Woolf et al's "GWAS by subtraction" is not useful for cross-generational Mendelian randomization studies.

Mendelian randomization (MR) is an epidemiological method that can be used to strengthen causal inference regarding the relationship between a modifiable environmental exposure and a medically relevant trait and to estimate the magnitude of this relationship [1]. Recently, there has been considerable interest in using MR to examine potential causal relationships between parental phenotypes and outcomes amongst their offspring [2–4] (interestingly one of the earliest exemplars of MR was confirmation that antenatal maternal folate was protective against offspring neural tube defects [1]). In a recent issue of BMC Research Notes, Woolf, Sallis, Munafo and Gill (2023) [5] (abbreviated as WSMG from now on) present a method they call “GWAS by subtraction” (not to be confused with GWAS by subtraction via genomic SEM [6, 7]), to derive genome-wide summary statistics for paternal smoking and other “paternal phenotypes” with the goal that these estimates can then be used in downstream (including two sample) MR studies [8]. Whilst a potentially useful goal, WSMG (2023) focus on the wrong parameter of interest for useful genome-wide association studies (GWAS) and downstream cross-generational MR studies, and the estimator that they derive is neither efficient nor appropriate for such use.