Table 1 Key providing the full forms of variables used in equations
From: Deriving GWAS summary estimates for paternal smoking in UK biobank: a GWAS by subtraction
Variable initial | Manuscript section | Full form | Contribution to analyses |
|---|---|---|---|
\({\upbeta}_{{{\text{CG}} \_ {\text{CP}}}}\) | Derivation of the linear model | The association between the child’s genotype and child’s phenotype (i.e. his/her genetic liability towards the phenotype) | This is estimated from a GWAS of smoking. Paternal smoking summary statistics are derived by subtracting \({\upbeta}_{{{\text{CG}} \_ {\text{MG}}}}\) from this variable |
\({\upbeta}_{{{\text{FG}} \_ {\text{FP}}}}\) | The association between the father’s genotype and father’s phenotype | NA | |
\({\upbeta}_{{{\text{MG}} \_ {\text{MP}}}}\) | The association between the mother’s genotype and the mother’s phenotype | NA | |
\({\upbeta}_{{{\text{CG}} \_ {\text{FP}}}}\) | The association between the child’s genotype and the father’s phenotype | This is the target estimand of the WLM | |
\({\upbeta}_{{{\text{CG}} \_ {\text{FG}}}}\) | The association between the child’s genotype and the father’s genotype | NA | |
\({\upbeta}_{{{\text{CG}} \_ {\text{MP}}}}\) | The association between the child’s genotype and the mother’s phenotype | This is estimated from a GWAS of maternal smoking. Paternal smoking summary statistics are derived by subtracting this variable from \({\upbeta}_{{{\text{CG}} \_ {\text{CP}}}}\) | |
\({\upbeta}_{{{\text{CG}} \_ {\text{MG}}}}\) | The association between the child’s genotype and the mother’s genotype | NA | |
\({se}({{{\hat{\upbeta}}_{{\rm{CG}} \_{{\rm{FP}}}}}})\) | Standard error of the estimate of \({\upbeta}_{{{\text{CG}} \_ {\text{FG}}}}\) | Uncertainty in WLM estimates | |
\({se}({{{\hat{\upbeta}}_{{\rm{CG}} \_{{\rm{FP}}}}}})\) | Standard error of the estimate of \({\upbeta}_{{{\text{CG}} \_ {\text{CP}}}}\) | Uncertainty in the estimates from the smoking GWAS | |
\({se}({{{\hat{\upbeta}}_{{\rm{CG}} \_{{\rm{FP}}}}}})\) | Standard error of the estimate of \({\upbeta}_{{{\text{CG}} \_ {\text{MP}}}}\) | Uncertainty in the estimates from the maternal smoking GWAS | |
Fi | Validation situation | Allele inherited from the father | NA |
Mi | Allele inherited from the mother | NA | |
Cg | Child’s unweighted allele score | Exposure in all GWASs | |
W | Variant-phenotype association (i.e. allele score weights) | NA | |
Cp | Child’s phenotype | Outcome in GWAS of smoking | |
Mg | Maternal allele score (i.e. with both inherited and non-inherited allele) | NA | |
Mp | Mother's phenotype | Outcome in GWAS of maternal smoking | |
Fp | Father’s phenotype | Outcome in the traditional GWAS of paternal smoking |