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247 nips-2010-Sparse Instrumental Variables (SPIV) for Genome-Wide Studies

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Author: Paul Mckeigue, Jon Krohn, Amos J. Storkey, Felix V. Agakov

Abstract: This paper describes a probabilistic framework for studying associations between multiple genotypes, biomarkers, and phenotypic traits in the presence of noise and unobserved confounders for large genetic studies. The framework builds on sparse linear methods developed for regression and modiﬁed here for inferring causal structures of richer networks with latent variables. The method is motivated by the use of genotypes as “instruments” to infer causal associations between phenotypic biomarkers and outcomes, without making the common restrictive assumptions of instrumental variable methods. The method may be used for an effective screening of potentially interesting genotype-phenotype and biomarker-phenotype associations in genome-wide studies, which may have important implications for validating biomarkers as possible proxy endpoints for early-stage clinical trials. Where the biomarkers are gene transcripts, the method can be used for ﬁne mapping of quantitative trait loci (QTLs) detected in genetic linkage studies. The method is applied for examining effects of gene transcript levels in the liver on plasma HDL cholesterol levels for a sample of sequenced mice from a heterogeneous stock, with ∼ 105 genetic instruments and ∼ 47 × 103 gene transcripts. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 uk Abstract This paper describes a probabilistic framework for studying associations between multiple genotypes, biomarkers, and phenotypic traits in the presence of noise and unobserved confounders for large genetic studies. [sent-13, score-0.703]

2 The framework builds on sparse linear methods developed for regression and modiﬁed here for inferring causal structures of richer networks with latent variables. [sent-14, score-0.425]

3 The method is motivated by the use of genotypes as “instruments” to infer causal associations between phenotypic biomarkers and outcomes, without making the common restrictive assumptions of instrumental variable methods. [sent-15, score-1.208]

4 The method may be used for an effective screening of potentially interesting genotype-phenotype and biomarker-phenotype associations in genome-wide studies, which may have important implications for validating biomarkers as possible proxy endpoints for early-stage clinical trials. [sent-16, score-0.558]

5 Where the biomarkers are gene transcripts, the method can be used for ﬁne mapping of quantitative trait loci (QTLs) detected in genetic linkage studies. [sent-17, score-0.919]

6 The method is applied for examining effects of gene transcript levels in the liver on plasma HDL cholesterol levels for a sample of sequenced mice from a heterogeneous stock, with ∼ 105 genetic instruments and ∼ 47 × 103 gene transcripts. [sent-18, score-1.201]

7 1 Introduction A problem common to both epidemiology and to systems biology is to infer causal relationships between phenotypic measurements (biomarkers) and disease outcomes or quantitative traits. [sent-19, score-0.597]

8 The problem is complicated by the fact that in large bio-medical studies, the number of possible genetic and environmental causes is very large, which makes it implausible to conduct exhaustive interventional experiments. [sent-20, score-0.291]

9 Moreover, it is generally impossible to remove the confounding bias due to unmeasured latent variables which inﬂuence associations between biomarkers and outcomes. [sent-21, score-0.681]

10 Also, in situations when the biomarkers are mRNA transcript levels, the measurements are known to be quite noisy; additionally, the number of unique candidate causes may exceed the number of observations by several orders of magnitude (the p ≫ n problem). [sent-22, score-0.611]

11 Developing an efﬁcient framework for addressing this problem may be fundamental for overcoming bottlenecks in drug development, with possible applications in the validation of biomarkers as causal risk factors, or developing proxies for clinical trials. [sent-24, score-0.712]

12 Pearl [28] argues that causal assumptions cannot be veriﬁed unless one makes a recourse 1 to experimental control, and that there is nothing in the probability distribution p(x, y) which can tell whether a change in x may have an effect on y. [sent-26, score-0.291]

13 If the causal effects are shown to be identiﬁable, their magnitudes can be obtained by statistical estimation, which for common models often reduces to solving systems of linear equations. [sent-30, score-0.394]

14 In this paper we are leaving aside debates about the nature of causality and focus instead on identifying a set of candidate causes for a large partially observed under-determined genetic problem. [sent-37, score-0.29]

