we advise researchers to clarify to the readers which types of effects are presented when adjusting for outcome risk factors in immigrant datasets., (© 2023. The Author(s).)

COVID-19 research has relied heavily on convenience-based samples, which-though often necessary-are susceptible to important sampling biases. We begin with a theoretical overview and introduction to the dynamics that underlie sampling bias. We then empirically examine sampling bias in online COVID-19 surveys and evaluate the degree to which common statistical adjustments for demographic covariates successfully attenuate such bias. This registered study analysed responses to identical questions from three convenience and three largely representative samples (total N = 13,731) collected online in Canada within the International COVID-19 Awareness and Responses Evaluation Study ( www.icarestudy.com ). We compared samples on 11 behavioural and psychological outcomes (e.g., adherence to COVID-19 prevention measures, vaccine intentions) across three time points and employed multiverse-style analyses to examine how 512 combinations of demographic covariates (e.g., sex, age, education, income, ethnicity) impacted sampling discrepancies on these outcomes. Significant discrepancies emerged between samples on 73% of outcomes. Participants in the convenience samples held more positive thoughts towards and engaged in more COVID-19 prevention behaviours. Covariates attenuated sampling differences in only 55% of cases and increased differences in 45%. No covariate performed reliably well. Our results suggest that online convenience samples may display more positive dispositions towards COVID-19 prevention behaviours being studied than would samples drawn using more representative means. Adjusting results for demographic covariates frequently increased rather than decreased bias, suggesting that researchers should be cautious when interpreting adjusted findings. Using multiverse-style analyses as extended sensitivity analyses is recommended., (© 2022. Springer Nature B.V.)

Previous papers have mentioned that conditioning on a binary collider would introduce an association between its causes in at least 1 stratum. In this paper, we prove this statement and, along with intuitions, formally examine the direction and magnitude of the associations between 2 risk factors of a binary collider using interaction contrasts. Among level one of the collider, 2 variables are independent, positively associated, and negatively associated if multiplicative risk interaction contrast is equal to, more than, and less than 0, respectively; the same results hold for the other level of the collider if the multiplicative survival interaction contrast, equal to multiplicative risk interaction contrast minus the additive risk interaction contrast, is compared with 0. The strength of the association depends on the magnitude of the interaction contrast: The stronger the interaction is, the larger the magnitude of the association will be. However, the common conditional odds ratio under the homogeneity assumption will be bounded. A figure is presented that succinctly illustrates our results and helps researchers to better visualize the associations introduced upon conditioning on a collider., (© The Author(s) 2022. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.)

In this study, we test principal component analysis (PCA) of measured confounders as a method to reduce collider bias in polygenic association models. We present results from simulations and application of the method in the Collaborative Study of the Genetics of Alcoholism (COGA) sample with a polygenic score for alcohol problems, DSM-5 alcohol use disorder as the target phenotype, and two collider variables: tobacco use and educational attainment. Simulation results suggest that assumptions regarding the correlation structure and availability of measured confounders are complementary, such that meeting one assumption relaxes the other. Application of the method in COGA shows that PC covariates reduce collider bias when tobacco use is used as the collider variable. Application of this method may improve PRS effect size estimation in some cases by reducing the effect of collider bias, making efficient use of data resources that are available in many studies., (© 2022. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

Mendelian randomization (MR) uses genetic variants as instrumental variables to investigate the causal effect of a risk factor on an outcome. A collider is a variable influenced by two or more other variables. Naive calculation of MR estimates in strata of the population defined by a collider, such as a variable affected by the risk factor, can result in collider bias. We propose an approach that allows MR estimation in strata of the population while avoiding collider bias. This approach constructs a new variable, the residual collider, as the residual from regression of the collider on the genetic instrument, and then calculates causal estimates in strata defined by quantiles of the residual collider. Estimates stratified on the residual collider will typically have an equivalent interpretation to estimates stratified on the collider, but they are not subject to collider bias. We apply the approach in several simulation scenarios considering different characteristics of the collider variable and strengths of the instrument. We then apply the proposed approach to investigate the causal effect of smoking on bladder cancer in strata of the population defined by bodyweight. The new approach generated unbiased estimates in all the simulation settings. In the applied example, we observed a trend in the stratum-specific MR estimates at different bodyweight levels that suggested stronger effects of smoking on bladder cancer among individuals with lower bodyweight. The proposed approach can be used to perform MR studying heterogeneity among subgroups of the population while avoiding collider bias., (© 2022. The Author(s).)

