Using Inverse Probability Weighting to Address Post-Outcome Collider Bias

We consider the problem of bias arising from conditioning on a post-outcome collider. We illustrate this with reference to Elwert and Winship (2014) but we go beyond their study to investigate the extent to which inverse probability weighting might offer solutions. We use linear models to derive expressions for the bias arising in different kinds of post-outcome confounding, and we show the specific situations in which inverse probability weighting will allow us to obtain estimates that are consistent or, if not consistent, less biased than those obtained via ordinary least squares regression.

Assortative mating and within-spouse pair comparisons

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

Avoiding bias in Mendelian randomization when stratifying on a collider

BackgroundMendelian 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 variable affected by the risk factor can result in collider bias.MethodsWe 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.ResultsThe 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.ConclusionsThe proposed approach can be used to perform MR studying heterogeneity among subgroups of the population while avoiding collider bias.

Exploiting collider bias to apply two-sample summary data Mendelian randomization methods to one-sample individual level data

Over the last decade the availability of SNP-trait associations from genome-wide association studies has led to an array of methods for performing Mendelian randomization studies using only summary statistics. A common feature of these methods, besides their intuitive simplicity, is the ability to combine data from several sources, incorporate multiple variants and account for biases due to weak instruments and pleiotropy. With the advent of large and accessible fully-genotyped cohorts such as UK Biobank, there is now increasing interest in understanding how best to apply these well developed summary data methods to individual level data, and to explore the use of more sophisticated causal methods allowing for non-linearity and effect modification. In this paper we describe a general procedure for optimally applying any two sample summary data method using one sample data. Our procedure first performs a meta-analysis of summary data estimates that are intentionally contaminated by collider bias between the genetic instruments and unmeasured confounders, due to conditioning on the observed exposure. These estimates are then used to correct the standard observational association between an exposure and outcome. Simulations are conducted to demonstrate the method’s performance against naive applications of two sample summary data MR. We apply the approach to the UK Biobank cohort to investigate the causal role of sleep disturbance on HbA1c levels, an important determinant of diabetes. Our approach can be viewed as a generalization of Dudbridge et al. (Nat. Comm. 10: 1561), who developed a technique to adjust for index event bias when uncovering genetic predictors of disease progression based on case-only data. Our work serves to clarify that in any one sample MR analysis, it can be advantageous to estimate causal relationships by artificially inducing and then correcting for collider bias.

Collider bias in administrative workers’ compensation claims data: A challenge for cross-jurisdictional research

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 and confound 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 on simulated data showed left-censoring can also 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 collider bias affects interpretation of results.

Collider and Reporting Biases Involved in the Analyses of Cause of Death Associations in Death Certificates: an Illustration with Cancer and Suicide

Background: Data 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). Methods: We aimed to assess to what extent associations of causes of death estimated from individual mortality data can be extrapolated to the general population. 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). Results: 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. 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 death certificates. If these biases cannot be corrected, results from these analyses should not be extrapolated to the general population.

Older biological age is associated with adverse COVID-19 outcomes: A cohort study in UK Biobank

Background: Older chronological age is the most powerful risk factor for adverse coronavirus disease-19 (COVID-19) outcomes. It is uncertain, however, whether older biological age, as assessed by leucocyte telomere length (LTL), is also associated with COVID-19 outcomes. Methods: We associated LTL values obtained from participants recruited into UK Biobank (UKB) during 2006-2010 with adverse COVID-19 outcomes recorded by 30 November 2020, defined as a composite of any of the following: hospital admission, need for critical care, respiratory support, or mortality. Using information on 131 LTL-associated genetic variants, we conducted exploratory Mendelian randomisation (MR) analyses in UKB to evaluate whether observational associations might reflect cause-and-effect relationships. Findings: Of 6,775 participants in UKB who had tested positive for infection with SARS-CoV-2 in the community, there were 914 (13.5%) with adverse COVID-19 outcomes. The odds ratio (OR) for adverse COVID-19 outcomes was 1.17 (95% CI 1.05-1.31; P=0.004) per 1-SD shorter usual LTL, after adjustment for chronological age, sex and ethnicity. Similar ORs were observed in analyses that: adjusted for additional risk factors; disaggregated the composite outcome and reduced the scope for selection or collider bias. In MR analyses, the OR for adverse COVID-19 outcomes was directionally concordant but non-significant. Interpretation: Shorter LTL, indicative of older biological age, is associated with higher risk of adverse COVID-19 outcomes, independent of several major risk factors for COVID-19 including chronological age. Further data are needed to determine whether this association reflects causality.

Lung function & cardiovascular disease. A Two Sample Mendelian Randomisation Study

BackgroundObservational studies suggest an association between reduced lung function and risk of coronary artery disease and ischaemic stroke, independent of shared cardiovascular risk factors such as cigarette smoking. We use the latest genetic epidemiological methods to determine if impaired lung function is causally associated with an increased risk of cardiovascular disease.Methods and FindingsMendelian Randomisation uses genetic variants as instrumental variables to investigate causation. Preliminary analysis used two sample Mendelian Randomisation with lung function single nucleotide polymorphisms. To avoid collider bias the main analysis used single nucleotide polymorphisms for lung function identified from UKBiobank in a Multivariable Mendelian Randomisation model conditioning for height, body mass index and smoking.Multivariable Mendelian Randomisation shows strong evidence that reduced FVC causes increased risk of coronary artery disease, Odds Ratio:1·32 (1·19–1·46) per Standard Deviation. Reduced FEV1 is unlikely to be cause increased risk of coronary artery disease as evidence of its effect becomes weak after conditioning for height 1·08 (0·89, 1·30). There is weak evidence that reduced lung function increases risk of ischaemic stroke.ConclusionThere is strong evidence that reduced FVC is independently and causally associated with coronary artery disease. Although the mechanism remains unclear, FVC could be taken into consideration when assessing cardiovascular risk and considered a potential target for reducing cardiovascular events. FEV1 and airflow obstruction do not appear to cause increased cardiovascular events, confounding and collider bias may explain previous findings of a causal association.