Nonrandom selection in one-sample Mendelian Randomization (MR) results in biased estimates and inflated type I error rates only when the selection effects are sufficiently large. In two-sample MR, the different selection mechanisms in two samples may more seriously affect the causal effect estimation. Firstly, we propose sufficient conditions for causal effect invariance under different selection mechanisms using two-sample MR methods. In the simulation study, we consider 49 possible selection mechanisms in two-sample MR, which depend on genetic variants (G), exposures (X), outcomes (Y) and their combination. We further compare eight pleiotropy-robust methods under different selection mechanisms. Results of simulation reveal that nonrandom selection in sample II has a larger influence on biases and type I error rates than those in sample I. Furthermore, selections depending on X+Y, G+Y, or G+X+Y in sample II lead to larger biases than other selection mechanisms. Notably, when selection depends on Y, bias of causal estimation for non-zero causal effect is larger than that for null causal effect. Especially, the mode based estimate has the largest standard errors among the eight methods. In the absence of pleiotropy, selections depending on Y or G in sample II show nearly unbiased causal effect estimations when the casual effect is null. In the scenarios of balanced pleiotropy, all eight MR methods, especially MR-Egger, demonstrate large biases because the nonrandom selections result in the violation of the Instrument Strength Independent of Direct Effect (InSIDE) assumption. When directional pleiotropy exists, nonrandom selections have a severe impact on the eight MR methods. Application demonstrates that the nonrandom selection in sample II (coronary heart disease patients) can magnify the causal effect estimation of obesity on HbA1c levels. In conclusion, nonrandom selection in two-sample MR exacerbates the bias of causal effect estimation for pleiotropy-robust MR methods.

Purpose We aimed to investigate whether obtaining a higher level of education was causally associated with lower breast cancer risk and to identify the causal mechanism linking them. Methods The main data analysis used publicly available summary-level data from 2 large genome-wide association study consortia. Mendelian randomization (MR) analysis used 65 genetic variants derived from the Social Science Genetic Association Consortium as instrumental variables for years of schooling. The outcomes from the Breast Cancer Association Consortium (BCAC) were the overall breast cancer risk (122,977 cases/105,974 controls in women) and the two subtypes: estrogen receptor (ER)-positive breast cancer and ER-negative breast cancer. Fixed and random effects inverse variance weighted methods were used to estimate the causal effects, along with other additional MR methods for sensitivity analyses. Results Results showed that each additional standard deviation of 4.2 years of education was causally associated with a 27% lower risk of ER-negative breast cancer (odds ratio, 0.73; 95% confidence interval, 0.64–0.84; p -value < 0.001). This finding was consistent with the results of the sensitivity analyses. Physical activities can help improve the protective effect of education against breast cancer, with relatively large mediation proportions. Education increases the risk of ER-positive breast cancer due to alterations in high-density lipoprotein level, triglyceride level, height, waist-to-hip ratio, body mass index, and smoking status, with relative medium mediation proportions. Other mediators including low-density lipoprotein, hip circumference, number of cigarettes smoked per day, time spent performing light physical activity, and performing vigorous physical activity for > 10 minutes explain a small part of the causal effect of education on the risk of developing breast cancer, and their mediation proportion is approximately 1%. Conclusion A low level of education is a causal risk factor in the development of breast cancer as it is associated with poor lipid profile, obesity, smoking, and types of physical activity.