Purpose: Workers' compensation claims consist of occupational injuries severe enough to meet a compensability threshold. Theoretically, systems with higher thresholds should have fewer claims but greater average severity. For research that relies on claims data, particularly cross-jurisdictional comparisons of compensation systems, this results in collider bias that can lead to spurious associations confounding analyses. In this study, I use real and simulated claims data to demonstrate collider bias and problems with methods used to account for it., Methods: Using Australian claims data, I used a linear regression to test the association between claim rate and mean disability durations across Statistical Areas. Analyses were repeated with nesting by state/territory to account for variations in compensability thresholds across compensation systems. Both analyses are repeated on left-censored data. Simulated claims data are analysed with Cox survival analyses to illustrate how left-censoring can reverse effects., Results: The claim rate within a Statistical Area was inversely associated with disability duration. However, this reversed when Statistical Areas were nested by state/territory. Left-censoring resulted in an attenuation of the unnested association to non-significance, while the nested association remained significantly positive. Cox regressions with simulated claims data demonstrated how left-censoring can reverse effects., Conclusions: Collider bias can seriously confound work disability research, particularly cross-jurisdictional comparisons. Work disability researchers must grapple with this challenge by using appropriate study designs and analytical approaches, and considering how it affects the interpretation of results., (© 2021. The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.)

There is substantial evidence in support of an association between periodontitis and cardiovascular disease. The most important open question related to this association is causality. This article revisits the question of causality by reviewing intervention studies and systematic reviews and meta analyses published in the last 3 years. Where are we now in answering this question? Whilst systematic reviews and epidemiological studies continue to support an association between the diseases, intervention studies fall short in determining causality. There is a dearth of good-quality, blinded randomised control trials with cardiovascular disease outcomes. Most studies use surrogate markers/biomarkers for endpoints, and this is problematic as they may not be reflective of cardiovascular disease status. This review further highlights another issue with surrogate markers/biomarkers: the potential for collider bias. Ethical considerations surrounding nontreatment have led to calls for a well-annotated database containing in-depth dental health data. Finally, a relatively new and important risk factor for cardiovascular disease, clonal haematopoiesis of indeterminate potential, is discussed. Clonal haematopoiesis of indeterminate potential increases cardiovascular risk by more than 40%, and inflammation is a contributing factor. The impact of periodontal disease on this emerging risk factor has yet to be explored. Although the question of causality in the association between periodontal disease and cardiovascular disease remains unanswered, the importance of good oral health in maintaining good heart health is reiterated., Competing Interests: Conflict of interest None disclosed., (Copyright © 2021 The Authors. Published by Elsevier Inc. All rights reserved.)

For many research questions in perinatal epidemiology, gestational age is a mediator that features the causal pathway between exposure and outcome. A mediator is an intermediate variable between an exposure and outcome, which is influenced by the exposure on the causal pathway to the outcome. Therefore, conventional analyses that adjust, stratify, or match for gestational age or its proxy (eg, preterm vs term deliveries) are problematic. This practice, which is entrenched in perinatal research, induces an overadjustment bias. Depending on the causal question, it may be inappropriate to adjust (or condition) for a mediator, such as gestational age, by either design or statistical analysis, but its effect can be quantified through causal mediation analysis. In an exposition of such methods, we demonstrated the relationship between the exposure and outcome and provided a formal analytical framework to quantify the extent to which a causal effect is influenced by a mediator. We reviewed concepts of confounding and causal inference, introduced the concept of a mediator and illustrated the perils of adjusting for a mediator in an exposure-outcome paradigm for a given causal question, adopted causal methods that call for an evaluation of a mediator in a causal exposure effect on the outcome, and discussed unmeasured confounding assumptions in mediation analysis. Furthermore, we reviewed other developments in the causal mediation analysis literature, including decomposition of a total effect when the mediator interacts with the exposure (4-way decomposition), methods for multiple mediators, mediation methods for case-control studies, mediation methods for time-to-event outcomes, sample size and power analysis for mediation analysis, and available software to apply these methods. To illustrate these methods, we provided a clinical example to estimate the risk of perinatal mortality (outcome) concerning placental abruption (exposure) and to determine the extent to which preterm delivery (mediator; a proxy for gestational age) plays a role in this causal effect. We hoped that the adoption of mediation methods described in this review will move research in perinatal epidemiology away from biased adjustments of mediators toward a more nuanced quantification of effects that pose unique challenges and provide unique insights in our field., (Copyright © 2021 Elsevier Inc. All rights reserved.)

