One possible way to overcome bias from residual confounding and reverse causation is Mendelian randomisation (MR) (Davey Smith & Ebrahim, 2003). This method uses genetic variants to proxy for an exposure in an instrumental variable analysis to estimate the causal effect on an outcome (Lawlor et al., 2008). Previous MR studies have failed to show any clear evidence for an effect of smoking on depression (Bjørngaard et al., 2013; Taylor, Fluharty et al., 2014; Wium-Andersen, Ørsted, & Nordestgaard, 2015) and show suggestive but inconclusive evidence for an effect of smoking on schizophrenia (Gage et al., 2017; Wium-Andersen et al., 2015). However, the genetic instruments for smoking used in these MR studies are limited, only capturing individual aspects of smoking behaviour and only having identified limited numbers of suitable genetic variants (Bjørngaard et al., 2013; Gage et al., 2017; Taylor, Fluharty et al., 2014; Wium-Andersen et al., 2015). Furthermore, any instrument for smoking heaviness requires stratifying samples into smokers and non-smokers. Stratification is not possible using the most common MR method, two-sample MR. In two-sample MR, single-nucleotide polymorphism (SNP)-exposure and SNP-outcome
