Collider Bias Research Articles

Causal Inference and Bias in Learning Analytics

As a research field geared toward understanding and improving learning, Learning Analytics (LA) must be able to provide empirical support for causal claims. However, as a highly applied field, tightly controlled randomized experiments are not always feasible nor desirable. Instead, researchers often rely on observational data, based on which they may be reluctant to draw causal inferences. The past decades have seen much progress concerning causal inference in the absence of experimental data. This paper introduces directed acyclic graphs (DAGs), an increasingly popular tool to visually determine the validity of causal claims. Based on this, three basic pitfalls are outlined: confounding bias, overcontrol bias, and collider bias. Further, the paper shows how these pitfalls may be present in the published LA literature alongside possible remedies. Finally, this approach is discussed in light of practical constraints and the need for theoretical development.

Body mass index versus surrogate measures of central adiposity as independent predictors of mortality in type 2 diabetes

BackgroundAn “obesity paradox” for mortality has been shown in chronic disorders such as diabetes, and attributed to methodological bias, including the use of body mass index (BMI) for obesity definition. This analysis investigated the independent association of BMI versus surrogate measures of central adiposity with all-cause mortality in individuals with type 2 diabetes.MethodsThe Renal Insufficiency And Cardiovascular Events Italian Multicentre Study is a prospective cohort study that enrolled 15,773 patients in 19 Italian centres in 2006–2008. Exposures were BMI and the surrogate measures of central adiposity waist circumference (WC), waist-to-height ratio (WHtR), and A Body Shape Index (ABSI). Vital status was retrieved on 31 October 2015 for 15,656 patients (99.3%),ResultsAge- and sex-adjusted hazard ratios and 95% confidence intervals were significantly higher in BMI-based underweight (1.729 [1.193–2.505), P = 0.004), moderately obese (1.214 [1.058–1.392), P = 0.006) and severely obese (1.703 [1.402–2.068), P < 0.0001), lower in overweight (0.842 [0.775–0.915), P < 0.0001) and similar in mildly obese (0.950 [0.864–1.045), P = 0.292), compared to normal-weight individuals. When further adjusting for smoking, physical activity (PA), and comorbidities, risk was lower also in mildly obese versus normal-weight patients. The BMI-mortality relationship did not change after sequentially excluding ever smokers, individuals with comorbidities, and those died within two years from enrollment and when analyzing separately participants below and above the median age. Conversely, a paradox relationship was observed among inactive/moderately inactive, but not moderately/highly active patients. Mortality risk adjusted for age, gender, smoking, PA and comorbidities was significantly higher in the highest tertile of WC (1.279 [1.089–1.501], P = 0.003), WHtR (1.372 [1.165–1.615], P < 0.0001), and ABSI (1.263 [1.067–1.495], P = 0.007) versus the lowest tertile. However, risk was lower in the intermediate versus lowest tertile for WC (0.823 [0.693–0.979], P = 0.028), similar for WHtR, and higher, though not significantly, for ABSI.ConclusionsAn “overweight paradox” remained after controlling for age, smoking, and comorbidities, arguing against a collider bias or reverse causation. However, it could be partly explained by confounding from PA level, possibly through its impact on lean mass and cardiorespiratory fitness. No obesity paradox was observed with WHtR and especially ABSI, which predicted mortality risk associated with central adiposity better than WC.Trial registration ClinicalTrials.gov, NCT00715481, 15 July, 2008

Applying the structural causal model framework for observational causal inference in ecology

AbstractEcologists are often interested in answering causal questions from observational data but generally lack the training to appropriately infer causation. When applying statistical analysis (e.g., generalized linear model) on observational data, common statistical adjustments can often lead to biased estimates between variables of interest due to processes such as confounding, overcontrol, and collider bias. To overcome these limitations, we present an overview of structural causal modeling (SCM), an emerging causal inference framework that can be used to determine cause‐and‐effect relationships from observational data. The SCM framework uses directed acyclic graphs (DAGs) to visualize researchers' assumptions about the causal structure of a system or process under study. Following this, a DAG‐based graphical rule known as the backdoor criterion can be applied to determine statistical adjustments (or lack thereof) required to determine causal relationships from observational data. In the presence of unobserved confounding variables, an additional rule called the frontdoor criterion can be employed to determine causal effects. Here, we use simulated ecological examples to review how the backdoor and frontdoor criteria can return accurate causal estimates between variables of interest, as well as how biases can arise when these criteria are not used. We further provide an overview of studies that have applied the SCM framework in ecology. SCM, along with its application of DAGs, has been widely used in other disciplines to make valid causal inferences from observational data. Their use in ecology holds tremendous potential for quantifying causal relationships and investigating a range of ecological questions without randomized experiments.