15 The approach builds on the instrumental variable methods that were historically used in epidemiological studies, and on approximate Bayesian inference in sparse linear latent variable models. [sent-38, score-0.383]

16 Speciﬁc modeling hypotheses are tested by comparing approximate marginal likelihoods of the corresponding direct, reverse, and pleiotropic models with and without latent confounders, where we follow [21] in allowing for ﬂexible priors. [sent-39, score-0.48]

17 2 Previous work Inference of causal direction of x on y is to some extent simpliﬁed if we assume existence of an auxiliary variable g, such that g’s effect on x may only be causal, and g’s effect on y may only be through x. [sent-41, score-0.291]

18 The idea is exploited in instrumental variable methods [3, 2, 29] which typically deal with low-dimensional linear models, where the strength of the causal effect may be estimated as wx→y = cov(g, y)/cov(g, x). [sent-42, score-0.484]

19 Selecting a plausible instrument g may be difﬁcult in some domains; however, in genetic studies it may be possible to exploit as an instrument a measure of genotypic variation. [sent-46, score-0.523]

20 In quantitative genetics, such applications of instrumental variable methods have been termed Mendelian randomization [15, 34]. [sent-47, score-0.251]

21 In accordance with the requirements of the classic instrumental variable methods, it is assumed that effects of the genetic instrument g on the biomarker x are unconfounded, and that effects of the instrument on the outcome y are mediated only through the biomarker (i. [sent-48, score-1.17]

22 However, the assumption of no hidden pleiotropy severely restricts the application of this approach, as most genotypic effects on complex traits are not sufﬁciently well understood to exclude pleiotropy as a possible explanation of an association. [sent-52, score-0.509]

23 Thus the classical instrumental variable argument is limited to biomarkers for which suitable non-pleiotropic instruments exist, and cannot be easily extended to exploit studies with multiple biomarkers and genome-wide data. [sent-53, score-1.189]

24 A more general approach to exploiting genotypic variation to infer causal relationships between gene transcript levels and quantitative traits has been developed by Schadt et. [sent-54, score-0.811]

25 The histogram shows the difference of the AIC scores for the causal and reverse models for a ﬁxed biomarker and outcome, and various choices of loci from predictive regions. [sent-67, score-0.642]

26 Right: AIC scores of the causal (top) and reverse (bottom) models for each choice of instrument gi (the straight lines link the scores for a ﬁxed choice of gi ). [sent-68, score-0.598]

27 Scores were centered relative to those of the pleiotropic model. [sent-69, score-0.305]

28 Biomarker and outcome are liver expressions of Cyp27b1 and plasma HDL measurements for heterogeneous mice. [sent-70, score-0.263]

29 Based on the choice of gi , either causal or reverse explanations are favored. [sent-71, score-0.445]

30 First, effects of loci and biomarkers on outcomes are not modeled jointly, so widely varying inferences are possible depending on the choice of the triads {gi , xj , y}. [sent-73, score-0.695]

31 Figure 1 center, right compares differences in the AIC scores for the causal and reverse models constructed for a ﬁxed biomarker and outcome, and for various choices of the genetic instruments from the predictive region. [sent-74, score-0.899]

32 Depending on the choice of instrument gi , either causal or reverse explanations are favored. [sent-75, score-0.527]

33 A second key limitation is that the LCMS method does not allow for dependencies between multiple biomarkers, measurement noise, or latent variables (such as unobserved confounders of the biomarker-outcome associations). [sent-76, score-0.309]

34 Thus, for instance, without allowance for noise in the biomarker measurements, non-zero conditional mutual information I(gi , y|xj ) will be interpreted as evidence of pleiotropy or reverse causation even when the relation between the underlying biomarker and outcome is causal. [sent-77, score-0.677]

35 For example, their method does not allow for an easy integration of unmeasured confounders with unknown correlations with the intermediate and outcome variables. [sent-80, score-0.313]

36 Another approach to modeling joint effects of genetic loci and biomarkers (gene expressions) was described by [41]. [sent-81, score-0.803]

