Biases incurred from non-random repeat testing of haemoglobin levels in blood donors. Selective testing and its implications

To help prevent anaemia, it is a requisite for blood donors to undergo a haemoglobin test to ensure levels are not too low before donation. It is therefore important to have an accurate testing device and strategy to ensure donors are not being inappropriately bled. A recent study in blood donors used a selective testing strategy where if a donor's haemoglobin level is below the level required for donation, then another reading is taken and if this occurs again, a third and final reading is used. This strategy can reduce the average number of readings required per donor compared to taking three measurements for all donors. However, the final decision‐making measurement will on average be higher than a single measurement. In this paper, a selective testing strategy is compared against other strategies. Individual‐level biases are derived for the selective strategy and are shown to depend on how close a donor's true haemoglobin level is to the donation threshold and the magnitude of error in the testing device. A simulation study was conducted using the distribution of haemoglobin levels from a large donor population to investigate the effects different strategies have on population performance. We consider scenarios based on varying the measurement device bias and error, including differential biases that depend on the underlying haemoglobin level. Discriminatory performance is shown to be affected when using the selective testing strategies, especially when measurement error is large and when differential bias is present in the device. We recommend that the average of a number of readings should be used in preference to selective testing strategies if multiple measurements are available

Log odds ratio and 95% confidence intervals for Alzheimer’s per 1 standard deviation increase in low-density lipoprotein cholesterol for different values of the tuning parameter (λ = 0.1, 0.2, …, 4.9, 5.0, 5.2, 5.4, …, 9.8, 10.0) included in the Lasso regression model.

The number of genetic variants included in the IVW models are also displayed. The dotted line at λ = 3.4 is the value of the tuning parameter chosen by the heterogeneity stopping rule. The dashed line at λ = 4.00 is the value chosen by cross-validation.</p

Mean estimate (mean standard error), standard deviation, coverage of the 95% confidence interval (%), and power at the 5% significance level (%) of the estimates from the IVW model with: 1) the <i>J</i> genetic variants (IVW); 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights for Scenario 1 with a null (<i>θ</i> = 0) or positive (<i>θ</i> = 0.3) causal effect.

Results from Lasso penalization with the heterogeneity stopping rule, simple (unweighted) median, weighted median and MR-Egger methods are also provided.</p

Robust methods in Mendelian randomization via penalization of heterogeneous causal estimates.

Methods have been developed for Mendelian randomization that can obtain consistent causal estimates under weaker assumptions than the standard instrumental variable assumptions. The median-based estimator and MR-Egger are examples of such methods. However, these methods can be sensitive to genetic variants with heterogeneous causal estimates. Such heterogeneity may arise from over-dispersion in the causal estimates, or specific variants with outlying causal estimates. In this paper, we develop three extensions to robust methods for Mendelian randomization with summarized data: 1) robust regression (MM-estimation); 2) penalized weights; and 3) Lasso penalization. Methods using these approaches are considered in two applied examples: one where there is evidence of over-dispersion in the causal estimates (the causal effect of body mass index on schizophrenia risk), and the other containing outliers (the causal effect of low-density lipoprotein cholesterol on Alzheimer's disease risk). Through an extensive simulation study, we demonstrate that robust regression applied to the inverse-variance weighted method with penalized weights is a worthwhile additional sensitivity analysis for Mendelian randomization to provide robustness to variants with outlying causal estimates. The results from the applied examples and simulation study highlight the importance of using methods that make different assumptions to assess the robustness of findings from Mendelian randomization investigations with multiple genetic variants

Causal directed acyclic graph illustrating the instrumental variable assumptions for the instrumental variable <i>G</i>, exposure <i>X</i>, outcome <i>Y</i>, and the set of variables (<i>U</i>) that confound the association between <i>X</i> and <i>Y</i>.

Causal directed acyclic graph illustrating the instrumental variable assumptions for the instrumental variable G, exposure X, outcome Y, and the set of variables (U) that confound the association between X and Y.</p

Mean estimate (mean standard error), standard deviation, coverage of the 95% confidence interval (%), and power at the 5% significance level (%) of the estimates from the IVW model with: 1) the <i>J</i> genetic variants (IVW); 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights (R and P) for Scenarios 2-4 with a null causal effect (<i>θ</i> = 0) by the number of invalid IVs.

Results from Lasso penalization with the heterogeneity stopping rule, simple median, weighted median and MR-Egger methods are also provided.</p

Decomposition of the association between the genetic variant <i>G</i>_<i>j</i> and the outcome <i>Y</i> into the indirect effect via the risk factor <i>X</i> and direct (pleiotropic) effect <i>α</i>_<i>j</i>.

Decomposition of the association between the genetic variant Gj and the outcome Y into the indirect effect via the risk factor X and direct (pleiotropic) effect αj.</p

Results from the simulation study when 100 genetic variants were simulated for 1 000 datasets.

Mean estimate (mean standard error), standard deviation, coverage of the 95% confidence interval (%), and power at the 5% significance level (%) of the estimates from the IVW model with: 1) the J genetic variants (IVW); 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights (R and P) for Scenarios 2-4 with a null causal effect (θ = 0) and positive causal effect (θ = 0.3) by the number of invalid instrumental variables. Results from the Lasso penalization method with the heterogeneity stopping rule are also presented.</p

Estimates (standard errors) and 95% confidence intervals of the causal effect of body mass index on schizophrenia risk (log odds ratio for schizophrenia per 1 standard deviation increase in body mass index) and low-density lipoprotein cholesterol on Alzheimer’s disease risk (log odds ratio for Alzheimer’s per 1 standard deviation increase in low-density lipoprotein cholesterol) from the IVW method with: 1) the full set of genetic variants (IVW); 2) robust regression; 3) penalized weights; and 4) robust regression and penalized weights.

Results from Lasso penalization with the heterogeneity stopping rule and cross-validation, simple median, weighted median and MR-Egger methods are also presented.</p

Causal directed acyclic graph used in the data generating model for the simulation study.

U represents the set of variables that confound the association between the risk factor X and outcome Y. The genetic effect of Gj on X is , the direct (pleiotropic) effect of Gj on Y is αj, the effect of Gj on U is ϕj, and the causal effect of X on Y is θ.</p