Potential for Collider Bias in Studies Examining the Association of Central Corneal Thickness With Glaucoma.

Central corneal thickness (CCT) may be biologically related to glaucoma or observed as associated with glaucoma simply due to its effect on intraocular pressure (IOP) measurement. We aimed to determine if the previously reported CCT-glaucoma associations, in which the analyses were adjusted for IOP or participants were selected on IOP, could be explained by collider bias. We simulated datasets mimicking a longitudinal population-based study (Los Angeles Latino Eye Study) and a trial (Ocular Hypertension Treatment Study) such that: (i) CCT was not truly associated with glaucoma, (ii) CCT and true IOP both contribute to measured IOP, and (iii) true IOP contributes to glaucoma risk. We then tested whether an association between CCT and glaucoma could be spuriously induced simply by adjusting for or selecting on measured IOP. A thinner CCT was significantly associated with higher glaucoma incidence in the simulated longitudinal population-based study when adjusted for measured IOP, but not crudely (unadjusted). A thinner CCT was crudely associated with glaucoma incidence in the simulated trial in which the participants were selected for high measured IOP. Effect sizes in the simulations were similar to those observed in the original studies. Our findings question whether CCT is biologically associated with glaucoma and suggest that current evidence may be due to collider bias. This indicates that CCT alone cannot be used as a factor to identify people at high risk of glaucoma in the general population. Using CCT in combination with IOP may be superior to using IOP alone.

Comparative hospitalization risk for SARS-CoV-2 Omicron and Delta variant infections, by variant predominance periods and patient-level sequencing results, New York City, August 2021-January 2022.

Comparing disease severity between SARS-CoV-2 variants among populations with varied vaccination and infection histories can help characterize emerging variants and support healthcare system preparedness. We compared COVID-19 hospitalization risk among New York City residents with positive laboratory-based SARS-CoV-2 tests when ≥98% of sequencing results were Delta (August-November 2021) or Omicron (BA.1 and sublineages, January 2022). A secondary analysis defined variant exposure using patient-level sequencing results during July 2021-January 2022, comprising 1-18% of weekly confirmed cases. Hospitalization risk was lower among patients testing positive when Omicron (16,025/488,053, 3.3%) than when Delta predominated (8268/158,799, 5.2%). In multivariable analysis adjusting for demographic characteristics and prior diagnosis and vaccination status, patients testing positive when Omicron predominated, compared with Delta, had 0.72 (95% CI: 0.63, 0.82) times the hospitalization risk. In a secondary analysis of patients with sequencing results, hospitalization risk was similar among patients infected with Omicron (2042/29,866, 6.8%), compared with Delta (1780/25,272, 7.0%), and higher among the subset who received two mRNA vaccine doses (adjusted relative risk 1.64; 95% CI: 1.44, 1.87). Hospitalization risk was lower among patients testing positive when Omicron predominated, compared with Delta. This finding persisted after adjusting for prior diagnosis and vaccination status, suggesting intrinsic virologic properties, not population-based immunity, explained the lower severity. Secondary analyses demonstrated collider bias from the sequencing sampling frame changing over time in ways associated with disease severity. Representative data collection is necessary to avoid bias when comparing disease severity between previously dominant and newly emerging variants.

Constructing an atlas of associations between polygenic scores from across the human phenome and circulating metabolic biomarkers.

Polygenic scores (PGS) are becoming an increasingly popular approach to predict complex disease risk, although they also hold the potential to develop insight into the molecular profiles of patients with an elevated genetic predisposition to disease. We sought to construct an atlas of associations between 125 different PGS derived using results from genome-wide association studies and 249 circulating metabolites in up to 83,004 participants from the UK Biobank. As an exemplar to demonstrate the value of this atlas, we conducted a hypothesis-free evaluation of all associations with glycoprotein acetyls (GlycA), an inflammatory biomarker. Using bidirectional Mendelian randomization, we find that the associations highlighted likely reflect the effect of risk factors, such as adiposity or liability towards smoking, on systemic inflammation as opposed to the converse direction. Moreover, we repeated all analyses in our atlas within age strata to investigate potential sources of collider bias, such as medication usage. This was exemplified by comparing associations between lipoprotein lipid profiles and the coronary artery disease PGS in the youngest and oldest age strata, which had differing proportions of individuals undergoing statin therapy. Lastly, we generated all PGS-metabolite associations stratified by sex and separately after excluding 13 established lipid-associated loci to further evaluate the robustness of findings. We envisage that the atlas of results constructed in our study will motivate future hypothesis generation and help prioritize and deprioritize circulating metabolic traits for in-depth investigations. All results can be visualized and downloaded at http://mrcieu.mrsoftware.org/metabolites_PRS_atlas. This work is supported by funding from the Wellcome Trust, the British Heart Foundation, and the Medical Research Council Integrative Epidemiology Unit.