37 The vast majority of other recent model selection and structure learning methods from machine learning literature are also either not easily extended to include latent confounders (e. [sent-84, score-0.28]

38 3 Methods To address the problem of causal discovery in large bio-medical studies, we need a uniﬁed framework for modeling relations between genotypes, biomarkers, and outcomes that is computationally tractable to handle a large number of variables. [sent-89, score-0.356]

39 Our approach extends LCMS and the instrumental variable methods by the joint modeling of effects of genetic loci and biomarkers, and by allowing for both pleiotropic genotypic effects and latent variables that generate couplings between biomarkers and confound the biomarker-outcome associations. [sent-90, score-1.691]

40 For intermediate γ1 ’s and high empirical correlations, there is a strong preference for the causal model. [sent-128, score-0.291]

41 Bayesian framework allows prior biological information to be included if available: for instance, cis-acting genotypic effects on transcript levels are likely to be stronger and less pleiotropic than trans-acting effects on transcript levels. [sent-129, score-0.963]

42 Here it is used in the context of sparse multi-factor instrumental variable analysis in the presence of unobserved confounders, pleiotropy, and noise. [sent-136, score-0.271]

43 Model Parameterization Our sparse instrumental variables model (SPIV) is speciﬁed with four classes of variables: genotypic and environmental covariates g ∈ R|g| , phenotypic biomarkers x ∈ R|x| , outcomes y ∈ R|y| , and latent factors z1 , . [sent-137, score-1.098]

44 The biomarkers x and outcomes y are speciﬁed as hidden x y variables inferred from noisy observations ˜ ∈ R|˜| and ˜ ∈ R|˜| (note that |˜| = |x|, |˜| = |y|). [sent-143, score-0.489]

45 The x y x y effects of genotype on biomarkers and outcome are assumed to be unconfounded. [sent-144, score-0.581]

46 Pleiotropic effects of genotype (effects on outcome that are not mediated through the phenotypic biomarkers) are accounted for by an explicit parameterization of p(y|g, x, z). [sent-145, score-0.29]

47 It is clear that the SPIV structure extends that of the instrumental variable methods [2, 3, 29] by allowing for the pleiotropic links, and also extends the pleiotropic model of Schadt et. [sent-147, score-0.803]

48 [30] (Figure 1 left (iii)) by allowing for multiple instruments and latent variables. [sent-149, score-0.25]

49 are speciﬁed y with inverse Gamma priors Γ−1 (ai , bi ), with hyperparameters ai and bi ﬁxed at values motivating the prior beliefs about the projection noise (often available to lab technicians collecting trait or biomarker measurements). [sent-154, score-0.29]

50 One way to view the latent confounders z is as missing genotypes or environmental covariates, so that prior variances of the latent factors are peaked at values representative of the empirical variances of the instruments g. [sent-155, score-0.651]

51 Some additional intuition of the inﬂuence of the sparse prior on the causal inference may be gained by numerically comparing the marginal likelihoods of the Markov-equivalent models with and without confounders Mx←z→y , Mx→y . [sent-170, score-0.591]

52 Figure 2 shows that when the empirical correlations are strong and γ1 is at intermediate levels, there is a strong preference for a causal model. [sent-172, score-0.319]

53 Also, as the number of genetic instruments grows, evidence in favor of the causal or pleiotropic model will be less dependent upon the priors on model parameters. [sent-175, score-0.999]

54 For instance, with two genotypic variables that perturb a single transcript, the causal model has three adjustable parameters, but the pleiotropic model has ﬁve (see Figure 1 left, (iv)). [sent-176, score-0.743]

55 Note that the MAP solution for SPIV may also be easily derived for the semi-supervised case where the biomarker and outcome vectors are only partially observed. [sent-180, score-0.245]

56 on sampling or expectation propagation [26, 31], the MAP approximation allows for an efﬁcient handling of very large networks with multiple instruments and biomarkers, and makes it straightforward to incorporate latent confounders. [sent-183, score-0.25]