Bone research is a dynamic area of scientific investigation that usually encompasses multidisciplines. Virtually all basic cellular research, clinical research and epidemiologic research rely on statistical concepts and methodology for inference. This paper discusses common issues and suggested solutions concerning the application of statistical thinking in bone research, particularly in clinical and epidemiological investigations. The issues are sample size estimation, biases and confounders, analysis of longitudinal data, categorization of continuous data, selection of significant variables, over-fitting, P-values, false positive finding, confidence interval, and Bayesian inference. It is hoped that by adopting the suggested measures the scientific quality of bone research can improve., Competing Interests: The author declares no competing interests., (© 2020 The Korean Society of Osteoporosis. Publishing services by Elsevier B.V.)

Background: Compositional data comprise the parts of some whole, for which all parts sum to that whole. They are prevalent in many epidemiological contexts. Although many of the challenges associated with analysing compositional data have been discussed previously, we do so within a formal causal framework by utilizing directed acyclic graphs (DAGs)., Methods: We depict compositional data using DAGs and identify two distinct effect estimands in the generic case: (i) the total effect, and (ii) the relative effect. We consider each in the context of three specific example scenarios involving compositional data: (1) the relationship between the economically active population and area-level gross domestic product; (2) the relationship between fat consumption and body weight; and (3) the relationship between time spent sedentary and body weight. For each, we consider the distinct interpretation of each effect, and the resulting implications for related analyses., Results: For scenarios (1) and (2), both the total and relative effects may be identifiable and causally meaningful, depending upon the specific question of interest. For scenario (3), only the relative effect is identifiable. In all scenarios, the relative effect represents a joint effect, and thus requires careful interpretation., Conclusions: DAGs are useful for considering causal effects for compositional data. In all analyses involving compositional data, researchers should explicitly consider and declare which causal effect is sought and how it should be interpreted., (© The Author(s) 2020. Published by Oxford University Press on behalf of the International Epidemiological Association.)

Aims/hypothesis: There is controversy on whether an obesity paradox exists in type 2 diabetes, ie, that mortality is lowest in overweight or obesity. We examined the role of potential biases in the obesity paradox., Methods: From two regional population-based German cohort studies - the Heinz Nixdorf Recall Study and the Study of Health in Pomerania (baseline examinations 2000-2003/1997-2001) - 1187 persons with diabetes at baseline were included (mean age 62.6 years, 60.9% males). Diabetes was ascertained by self-report of physician's diagnosis, antidiabetic medication, fasting/random glucose or haemoglobin A1c. Mortality data were assessed for up to 17.7 years. We used restricted cubic splines and Cox regression models to assess associations between body mass index (BMI) and mortality. Sensitivity analyses addressed, inter alia, exclusion of early death cases, of persons with cancer, kidney disease or with history of cardiovascular diseases, and of ever smokers. Furthermore, we examined the role of treatment bias and collider bias for the obesity paradox., Results: In spline models, mortality risk was lowest for BMI at about 31 kg/m 2 . Sensitivity analyses carried out one after another had hardly any impact on this result. In our cohort, persons with diabetes and BMI ≥30 kg/m 2 did not have better treatment than non-obese patients, and we found that collider bias played only a minor role in the obesity paradox., Conclusion: In a cohort of 1187 persons with diabetes, mortality risk was lowest in persons with moderate obesity. We cannot explain this result by a variety of sensitivity analyses., Competing Interests: There are no competing interests to declare., (© 2020 Kowall et al.)

Longitudinal studies have sought to establish whether environmental exposures such as smoking accelerate the attrition of individuals' telomeres over time. These studies typically control for baseline telomere length (TL) by including it as a covariate in statistical models. However, baseline TL also differs between smokers and non-smokers, and telomere attrition is spuriously linked to baseline TL via measurement error and regression to the mean. Using simulated datasets, we show that controlling for baseline TL overestimates the true effect of smoking on telomere attrition. This bias increases with increasing telomere measurement error and increasing difference in baseline TL between smokers and non-smokers. Using a meta-analysis of longitudinal datasets, we show that as predicted, the estimated difference in telomere attrition between smokers and non-smokers is greater when statistical models control for baseline TL than when they do not, and the size of the discrepancy is positively correlated with measurement error. The bias we describe is not specific to smoking and also applies to other exposures. We conclude that to avoid invalid inference, models of telomere attrition should not control for baseline TL by including it as a covariate. Many claims of accelerated telomere attrition in individuals exposed to adversity need to be re-assessed., Competing Interests: The authors declare no competing interests., (© 2019 The Authors.)

