Selection Bias

The UK Biobank cohort is a population-based cohort of 500,000 participants recruited in the United Kingdom (UK) between 2006 and 2010. Approximately 9.2 million individuals aged 40-69 years who lived within 25 miles (40 km) of one of 22 assessment centers in England, Wales, and Scotland were invited to enter the cohort, and 5.5% participated in the baseline assessment. The representativeness of the UK Biobank cohort was investigated by comparing demographic characteristics between nonresponders and responders. Sociodemographic, physical, lifestyle, and health-related characteristics of the cohort were compared with nationally representative data sources. UK Biobank participants were more likely to be older, to be female, and to live in less socioeconomically deprived areas than nonparticipants. Compared with the general population, participants were less likely to be obese, to smoke, and to drink alcohol on a daily basis and had fewer self-reported health conditions. At age 70-74 years, rates of all-cause mortality and total cancer incidence were 46.2% and 11.8% lower, respectively, in men and 55.5% and 18.1% lower, respectively, in women than in the general population of the same age. UK Biobank is not representative of the sampling population; there is evidence of a "healthy volunteer" selection bias. Nonetheless, valid assessment of exposure-disease relationships may be widely generalizable and does not require participants to be representative of the population at large.

Propensity-score matching allows one to reduce the effects of treatment-selection bias or confounding when estimating the effects of treatments when using observational data. Some authors have suggested that methods of inference appropriate for independent samples can be used for assessing the statistical significance of treatment effects when using propensity-score matching. Indeed, many authors in the applied medical literature use methods for independent samples when making inferences about treatment effects using propensity-score matched samples. Dichotomous outcomes are common in healthcare research. In this study, we used Monte Carlo simulations to examine the effect on inferences about risk differences (or absolute risk reductions) when statistical methods for independent samples are used compared with when statistical methods for paired samples are used in propensity-score matched samples. We found that compared with using methods for independent samples, the use of methods for paired samples resulted in: (i) empirical type I error rates that were closer to the advertised rate; (ii) empirical coverage rates of 95 per cent confidence intervals that were closer to the advertised rate; (iii) narrower 95 per cent confidence intervals; and (iv) estimated standard errors that more closely reflected the sampling variability of the estimated risk difference. Differences between the empirical and advertised performance of methods for independent samples were greater when the treatment-selection process was stronger compared with when treatment-selection process was weaker. We recommend using statistical methods for paired samples when using propensity-score matched samples for making inferences on the effect of treatment on the reduction in the probability of an event occurring.

BackgroundSelection 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.MethodsWe 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.ResultsSelection 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.ConclusionsSelection 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.

When analyzing a selected sample from a general population, selection bias can arise relative to the causal average treatment effect (ATE) for the general population, and also relative to the ATE for the selected sample itself. In this paper, we provide simple graphical rules that indicate (1) whether a selected-sample analysis will be unbiased for each ATE and (2) whether adjusting for certain covariates could eliminate selection bias. The rules can easily be checked in a standard single-world intervention graph. When the treatment could affect selection, a third estimand of potential scientific interest is the "net treatment difference"-namely the net change in outcomes that would occur for the selected sample if all members of the general population were treated versus not treated, including any effects of the treatment on which individuals are in the selected sample. We provide graphical rules for this estimand as well. We decompose bias in a selected-sample analysis relative to the general-population ATE into (1) "internal bias" relative to the net treatment difference and (2) "net-external bias," a discrepancy between the net treatment difference and the general-population ATE. Each bias can be assessed unambiguously via a distinct graphical rule, providing new conceptual insight into the mechanisms by which certain causal structures produce selection bias.