57 For example, the ﬁxed-point update for ui ∈ R|g| linking biomarker xi with the vector of instruments g is easily expressed as (t) 2 ´ (t−1) + γ2 I|g| ui = GT G + σxi γ1 Ui 5 −1 GT xi − GT Z vi , (4) Figure 3: Top: SPIV for artiﬁcial datasets. [sent-187, score-0.326]

58 Bottom: SPIV for a genome-wide study of causal effects on HDL in heterogeneous stock mice. [sent-192, score-0.5]

59 Left/right plots show maximum a-posteriori weights θM AP and the mutual information I(xi , y|e) between the unobserved biomarkers and outcome evaluated from the model at θM AP , under the joint Gaussian assumption. [sent-193, score-0.565]

60 A cluster of pleiotropic links on chromosome 1 at about 173 MBP is consistent with biology. [sent-194, score-0.399]

61 Transcripts that are most predictive of HDL through their links with pleiotropic genetic markers on chrom 1 are Uap1, Rgs5, Apoa2, and Nr1i3. [sent-196, score-0.538]

62 4 Results Artiﬁcial data: We applied SPIV to several simulated datasets, and compared speciﬁc modeling hypotheses for the biomarkers retained in the posterior modes. [sent-212, score-0.472]

63 Subsequent testing of the speciﬁc modeling hypotheses for the most important factors resulted in the correct discrimination of causal and confounded associations in ≈86% of cases. [sent-219, score-0.473]

64 Genome-wide study of HDL cholesterol in mice: To demonstrate our method for a large-scale practical application, we examined effects of gene transcript levels in the liver on plasma highdensity lipoprotein (HDL) cholesterol levels for a mice from a heterogeneous stock. [sent-220, score-0.821]

65 The genetic factors inﬂuencing HDL in mice have been well explored in biology e. [sent-221, score-0.317]

66 0 MAP Trpv3 5530401A14Rik Tbx2 1110001A07Rik MI between biomarkers and HDL at Θ foundation. [sent-230, score-0.396]

67 At each of the 12500 marker loci, genotypes were described by 8-D vectors of expected founder ancestry proportions inferred from the raw marker genotypes by an HMM-based reconstruction method [23]. [sent-231, score-0.244]

68 Mouse-speciﬁc covariates included age and sex, which were used to augment the set of genetic instruments. [sent-232, score-0.231]

69 The full set of phenotypic biomarkers consisted of 47429 transcript levels, appropriately transformed and cleaned. [sent-233, score-0.641]

70 Indeed, the considered case of ∼ O(105 ) instruments and 47K biomarkers would give rise to O(109 ) interaction weights, which is expensive to analyze or even keep in memory. [sent-238, score-0.559]

71 In this case and for the considered sparseness-inducing priors, no hidden confounders appear to have strong effects on the outcome in the posterior1 . [sent-245, score-0.348]

72 The spikes of the pleiotropic activations in sex chromosome 20 and around chromosome 1 are consistent with the biological knowledge [38]. [sent-246, score-0.479]

73 The biomarker with the strongest direct effect on HDL (computed as the mean MAP weight wi : xi → y divided by its standard deviation over multiple runs, where each mean weight exceeds a threshold) is the expression of Cyp27b1 (gene responsible for vitamin D metabolism). [sent-247, score-0.271]

74 Knockout of the Cyp27b1 gene in mice has been shown to alter body fat stores [24], which might be expected to affect HDL cholesterol levels. [sent-248, score-0.275]

75 Recently it has also been shown that quantitative trait locus for circulating vitamin D levels in humans includes a gene that codes for the enzyme that synthesizes cholesterol [1]. [sent-249, score-0.434]

76 To demonstrate an application to gene ﬁne-mapping studies, Figure 3 (bottom right) shows the approximate mutual information I(xi , y|e = {age, sex}) between the underlying biomarkers and unobserved HDL levels expressed from the model at θM AP . [sent-254, score-0.606]

77 The mutual information takes into account not only the strength of the direct effect of xi on y, but also associations with the pleiotropic instruments, strengths of the pleiotropic effects, and dependencies between the instruments. [sent-255, score-0.796]