Background: Selection bias affects Mendelian randomization investigations when selection into the study sample depends on a collider between the genetic variant and confounders of the risk factor-outcome association. However, the relative importance of selection bias for Mendelian randomization compared with other potential biases is unclear., Methods: We performed an extensive simulation study to assess the impact of selection bias on a typical Mendelian randomization investigation. We considered inverse probability weighting as a potential method for reducing selection bias. Finally, we investigated whether selection bias may explain a recently reported finding that lipoprotein(a) is not a causal risk factor for cardiovascular mortality in individuals with previous coronary heart disease., Results: Selection bias had a severe impact on bias and Type 1 error rates in our simulation study, but only when selection effects were large. For moderate effects of the risk factor on selection, bias was generally small and Type 1 error rate inflation was not considerable. Inverse probability weighting ameliorated bias when the selection model was correctly specified, but increased bias when selection bias was moderate and the model was misspecified. In the example of lipoprotein(a), strong genetic associations and strong confounder effects on selection mean the reported null effect on cardiovascular mortality could plausibly be explained by selection bias., Conclusions: Selection bias can adversely affect Mendelian randomization investigations, but its impact is likely to be less than other biases. Selection bias is substantial when the effects of the risk factor and confounders on selection are particularly large., (© The Author(s) 2018. Published by Oxford University Press on behalf of the International Epidemiological Association.)

Aims/hypothesis: There is conflicting evidence about the obesity paradox-the counterintuitive survival advantage of obesity among certain subpopulations of individuals with chronic conditions. It is believed that results supporting the obesity paradox are due to methodological flaws, such as collider bias. The aim of this study was to examine the association between obesity and mortality in Australian men and women. In addition, we explored whether obesity would appear to be protective if the analysis was restricted to a subpopulation with disease, and to discuss the potential role of collider bias in producing such a result., Methods: The examined cohort included 10,575 Australian adults (4844 men and 5731 women) aged 25-91 years who were recruited for the AusDiab baseline survey in 1999 and followed-up through 2014. The main predictor variable was BMI categorised as normal weight (18.5 to <25 kg/m 2 ), overweight (25 to <30 kg/m 2 ) and obese (≥30 kg/m 2 ), and the outcome of interest was all-cause mortality. Hazard ratios were estimated from Cox proportional hazards regression models in the entire cohort and then in subpopulations with and without diabetes., Results: A total of 1477 deaths occurred during 145,384 person-years (median 14.6 years) of follow-up. Mortality was higher in obese than in normal-weight individuals for the full population (HR 1.18; 95% CI 1.05, 1.32). When an interaction between diabetes status and BMI category was added to the model, there was no evidence of an interaction between BMI and diabetes status (p = 0.92). When participants with and without diabetes were analysed separately, there was no evidence of an association between obesity and mortality in those with diabetes (HR 0.91; 95% CI 0.62, 1.33)., Conclusions/interpretation: In the entire AusDiab cohort, we found a significantly higher mortality among obese participants as compared with their normal-weight counterparts. We found no difference in the obesity-mortality association between individuals with and without diabetes.

There is debate as to whether cohort studies are valid when they are based on a source population that is non-representative of a given general population. This baseline selection may introduce collider bias if the exposure of interest and some other outcome risk factors affect the probability of being in the source population, thus altering the associations between the exposure and those risk factors. We argue that this mechanism is not specific to 'selected cohorts' and also occurs in 'representative cohorts' due to the selection processes that occur in any population. These selection processes are for example linked to the life status, immigration and emigration, which, in turn, may be affected by environmental and social determinants, lifestyles and genetics. We provide real-world examples of this phenomenon using data on the population of the Piedmont region, Italy. In addition to well-recognised mechanisms, such as shared common causes, the associations between the exposure of interest and the risk factors for the outcome of interest in any source population are potentially shaped by collider bias due to the underlying selection processes. We conclude that, when conducting a cohort study, different source populations, whether 'selected' or 'representative', may lead to different exposure-outcome risk factor associations, and thus different degrees of lack of exchangeability, but that one approach is not inherently more or less biased than the other. The key issue is whether the relevant risk factors can be identified and controlled., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2019. No commercial re-use. See rights and permissions. Published by BMJ.)

