Description Usage Arguments Value Author(s) Examples

Fit the probabilistic MR model with summary data while accounting for the correlated instruments and horizontal pleiotropy in TWAS framework.

1 2 | ```
PMR_summary(betaxin, betayin, Sigma1sin, Sigma2sin, samplen1, samplen2,
gammain, alphain, max_iterin, epsin)
``` |

`betaxin` |
the cis-SNP effect size vector for one specific gene in eQTL data, which must be calculated based on both the standardized gene expression value and the standardized cis-genotype matrix. |

`betayin` |
the cis-SNP effect size vector for one specific gene in GWAS data, which be calculated based on both the standardized complex trait value and the standardized cis-genotype matrix. |

`Sigma1sin` |
the LD matrix in eQTL data. |

`Sigma2sin` |
the LD matrix in GWAS data. Both |

`samplen1` |
the sample size of eQTL data. |

`samplen2` |
the sample size of GWAS data. |

`gammain` |
indicator variable for constrained model, with 1 for the null model that there is no horizontal pleiotropy. |

`alphain` |
indicator variable for constrained model, with 1 for the null model that there is no causal effect. |

`max_iterin` |
The maximum iteration. |

`epsin` |
The convergence tolerance of the absolute value of the difference between the nth and (n+1)th log likelihood. |

A list of estimates of model parameters, including the causal effect
`alpha`

, the horizontal pleiotropy effect `gamma`

, and the two corresponding p values.

Zhongshang Yuan, Xiang Zhou.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
data(Examplesummary)
attach(Examplesummary)
fmH1=PMR_summary(betaxin=betax,betayin=betay,Sigma1sin=Sigma1,Sigma2sin=Sigma2,
samplen1=n1,samplen2=n2,gammain=0,alphain=0,max_iterin =1000, epsin=1e-5)
fmH0alpha=PMR_summary(betaxin=betax,betayin=betay,Sigma1sin=Sigma1,Sigma2sin=Sigma2,
samplen1=n1,samplen2=n2,gammain=0,alphain=1,max_iterin =1000, epsin=1e-5)
fmH0gamma=PMR_summary(betaxin=betax,betayin=betay,Sigma1sin=Sigma1,Sigma2sin=Sigma2,
samplen1=n1,samplen2=n2,gammain=1,alphain=0,max_iterin =1000, epsin=1e-5)
loglikH1=max(fmH1$loglik,na.rm=TRUE)
loglikH0alpha=max(fmH0alpha$loglik,na.rm=TRUE)
loglikH0gamma=max(fmH0gamma$loglik,na.rm=TRUE)
stat_alpha = 2 * (loglikH1 - loglikH0alpha)
pvalue_alpha = pchisq(stat_alpha,1,lower.tail=FALSE)
stat_gamma = 2 * (loglikH1 - loglikH0gamma)
pvalue_gamma = pchisq(stat_gamma,1,lower.tail=FALSE)
``` |

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