A Multivariable Mendelian Randomization Method for Inferring the Causal Relationship between Imaging and Phenotype

Abstract

The present invention discloses a multivariable Mendelian randomization method for inferring the causal relationship between images and phenotypes, including integrating genomic, radiomic, and phenomic data for causal inference between brain imaging feature metrics and phenotypes, considering the correlations of multiple brain imaging feature metrics in the causal inference and correcting possible biases, specifically including the following steps: S1: Obtain initial instrumental variables, risk factor variables, and phenotypes; S2: Bias correction, screening the initial instrumental variables and risk factor variables; S3: Use a two-stage method to infer the causal relationship and screen out the brain imaging feature metrics that have a causal relationship with the phenotype; S4: Use Sargan for horizontal pleiotropy test to check whether the part of the said phenotype that cannot be explained by the risk factor is significantly correlated with the initial instrumental variable. Compared with traditional methods, the present invention can obtain more accurate causal effect estimates, and the type I error rate of the selected risk factors is lower.

Description

Technical Field

[0001] The present invention relates to the technical field of biomedical engineering and applied mathematics, and particularly relates to a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes. Background Art

[0002] Mendelian randomization provides a method to infer the causal relationship between risk factors and outcome variables by using genetic data as instrumental variables. Effective Mendelian randomization is based on a series of premise assumptions: (1) each genetic variant (usually single nucleotide polymorphism SNP) must be strongly correlated with the risk factor; (2) the genetic variant cannot be associated with any confounding factors in the risk factor-outcome variable relationship; (3) the genetic variant cannot be associated with the outcome variable through any pathway other than the risk factor. Among them, assumption (1) is relatively easy to verify, while assumptions (2) and (3) are difficult to verify because due to the existence of linkage disequilibrium (LD), the same SNP may be significantly correlated with a large number of traits, resulting in a large number of confounding factors in the Mendelian randomization analysis, and leading to extensive pleiotropy of the SNP on the outcome variable.

[0003] The brain is the most important part of the human body and is intricately linked to our complex neural, psychological, and behavioral characteristics. At the same time, in recent years, large-scale comprehensive multi-omics databases have grown explosively, such as the ABCD database with a sample size of more than 10,000 adolescents, the ADNI database with about 3,800 Alzheimer's disease samples, the CHARGE database with a sample size of more than 20,000, and the UK BioBank database with a total sample size of more than 500,000. These databases contain genomic, imaging, and other multiple phenotypic data of participants on a scale of 1,000 or 10,000, enabling us to study the relationships between different brain regions and diseases / behaviors based on the data of the same large sample population.

[0004] Brain function relies on effective communication between different brain regions, resulting in strong correlations between these regions at the structural, functional, and genetic levels. Currently, many researchers in related fields are using Mendelian randomization to study the causal relationship between the brain and various disease pathologies. However, genetic variants may affect outcomes through multiple interconnected brain regions, i.e., horizontal pleiotropy. Therefore, compared to Mendelian randomization, which uses a single brain imaging trait as a risk factor, it is more reasonable to use multiple brain imaging traits as risk factors for modeling simultaneously, i.e., multivariate Mendelian randomization. Multivariate Mendelian randomization is an extension of standard (univariate) Mendelian randomization, allowing for the simultaneous modeling of multiple risk factors. Univariate MR assumes that genetic variants influence a single risk factor, while multivariate MR assumes that genetic variants influence a set of multiple measured risk factors, thereby accounting for measured pleiotropy. Existing multivariate MR methods are designed for a small number of risk factors, two samples, or by combining multiple risk factors into a single indicator through dimensionality reduction techniques. During the specific analysis process, multiple risk factors may be biased due to excessive correlations. Therefore, we seek to develop a method based on single-sample multivariate MR that can select causal risk factors from a large number of correlated or highly correlated candidate risk factors and correct the bias caused by selecting instrumental variables from imaging GWAS data. Summary of the Invention

[0005] The purpose of the present invention is to provide a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes, and to solve the following technical problems:

[0006] Based on the single-sample multivariate Mendelian randomization (MR) framework, risk factors can be selected from a large number of correlated or highly correlated candidate risk factors to estimate the causal effect value.