Collider bias and the obesity paradox.

Obesity paradoxes have been reported in many diseases to date. As the wording "paradox" indicates, our intuition rejects the hypothesis that obese people have a better life expectancy or fewer cardiovascular events. One of the most plausible explanations for the obesity paradox is collider bias, but controversy about this is ongoing. If the findings of the original research are affected by collider bias, meta-analyses of that research will also be affected by the same bias. It is to be hoped that the use of appropriate analytical techniques will enable the true nature of the obesity bias to become clear.

Kidney disease progression and collider bias in GWAS

New genome-wide meta-analysis for longitudinal kidney function decline identified several genetic loci related to kidney disease progression. The study illustrated the complexity of modeling longitudinal traits in genome-wide association studies and highlighted the issue of a collider bias that can be introduced when a kidney disease progression phenotype is adjusted for baseline kidney function. Herein, we briefly outline the key findings of this study, their limitations, and implications for future studies.

Limited Effect of Y Chromosome Variation on Coronary Artery Disease and Mortality in UK Biobank-Brief Report.

Background:The effect of genetic variation in the male-specific region of the Y chromosome (MSY) on coronary artery disease and cardiovascular risk factors has been disputed. In this study, we systematically assessed the association of MSY genetic variation on these traits using a kin-cohort analysis of family disease history in the largest sample to date.Methods:We tested 90 MSY haplogroups against coronary artery disease, hypertension, blood pressure, classical lipid levels, and all-cause mortality in up to 152 186 unrelated, genomically British individuals from UK Biobank. Unlike previous studies, we did not adjust for heritable lifestyle factors (to avoid collider bias) and instead adjusted for geographic variables and socioeconomic deprivation, given the link between MSY haplogroups and geography. For family history traits, subject MSY haplogroups were tested against father and mother disease as validation and negative control, respectively.Results:Our models find little evidence for an effect of any MSY haplogroup on cardiovascular risk in participants. Parental models confirm these findings.Conclusions:Kin-cohort analysis of the Y chromosome uniquely allows for discoveries in subjects to be validated using family history data. Despite our large sample size, improved models, and parental validation, there is little evidence to suggest cardiovascular risk in UK Biobank is influenced by genetic variation in MSY.

The Challenge of Generating Causal Hypotheses Using Network Models

Statistical network models based on Pairwise Markov Random Fields (PMRFs) are popular tools for analyzing multivariate psychological data, in large part due to their perceived role in generating insights into causal relationships: a practice known as causal discovery in the causal modeling literature. However, since network models are not presented as causal discovery tools, the role they play in generating causal insights is poorly understood among empirical researchers. In this paper, we provide a treatment of how PMRFs such as the Gaussian Graphical Model (GGM) work as causal discovery tools, using Directed Acyclic Graphs (DAGs) and Structural Equation Models (SEMs) as causal models. We describe the key assumptions needed for causal discovery and show the equivalence class of causal models that networks identify from data. We clarify four common misconceptions found in the empirical literature relating to networks as causal skeletons; chains of relationships; collider bias; and cyclic causal models.

Interaction Contrasts and Collider Bias.

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.

Principal Component Analysis Reduces Collider Bias in Polygenic Score Effect Size Estimation.

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.

Avoiding collider bias in Mendelian randomization when performing stratified analyses

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.

A 'compensatory selection' effect with standardized tests: Lack of correlation between test scores and success is evidence that test scores are predictive of success.

We introduce the statistical concept of ’compensatory selection’, which arises when selecting a subset of applicants based on multiple predictors, such as when standardized test scores are used in combination with other predictors required in a school application (e.g., previous grades, references letters, and personal statements). Post-hoc analyses often fail to find a positive correlation between test scores and subsequent success, and this failure is sometimes taken as evidence against the predictive validity of the standardized test. The present analysis reveals that the failure to find a negative correlation indicates that the standardized test is in fact a valid predictor of success. This is due to compensation between predictors during selection: Some students are admitted despite a low test score because their application is exceptional in other respects, while other students are admitted primarily based on a high test score despite weakness in the rest of their application. This compensatory selection process introduces a negative correlation between test scores and other predictors among those admitted (a ’collider bias’ or ’Berkson’s paradox’ effect). If test scores are valid predictors of success, this negative correlation between the predictors counteracts the positive correlation between test scores and success that would have been observed if all applicants were admitted. If test scores are not predictive of success, but were nevertheless used in a compensatory selection process, there would be a spurious negative correlation between test scores and success (i.e., an admitted student with a weak application except for a high test score would be unlikely to succeed). The selection effect that is described here is fundamentally different from the well-known ’restricted range’ problem and can powerfully alter results even in situations that accept most applicants.