Background: Controlling unobserved confounding still remains a great challenge in observational studies, and a series of strict assumptions of the existing methods usually may be violated in practice. Therefore, it is urgent to put forward a novel method. Methods: We are interested in the causal effect of an exposure on the outcome, which is always confounded by unobserved confounding. We show that, the causal effect of an exposure on a continuous or categorical outcome is nonparametrically identified through only two independent or correlated available confounders satisfying a nonlinear condition on the exposure. Asymptotic theory and variance estimators are developed for each case. We also discuss an extension for more than two binary confounders. Results: The simulations show better estimation performance by our approach in contrast to the traditional regression approach adjusting for observed confounders. A real application is separately applied to assess the effects of Body Mass Index (BMI) on Systolic Blood Pressure (SBP), Diastolic Blood Pressure (DBP), Fasting Blood Glucose (FBG), Triglyceride (TG), Total Cholesterol (TC), High Density Lipoprotein (HDL) and Low Density Lipoprotein (LDL) with individuals in Shandong Province, China. Our results suggest that SBP increased 1.60 (95% CI: 0.99-2.93) mmol/L with per 1-kg/m 2 higher BMI and DBP increased 0.37 (95% CI: 0.03-0.76) mmol/L with per 1-kg/m 2 higher BMI. Moreover, 1-kg/m 2 increase in BMI was causally associated with a 1.61 (95% CI: 0.96-2.97) mmol/L increase in TC, a 1.66 (95% CI: 0.91-55.30) mmol/L increase in TG and a 2.01 (95% CI: 1.09-4.31) mmol/L increase in LDL. However, BMI was not causally associated with HDL with effect value − 0.20 (95% CI: − 1.71-1.44). And, the effect value of FBG per 1-kg/m 2 higher BMI was 0.56 (95% CI: − 0.24-2.18). Conclusions: We propose a novel method to control unobserved confounders through double binary confounders satisfying a non-linear condition on the exposure which is easy to access.

Background: Biological pathways play an important role in the occurrence, development and recovery of complex diseases, such as cancers, which are multifactorial complex diseases that are generally caused by mutation of multiple genes or dysregulation of pathways. Results: We propose a path-specific effect statistic (PSE) to detect the differential specific paths under two conditions (e.g. case VS. control groups, exposure Vs. nonexposure groups). In observational studies, the pathspecific effect can be obtained by separately calculating the average causal effect of each directed edge through adjusting for the parent nodes of nodes in the specific path and multiplying them under each condition. Theoretical proofs and a series of simulations are conducted to validate the path-specific effect statistic. Applications are also performed to evaluate its practical performances. A series of simulation studies show that the Type I error rates of PSE with Permutation tests are more stable at the nominal level 0.05 and can accurately detect the differential specific paths when comparing with other methods. Specifically, the power reveals an increasing trends with the enlargement of path-specific effects and its effect differences under two conditions. Besides, the power of PSE is robust to the variation of parent or child node of the nodes on specific paths. Application to real data of Glioblastoma Multiforme (GBM), we successfully identified 14 positive specific pathways in mTOR pathway contributing to survival time of patients with GBM. All codes for automatic searching specific paths linking two continuous variables and adjusting set as well as PSE statistic can be found in supplementary materials. Conclusion: The proposed PSE statistic can accurately detect the differential specific pathways contributing to complex disease and thus potentially provides new insights and ways to unlock the black box of disease mechanisms.

Background: Dietary habit plays an important role in the composition and function of gut microbiota which possibly manipulates host eating behavior. Gut microflora and nutritional imbalance are associated with telomere length (TL). However, the causality among them remains unclear. Methods: Firstly, we calculate the significance threshold based on genetic correlations. Then we perform bi-directional Mendelian Randomization (MR) analyses among 82 food intakes (FIs) (UK Biobank, N=455,146), 95 gut microbial traits (Flemish Gut Flora Project, N=2,223) and TL (genome-wide meta-analysis from 15 cohorts, N=37,684) using summary-level data from large genome-wide association studies. Fixed-effect inverse variance weighting is the main analysis method and the other eight two-sample MR methods and three sensitivity analyses are performed. Finally, GO enrichment analyses are used to investigate the bio-function. Results: Several bi-directional causal relationships among gut microbiota, FIs and TL are obtained by two-sample MR. Overall, we find suggestive evidence of three main causal pathways among them. Drinking more glasses of water per day is able to affect the habit of eating dried fruit through the host gut microbiota (Barnesiella). The change of one gut microbiota taxon (Collinsella) in the host causally influences another gut microbiota taxon (Lactonccus) through the diet habits (intake of oil-based spread). Additionally, the TL alters the habits of drinking ground coffee and further affects the gut microbiota (Acidaminococcaceae). GO enrichment analysis further confirmed the MR results. Conclusion: TL has an impact on diet habits and gut microbiota and there are bi-directional relationships between diet habits and gut microbiota.