Case fatality rates in severe falciparum malaria depend on the pattern and degree of vital organ dysfunction. Recent large-scale case-control analyses of pooled severe malaria data reported that glucose-6-phosphate dehydrogenase deficiency (G6PDd) was protective against cerebral malaria but increased the risk of severe malarial anaemia. A novel formulation of the balancing selection hypothesis was proposed as an explanation for these findings, whereby the selective advantage is driven by the competing risks of death from cerebral malaria and death from severe malarial anaemia. We re-analysed these claims using causal diagrams and showed that they are subject to collider bias. A simulation based sensitivity analysis, varying the strength of the known effect of G6PDd on anaemia, showed that this bias is sufficient to explain all of the observed association. Future genetic epidemiology studies in severe malaria would benefit from the use of causal reasoning., Competing Interests: JW, SL, JS, ND, AD, NW No competing interests declared, (© 2019, Watson et al.)

Background: Metabolomics techniques are increasingly applied in epidemiologic research. Many available assays are still relatively expensive and therefore measurements are often performed in small patient population studies such as case series or case-control designs with strong participant selection criteria. Subsequently, metabolomics data are frequently used to assess secondary associations for which the original study was not explicitly designed. Especially in these secondary analyses, there is a risk that the original selection criteria and the conditioning that takes place due to this selection are not properly accounted for which can lead to selection bias., Aim of Review: In this tutorial, we start with a brief theoretical introduction on the issue of selection bias. Subsequently, we demonstrate how selection bias can occur in metabolomics studies by means of an investigation into associations of metabolites with total body fat in a nested case-control study that was originally designed to study effects of elevated fasting glucose., Key Scientific Concepts of Review: We demonstrate that standard analytical methods, such as stratification or adjustment in regression analyses, are not suited to deal with selection bias and may even induce the bias when analysing metabolite-phenotype relationships in selected groups. Finally, we show that inverse probability weighting, also known as survey weighting, can be used in some situations to make unbiased estimates of the outcomes.

Background: Epidemiologic studies examining preconception risk factors on perinatal outcomes are typically restricted to livebirths. By including only non-terminated pregnancies, estimates for the underlying pregnancy cohort may be subject to selection bias. We examined if potential selection bias due to induced termination by maternal race may result in different estimates of the non-Hispanic black - non-Hispanic white risk ratio (RR) for preterm delivery (PTD) among a reconstructed pregnancy cohort ('pseudo-pregnancy cohort')., Methods: Using New York City registries of 1.6 million livebirths, spontaneous terminations, and induced terminations among non-Hispanic black and non-Hispanic white women (2000-12), we multiply imputed PTD (<37 weeks) and early PTD (<32 weeks) outcomes for induced terminations based on maternal race, age, parity, marital status, nativity, and medical care payer to construct the pseudo-pregnancy cohort., Results: Among non-Hispanic black and non-Hispanic white women, 55% and 19% of pregnancies ended in induced termination and 13% and 8% resulted in PTD, respectively. Although several factors were associated with both PTD and induced termination, PTD RRs in the birth (RR 1.64, 95% confidence interval (CI) 1.62, 1.66) and pseudo-pregnancy (RR 1.63, 95% CI 1.56, 1.71) cohorts were similar. However, early PTD RR was somewhat larger in the birth (RR 2.80, 95% CI 2.71, 2.89) than pseudo-pregnancy (RR 2.47, 95% CI 2.23, 2.73) cohort., Conclusions: Using birth certificate data - thereby excluding induced terminations - to estimate the PTD racial disparity did not produce biased estimates. Our data suggest observed PTD disparities likely are not artefacts of selection bias due to induced termination., (© 2016 John Wiley & Sons Ltd.)

This commentary discusses causal estimands of same-age and same-grade comparisons for assessing grade-retention effects on student ability and performance. Using potential outcomes notation, we show that same-age and same-grade comparisons refer to different retention-promotion contrasts and therefore assess different causal questions. We also comment on deleting versus censoring records of students who dropped out of the study or do not belong to the treatment regimes under investigation. Whereas deleting entire student records potentially induces collider bias, censoring circumvents bias if censoring is ignorable given the observed pretreatment covariates.