Deriving GWAS summary estimates for paternal smoking in UK biobank: a GWAS by subtraction.

Objective: To use genome-wide association study (GWAS) by subtraction, a method for deriving novel GWASs from existing summary statistics, to derive genome-wide summary statistics for paternal smoking.

Result: A GWAS by subtraction was implemented using a weighted linear model that defined the child-genotype paternal-phenotype association as the child-genotype child-phenotype association minus the child-genotype maternal-phenotype association. We first use the laws of inherence to derive the weighted linear model. We then implemented the linear model to create a GWAS of paternal smoking by subtracting the summary statistics from a GWAS of maternal smoking from the summary statistics of a GWAS of the index individual's smoking. We used a Monte-Carlo simulation to validate the model and showed that this approach performed similarly in terms of bias to performing a traditional GWAS of paternal smoking. Finally, we validated the summary statistics in a Mendelian randomisation analysis by demonstrating an association of genetically predicted paternal smoking with paternal lung cancer and emphysema.