[0007] The purpose of the present invention can be achieved through the following technical solutions:

[0008] A multivariate Mendelian randomization method for inferring causal relationships between imaging and phenotypes integrates genomic, imaging, and phenotypic data for causal inference between brain imaging feature indicators and phenotypes. The method incorporates the correlation between multiple brain imaging feature indicators into the causal inference and corrects for possible biases. The method specifically includes the following steps:

[0009] S1: Obtain initial instrumental variables, risk factor variables, and phenotypes, where the risk factor variables are brain imaging characteristic indicators, and the phenotypes are behaviors or diseases of the outcome variables;

[0010] S2: bias correction, screening of initial instrumental variables and risk factor variables;

[0011] S3: Infer the causal relationship using a two-stage method, and screen out the brain imaging feature indicators that have a causal relationship with the phenotype;

[0012] S4: Use Sargan to perform a pleiotropy test to check whether the part of the said phenotype that cannot be explained by the risk factors is significantly correlated with the initial instrumental variable.

[0013] As a further solution of the present invention: The specific methods for obtaining the initial instrumental variable and the risk factor variable in the step S1 include the following steps:

[0014] S11: Select the target brain imaging feature indicators as risk factors;

[0015] S12: Select the SNPs that are significantly correlated with at least one brain imaging feature indicator as the initial instrumental variables;

[0016] S13: Select the brain imaging feature indicators that are significantly correlated with at least one initial instrumental variable as the risk factor variables.

[0017] As a further solution of the present invention: The specific method for bias correction in the step S2 is:

[0018] S21: Given the P1 value of the SNP as the initial instrumental variable and the risk factor, and convert the P1 value into a t value: |t| = φ -1 (1 - p / 2);

[0019] S22: Shrink the t value, where when the selected threshold cutoff is stricter or the sample size N is larger, the correction intensity is lower: where C is the correction parameter, c = 20;

[0020] S23: Convert the corrected t value into a P value: P corrected = 2*(1 - φ(|t corrected |)).

[0021] As a further solution of the present invention: The step S2 further includes a secondary correction, and the specific steps are as follows:

[0022] S24: Judge whether the converted P value is less than the given threshold, that is, p corrected < cutoff, if the P value is greater than or equal to the given threshold, then discard the converted P value and enter step S25;

[0023] S25: Rescreen the risk factors included in the model, and use the brain imaging feature indicators that are significantly correlated with at least one initial instrumental variable as the risk factor variables, and repeat steps S21 - S23.

[0024] As a further solution of the present invention: in the step S3, it specifically includes:

[0025] S31: Extract data from the database according to the initial instrumental variable, risk factor variable and phenotype, perform data preprocessing and generate a genotype matrix, a brain imaging matrix and a phenotype vector;

[0026] S32: For the preprocessed genotype matrix, brain imaging matrix and phenotype vector, in the first stage, first use the partial least squares method to regress the genotype matrix G and the brain imaging matrix X, and use ten-fold cross-validation to select the optimal parameters: X = GC + E, and predict the fitted brain imaging matrix where represents the part of the brain imaging feature index explained by genes;

[0027] S33: In the second stage, use the Lasso regression algorithm to perform feature screening on the phenotype vector and the brain imaging matrix predicted in the first stage, and fit the causal effect of each brain imaging feature index Xk and the phenotype y:

[0028]

[0029] where β k (1 ≤ k ≤ K) is the coefficient fitted by the Lasso regression, and ε is the regression error obeying the normal distribution;

[0030] And use the desparsified Lasso method to calculate the P2 value for correcting the bias of the causal effect fitted value, then the brain imaging feature index having a causal relationship with the phenotype can be selected according to the desparsified Lasso P2 value corresponding to the selected imaging feature.

[0031] As a further solution of the present invention: in the step S4, the method for horizontal pleiotropy test specifically includes:

[0032] S41: Use the Sargan test to judge whether the part of the phenotype that cannot be explained by the risk factor is significantly correlated with the SNP used as the initial instrumental variable;

[0033] S42: If the p value of the Sargan test is greater than 0.1, then the part of the phenotype that cannot be explained by the risk factor is not related to the SNP used as the initial instrumental variable.

[0034] As a further solution of the present invention: if the p value of the Sargan test is less than or equal to 0.1, then the part of the phenotype that cannot be explained by the risk factor is related to the SNP used as the initial instrumental variable.

[0035] As a further solution of the present invention: the data preprocessing includes quality control, normalization, and imputation of missing values.

[0036] The present invention proposes a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes. This method is based on a single-sample multivariate Mendelian randomization framework, which can select risk factors with causal relationships from a large number of candidate risk factors and estimate the causal effect. The advantages of the present invention are as follows:

[0037] (1) The present invention takes into account the usually existing correlations between brain imaging feature indicators in the model, and can better estimate the causal relationship of each brain imaging feature indicator on behavior / disease;

[0038] (2) Due to the high genetic correlations between brain imaging feature indicators, based on the multivariate framework, it can better control the horizontal pleiotropy of instrumental variables on the outcome variables;

[0039] (3) The present invention corrects the "winner's curse" bias that usually appears in single-sample Mendelian randomization, effectively improving the accuracy of causal effect estimation. We evaluated the performance of the method we proposed in a simulation study and found that our method can obtain more accurate causal effect estimates, and the type I error rate of the selected risk factors is lower. Description of the Drawings

[0040] The present invention will be further described below with reference to the drawings.

[0041] Figure 1 is a schematic flowchart of a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes according to the present invention;

[0042] Figure 2 is a statistical comparison table of the effects of a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes according to the present invention;

[0043] Figure 3 is a schematic overall framework diagram of a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes according to the present invention;

[0044] Figure 4 is the mean square error situation before and after the correction of the "winner's curse" bias (WCC = 20) under different parameter settings in a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes according to the present invention;

[0045] Figure 5 is a schematic application diagram of a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes according to the present invention in the large database UK Biobank.

[0046] Figure 6Schematic diagram of some cases discovered after applying a multivariate Mendelian randomization method for inferring causal relationships between images and phenotypes in the large database UK Biobank. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] like Figure 1 and Figure 2 As shown, the present invention is a multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes, integrating genome, imaging group and phenotype group data for causal inference between brain imaging feature indicators and phenotypes, taking the correlation of multiple brain imaging feature indicators into account in causal inference and correcting for possible biases, and specifically comprising the following steps:

[0049] S1: Obtain the initial instrumental variable (SNP), risk factor variable and phenotype, wherein the risk factor variable is a brain imaging characteristic indicator, and the phenotype is a behavior or disease of the outcome variable;

[0050] S11: Based on the type of brain imaging characteristic indicators (such as white matter fiber tracts) that you want to study as risk factors, select a previous large-scale genome-wide association study (GWAS) study results for subsequent instrumental variable selection;

[0051] S12: Select SNPs that are significantly correlated with at least one brain imaging feature index (the p-value is less than a given threshold cutoff, usually a genome-wide significance level of 5e-8) as initial instrumental variables;

[0052] S13: Select brain imaging characteristic indicators that are significantly correlated with at least one initial instrumental variable as risk factor variables;

[0053] S2: bias correction, screening of initial instrumental variables and risk factor variables;

[0054] like Figure 3As shown, without correction represents the mean square error before correction, withoutcorrection (c=20) represents the mean square error after correction, and the horizontal axis represents different SNP screening thresholds cutoff. The "winner's curse" bias refers to the phenomenon that the association level between SNP and phenotype is overestimated in the data set. If the GWAS data for selecting instrumental variables and the data used for Mendelian randomization are the same data, then the "winner's curse" bias may occur. Here, a lasso-type correction method is used to correct the GWAS statistic t of the initial instrumental variable SNP, and the t value and p value of each SNP after correction are calculated. This can be done in the following three steps:

[0055] S21: Given the P1 value of the SNP and risk factor as the initial instrumental variable, convert the P1 value into a t value: |t| = φ -1 (1-p / 2);

[0056] S22: Shrink the t value. The stricter the cutoff or the larger the sample size N, the lower the correction strength. Where C is the correction parameter, c = 20;

[0057] S23: Convert the corrected t value into a P value: P corrected =2*(1-φ(|t corrected |)).

[0058] The step S2 also includes a secondary correction, and the specific steps are as follows:

[0059] S24: Determine whether the converted P value is less than a given threshold, that is, p corrected <cutoff, if the P value is greater than or equal to the given threshold, the converted P value is discarded and the process goes to step S25;

[0060] S25: Rescreen the risk factors included in the model, and use the brain imaging characteristic indicators that are significantly correlated with at least one initial instrumental variable as risk factor variables, and repeat steps S21-S23;

[0061] S3: Use a two-stage approach to infer causal relationships and screen out brain imaging feature indicators that have a causal relationship with the phenotype;

[0062] Specifically include:

[0063] S31: Extract data from the database based on the initial instrumental variables SNP, risk factor variables and phenotypes (behavior / disease of outcome variables), perform data preprocessing and generate genotype matrix, brain imaging matrix and phenotype vector;

[0064] S32: For the preprocessed genotype matrix, brain imaging matrix, and phenotype vector, in the first stage, the partial least squares method is first used to perform regression on the genotype matrix G and the brain imaging matrix X. Ten-fold cross-validation is adopted to select the optimal parameters: X = C·G + E, and the fitted brain imaging matrix is predicted. represents the part of the brain imaging feature index explained by genes;

[0065] S33: In the second stage, the phenotype vector and the brain imaging matrix predicted in the first stage are used with the Lasso regression algorithm for feature screening, and the causal effect of each brain imaging feature index Xk on the phenotype y is fitted:

[0066]

[0067] And the desparsified Lasso method is used to calculate the P2 value for bias correction of the causal effect fitted value. Then, the brain imaging feature indexes causally related to the phenotype can be selected according to the desparsified Lasso P2 values corresponding to the screened imaging features;

[0068] S4: Use Sargan for horizontal pleiotropy test to check whether the part of the said phenotype that cannot be explained by risk factors is significantly correlated with the initial instrumental variable;

[0069] S41: Use the Sargan test to determine whether the part of the phenotype that cannot be explained by risk factors is significantly correlated with the SNP used as the initial instrumental variable;

[0070] S42: If the p-value of the Sargan test is not significant (such as greater than 0.1), then there is no horizontal pleiotropy of the initial instrumental variable on the phenotype, and the causal inference result is feasible.

[0071] A multivariate Mendelian randomization method for inferring the causal relationship between imaging and phenotype provided in this embodiment has an effect as Figure 1 shown, and its overall framework is as Figure 1 shown. It can be seen that the method of the present invention has the best prediction effect and the highest prediction accuracy in terms of the mean squared error of prediction for parameter settings in different simulated data sets compared with other methods. Moreover, the prediction accuracy can be further improved by the "winner's curse" bias correction (WCC = 20).

[0072] The results of the "winner's curse" bias correction (WCC = 20) in different parameter settings in this example are as Figure 3As shown. It can be seen that after correction, for different simulation parameter settings and different selected GWAS threshold cutoffs, the mean square error of the predicted values of the causal effect has been significantly reduced. This indicates that through this bias correction, the accuracy of the prediction of this Mendelian randomization method can be further improved for various parameter scenarios, demonstrating the wide applicability of this bias correction.

[0073] In another preferred embodiment of the present invention, the application in the large database UK Biobank is as Figure 4 and Figure 5 shown. This method performed causal inference on 36 white matter fiber bundles and 204 human health-related phenotypes (shown in a total of 11 categories) in the UK Biobank. Among them, Figure 4 specifically shows an overall situation of the number of brain white matter fiber bundle → phenotypes found to have a causal relationship using the method of this invention patent in different categories and the specific causal effect values. This invention patent found a total of 229 white matter fiber bundle → phenotype causal relationships. For example, the uncinate white matter fiber bundle has a positive causal relationship with fluid intelligence.

[0074] Figure 5 shows some meaningful cases in the analysis results. Including (1) white matter fiber bundles that have a significant causal relationship with smoking, and a corresponding potential biological causal relationship pathway: SNP rs208829 → the left posterior part of the internal capsule of the white matter fiber bundle (Left RLIC) → the potential biological causal relationship pathway of the smoking cessation age; (2) white matter fiber bundles that have a significant causal relationship with human fluid intelligence. And a corresponding potential biological causal relationship pathway: SNP rs200481589 → the right fornix of the white matter fiber bundle (R FXST) → the potential biological causal relationship pathway of fluid intelligence.

[0075] Figure 6In the figure, (A) shows white matter fiber tracts with a significant causal relationship with smoking; (B) shows a potential biological causal pathway: SNP rs208829 → left posterior lens capsule (Left RLIC) → age of smoking cessation; (C) shows white matter fiber tracts with a significant causal relationship with fluid intelligence. (D) shows a potential biological causal pathway: SNP rs200481589 → right fornix (R FXST) → fluid intelligence. Abbreviations: SFO R (right superior fronto-occipital fasciculus); RLIC L (left retrolenticular part of internal capsule); PTR L (left posterior thalamic radiation); EC (external capsule); UNC (uncinate fasciculus); SS (sagittal stratum); PCR R (posterior corona radiata); CGCR (right cingulum cingulate gyrus); FXST R (right fornix cres + striaterminalis); FX (fornix); PLIC L (left posterior limb of internal capsule).

[0076] The above is a detailed description of an embodiment of the present invention. However, the content described is only a preferred embodiment of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A multivariate Mendelian randomization method for inferring the causal relationship between images and phenotypes, characterized in that Integrate genomic, radiomic, and phenomic data for causal inference between brain imaging feature metrics and phenotypes, taking into account the correlations of multiple brain imaging feature metrics in causal inference and correcting for possible biases. The specific steps are as follows: S1: Obtain initial instrumental variables, risk factor variables, and phenotypes. The risk factor variables are brain imaging feature metrics, and the phenotypes are behaviors or diseases of outcome variables. S2: Bias correction. Screen the initial instrumental variables and risk factor variables. S3: Use a two-stage method to infer causal relationships and screen out brain imaging feature metrics that have causal relationships with phenotypes. S4: Use Sargan to conduct a horizontal pleiotropy test to check whether the part of the phenotype that cannot be explained by the risk factors is significantly correlated with the initial instrumental variables. The specific methods for obtaining the initial instrumental variables and risk factor variables in step S1 are as follows: S11: Select target brain imaging feature metrics as risk factors. S12: Select SNPs that are significantly correlated with at least one brain imaging feature metric as initial instrumental variables. S13: Select brain imaging feature metrics that are significantly correlated with at least one initial instrumental variable as risk factor variables. The specific method for bias correction in step S2 is: S21: Given the significance level P1 value of the SNP as the initial instrumental variable and the risk factor in the genome-wide association study, and convert the P1 value into a t value: , where is the distribution function of the standard normal distribution; S22: Shrink the t-value, where the stricter the selected threshold cutoff or the larger the sample size N, the lower the correction intensity: , where C is a correction parameter and c = 20; S23: Convert the corrected t-value into a P-value: ; In step S3, it specifically includes: S31: Extract data from the database according to the initial instrumental variables, risk factor variables, and phenotypes, perform data preprocessing, and generate a genotype matrix, a brain imaging matrix, and a phenotype vector. S32: For the pre-processed genotype matrix, brain imaging matrix, and phenotype vector, in the first stage, the partial least squares method is first used to perform regression on the genotype matrix G and the brain imaging matrix X, and ten-fold cross-validation is adopted to select the optimal parameters: , and predict the fitted brain imaging matrix , where represents the part of the brain imaging feature index explained by genes; S33: In the second stage, the phenotypic vector and the brain imaging matrix predicted in the first stage are used for feature screening by the Lasso regression algorithm, and the causal effect of each brain imaging feature index feature X k on the phenotype y: Among them, (1 ≤ k ≤ K) is the coefficient of the Lasso regression fit, is the regression error that follows a normal distribution; Use the desparsified Lasso method to calculate the P2 value for correcting the bias of the causal effect fitting value. Then, the brain imaging feature metrics that have causal relationships with phenotypes can be selected according to the desparsified Lasso P2 values corresponding to the screened brain imaging feature metrics.

2. The multivariate Mendelian randomization method for inferring the causal relationship between imaging and phenotype according to claim 1, characterized in that Step S2 also includes secondary correction. The specific steps are as follows: S24: Determine whether the converted P value is less than the given threshold, that is , if the P value is greater than or equal to the given threshold, discard the converted P value and proceed to step S25; S25: Rescreen the risk factors included in the model. Select brain imaging feature metrics that are significantly correlated with at least one initial instrumental variable as risk factor variables, and repeat steps S21 - S23.

3. A multivariable Mendelian randomization method for inferring the causal relationship between imaging and phenotype according to claim 1, characterized in that, In step S4, the specific method for the horizontal pleiotropy test is as follows: S41: Use the Sargan test to determine whether the part of the phenotype that cannot be explained by the risk factors is significantly correlated with the SNPs used as initial instrumental variables. S42: If the p-value of the Sargan test is greater than 0.1, then the part of the phenotype that cannot be explained by the risk factors is not related to the SNPs used as initial instrumental variables.

4. A multivariable Mendelian randomization method for inferring the causal relationship between imaging and phenotype according to claim 3, characterized in that, If the p-value of the Sargan test is less than or equal to 0.1, then the part of the phenotype that cannot be explained by the risk factors is related to the SNPs used as initial instrumental variables.

5. A multivariable Mendelian randomization method for inferring the causal relationship between imaging and phenotype according to claim 1, characterized in that The data preprocessing includes quality control, normalization, and imputation of missing values.

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