78 Here Σgg ∈ R|g|×|g| is the empirical covariance of the instruments, wj ∈ R|x| , wzj ∈ R|z| , and wgj ∈ R|g| are the MAP weights of the couplings of yj with the biomarkers, confounders, and genetic instruments respectively. [sent-257, score-0.533]

79 An application of SPIV to proprietary human data for a study of effects of vitamins and calcium levels on colorectal cancer (which we are not yet allowed to publish) showed very strong effects of the latent confounders. [sent-260, score-0.346]

80 Note that the couplings are via the links with the pleiotropic genetic markers on chromosome 1. [sent-263, score-0.651]

81 Details of the data collection, microarray preprocessing, and feature selection, along with the detailed ﬁndings for other biomarkers and phenotypic outcomes will be made available online. [sent-267, score-0.566]

82 SPIV performs the screening of interesting biomarker-phenotype and genotype-biomarker-phenotype associations by exploiting the maximum-a-posteriori inference in a sparse linear latent variable model. [sent-270, score-0.325]

83 Intuitively, the approach is motivated by the observation that while independence of variables implies that they are not in a causal relation, a preference for an unconfounded causal model may indicate possible causality and require further controlled experiments. [sent-272, score-0.722]

84 Technically, SPIV may be viewed as an extension of LASSO and elastic net regression which allows for latent variables and pleiotropic dependencies. [sent-273, score-0.487]

85 While being particularly attractive for genetic studies, SPIV or its modiﬁcations may potentially be applied for addressing more general structure learning tasks. [sent-274, score-0.224]

86 While SPIV attempts to focus the attention on important biomarkers establishing strong direct associations with the phenotypes, modeling of the precisions may be used for ﬁltering out unimportant factors (conditionally) independent of the outcome variables. [sent-280, score-0.663]

87 Our future work will involve a direct estimation of the sparse conditional precision matrix Σ−1 of the biomarkers, outcomes, and unmeasured confounders (given the instruments), through xyz|g latent variable extensions of the recently proposed graphical LASSO and related methods [11, 18]. [sent-281, score-0.367]

88 The key purpose of this paper is to draw attention of the machine learning community to the problem of inferring causal relationships between phenotypic measurements and complex traits (disease risks), which may have tremendous implications in epidemiology and systems biology. [sent-282, score-0.574]

89 Our speciﬁc approach to the problem is inspired by the ideas of instrumental variable analysis commonly used in epidemiological studies, which we have extended to properly address situations when the genetic variables may be direct causes of the hypothesized outcomes. [sent-283, score-0.509]

90 The sparse instrumental variable framework (SPIV) overcomes limitations of the likelihood-based LCMS methods often used by geneticists, by modeling joint effects of genetic loci and biomarkers in the presence of noise and latent variables. [sent-284, score-1.13]

91 The approach is tractable enough to be used in genetic studies with tens of thousands of variables. [sent-285, score-0.24]

92 It may be used for identifying speciﬁc genes associated with phenotypic outcomes, and may have wide applications in identiﬁcation of biomarkers as possible targets for interventions, or as proxy endpoints for early-stage clinical trials. [sent-286, score-0.527]

93 Identiﬁcation of causal effects using instrumental variables (with discussion). [sent-302, score-0.615]

94 Statistical estimation of correlated genome associations to a quantitative trait network. [sent-401, score-0.249]

95 Mendelian randomization: using genes as instruments for making causal inferences in epidemiology. [sent-410, score-0.48]

96 Regression by dependence minimization and its application to causal inference in additive noise models. [sent-448, score-0.32]

97 An integrative genomics approach to infer causal associations between gene expression and disease. [sent-511, score-0.546]

98 Mendelian randomisation: can genetic epidemiology contribute to understanding environmental determinants of disease? [sent-534, score-0.292]

99 Genome-wide genetic association of complex traits in heterogeneous stock mice. [sent-562, score-0.38]

100 Increasing the power to detect causal associations by combining genotypic and expression data in segregating populations. [sent-581, score-0.565]

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