Background
Uncertainty quantification is central to evidence synthesis for risk assessment and policy-making. Frequentist meta-analysis - currently predominant in epidemiology - quantifies uncertainty through confidence intervals, while Bayesian meta-analysis provides posterior distributions. We performed frequentist and Bayesian meta-analyses to compare uncertainty quantification and applicability for risk assessment using lead exposure and children’s IQ as a case study.
Methods
We systematically searched PubMed and Scopus for epidemiological studies on blood lead level (BLL) and IQ score in children. After screening, risk of bias (RoB) in the identified studies was assessed and regression coefficients were harmonised to the scale. In both meta-analyses, we included the same effect estimates, assumed a multilevel structure and used random-effects models. The Bayesian meta-analysis employed a hierarchical model with weakly-informative priors. Sensitivity analyses examined robustness to RoB and prior specification. r2 and I2 were estimated as measures of between-study heterogeneity.
Results
Twelve studies were included in the meta-analysis. The frequentist model yielded a pooled estimate of -2.45 (95% confidence interval: -3.82 to -1.08) IQ points per unit increase in log e-transformed BLL (µg/dL) and a 95% predictive interval of -6.53 to 1.53. The Bayesian model yielded a mean pooled estimate of -2.28 (95% credible interval: -3.54 to -1.04) and a 95% predictive interval of -6.28 to 1.69. Between-study heterogeneity was substantial (frequentist: r2 = 3.32, I2 = 85.0%; Bayesian: posterior median r2 = 3.26, I2 = 84.7%). The Bayesian approach provided a full posterior distribution for heterogeneity, directly quantifying uncertainty from between-study variation. Sensitivity analyses showed both meta-analyses were robust to RoB, and Bayesian estimates were insensitive to tested priors. Depending on the specified prior configuration, the Bayesian model was less sensitive to studies reporting substantial uncertainty, resulting in a lower pooled effect compared to the frequentist model. This regularisation is particularly valuable in small meta-analyses, where frequentist heterogeneity estimates can be unstable.
Conclusions
We provide updated pooled estimates for the effect of lead on children’s IQ. The Bayesian framework provides posterior distributions, enabling direct probability statements, e.g. about exceeding risk thresholds, and comparative assessments between pollutants. These features are particularly valuable for risk assessment and policy-making.
Four different age-depth models have been calculated for a new sediment profile (HZM19) from Holzmaar (425 m a.s.l., 50°7'8'' N, 6°52' 45'' E) using Bayesian statistics with Bacon (version 4.1.1) for the R programming language and the latest radiocarbon calibration curve Intcal20. Model A is based on previously published radiocarbon measurements only, while the three Models B, C and D integrate the previously published varve chronology (VT-99) applying different approaches. Model B rests upon radiocarbon data, while parameter settings are derived from sedimentation rates of VT-99. Model C is based on radiocarbon dates and on VT-99 as normal-distributed tie-points. Model D is segmented into four sections: Sections 1 and 3 are based on VT-99, whereas Sections 2 and 4 are based on Bacon models including additional information from VT-99. All models cover an age range of approx. 16,000 years for a composite depth of 14.6 m. The varve chronology was transferred to HZM19 using 43 predefined marker layers and 41 radiocarbon sampling positions with their specific VT-99 age and error. In addition, Pb-210 and Cs-137 activities (61 samples with a thickness of 2 cm each) have been measured for the top of HZM19. With this exercise, VT-99 was updated and efficiently applied to HZM19 providing a very precise age-depth model for these new sediment cores, which will value all ongoing and high-resolution investigations for a better understanding of decadal Holocene environmental and climatic variabilities.