Adjusting for collider bias in genetic association studies using instrumental variable methods.

Genome‐wide association studies have provided many genetic markers that can be used as instrumental variables to adjust for confounding in epidemiological studies. Recently, the principle has been applied to other forms of bias in observational studies, especially collider bias that arises when conditioning or stratifying on a variable that is associated with the outcome of interest. An important case is in studies of disease progression and survival. Here, we clarify the links between the genetic instrumental variable methods proposed for this problem and the established methods of Mendelian randomisation developed to account for confounding. We highlight the critical importance of weak instrument bias in this context and describe a corrected weighted least‐squares procedure as a simple approach to reduce this bias. We illustrate the range of available methods on two data examples. The first, waist–hip ratio adjusted for body‐mass index, entails statistical adjustment for a quantitative trait. The second, smoking cessation, is a stratified analysis conditional on having initiated smoking. In both cases, we find little effect of collider bias on the primary association results, but this may propagate into more substantial effects on further analyses such as polygenic risk scoring and Mendelian randomisation.

What is Collider Bias and Why Should We Care?

Bias can threaten any study's internal validity compromising the findings. Bias is a nonrandom error that may affect the relationship between an exposure, risk factor, or treatment and the outcome. Bias can arise at any point in the research process, be it in the early stages of sample selection or the final stages of result rationalization and publication. There are 3 main types of bias: selection bias, information bias, and confounding bias.1

COVID-19 and kidney disease: insights from epidemiology to inform clinical practice.

Over the course of the COVID-19 pandemic, numerous studies have aimed to address the challenges faced by patients with kidney disease and their caregivers. These studies addressed areas of concern such as the high infection and mortality risk of patients on in-centre haemodialysis and transplant recipients. However, the ability to draw meaningful conclusions from these studies has in some instances been challenging, owing to barriers in aspects of usual care, data limitations and problematic methodological practices. In many settings, access to SARS-CoV-2 testing differed substantially between patient groups, whereas the incidence of SARS-CoV-2 infection varied over time and place because of differences in viral prevalence, targeted public health policies and vaccination rates. The absence of baseline kidney function data posed problems in the classification of chronic kidney disease and acute kidney injury in some studies, potentially compromising the generalizability of findings. Study findings also require attentive appraisal in terms of the effects of confounding, collider bias and chance. As this pandemic continues and in the future, the implementation of sustainable and integrated research infrastructure is needed in settings across the world to minimize infection transmission and both prevent and plan for the short-term and long-term complications of infectious diseases. Registries can support the real-world evaluation of vaccines and therapies in patients with advanced kidney disease while enabling monitoring of rare complications.

Collider Bias in Observational Studies.

The findings of observational studies can be distorted by a number of factors. So-called confounders are well known, but distortion by collider bias (CB) has received little attention in medical research to date. The goal of this article is to present the principle of CB, and measures that can be taken to avoid it, by way of a few illustrative examples. The findings of a selective review of the literature on CB are explained with illustrative examples. The simplest case of a collider variable is one that is caused by at least two other variables. An example of CB is the observation that, among persons with diabetes, obesity is associated with lower mortality, even though it is associated with higher mortality in the general population. The false protective association between obesity and mortality arises from the restriction of the study population to persons with diabetes. CB is a distortion that arises through restriction on or stratification by a collider variable, or through statistical adjustment for a collider variable in a regression model. CB can arise in many ways. The graphic representation of causal structures helps to identify potential sources of CB. It is important to distinguish confounders from colliders, as methods that serve to correct for confounding can themselves cause bias when applied to colliders. There is no generally applicable method for correcting CB.

A robust method for collider bias correction in conditional genome-wide association studies

Estimated genetic associations with prognosis, or conditional on a phenotype (e.g. disease incidence), may be affected by collider bias, whereby conditioning on the phenotype induces associations between causes of the phenotype and prognosis. We propose a method, ‘Slope-Hunter’, that uses model-based clustering to identify and utilise the class of variants only affecting the phenotype to estimate the adjustment factor, assuming this class explains more variation in the phenotype than any other variant classes. Simulation studies show that our approach eliminates the bias and outperforms alternatives even in the presence of genetic correlation. In a study of fasting blood insulin levels (FI) conditional on body mass index, we eliminate paradoxical associations of the underweight loci: COBLLI; PPARG with increased FI, and reveal an association for the locus rs1421085 (FTO). In an analysis of a case-only study for breast cancer mortality, a single region remains associated with more pronounced results.

The Impact of Collider Bias due to Confounder Measurement Error:

The Impact of Collider Bias due to Confounder Measurement Error: