Table 1.

Possible causal estimands in Mendelian Randomization studies of time-varying exposures and their identifiability assumptions

	Estimand (on the additive scale)	Assumptions required for identification
		With a single exposure measurement	With multiple exposure measurements
Point effect	Difference in mean counterfactual outcomes had everyone received exposure $a$ at time $m$ versus had everyone received exposure $a^{\prime }$ at time $m$: $\mathrm{E}\left[Y^{a_m}\right]-\mathrm{E}\left[Y^{a_m^{\prime }}\right]$	Instrumental conditions hold for the proposed instrument for exposure at time $m$. For instrumental condition 2 to hold, each component of the time-varying exposure other than at time $m$ must be unaffected by the instrument or have no effect on the outcome.a	N/A
Period effect b		Instrumental conditions hold for the exposure, as a whole, between times $m-p$ and $m$ (i.e., each component of the time-varying exposure outside of this time period is unaffected by the instrument or has no effect on the outcome)
Generalized form	Difference in mean counterfactual outcomes had everyone received the exposure trajectory $(a_{m-p},\dots ,a_{m-1},a_m)$ between times $m-p$ and $m$ versus had everyone received the exposure trajectory $(a_{m-p}^{\prime },\dots ,a_{m-1}^{\prime },a_m^{\prime })$ between times $m-p$ and $m$: $\mathrm{E}\left[Y^{a_{m-p},\dots ,a_{m-1},a_m}\right]-\mathrm{E}\left[Y^{a_{m-p}^{\prime },\dots ,{a_{m-1}^{\prime },a}_m^{\prime }}\right]$	No realistic assumptions for identification in MR studies	All relevant exposure time points have been measured and at least as many instruments as the number of exposure time points are available. The association between instrument-exposure must vary between time points for at least one instrument. No realistic assumptions for identification in MR studies if not all relevant exposure time points have been measured.
Shift in exposure trajectories	Difference in mean counterfactual outcomes had everyone received the exposure trajectory $(a_{m-p},\dots ,a_{m-1},a_m)$ between times $m-p$ and $m$ versus had everyone received the same exposure trajectory after shifting the exposure by one unit across the entire period $\mathrm{E}\left[Y^{a_{m-p}+1,\dots ,a_{m-1}+1,a_m+1}\right]-\mathrm{E}\left[Y^{a_{m-p},\dots ,a_{m-1},a_m}\right]$	1. The association between the instrument and the exposure is constant on the additive scale between times $m-p$ and $m$ c 2. Instrumental conditions hold for the exposure trajectory between times $m-p$ and $m$. For instrumental condition 2 to hold, each component of the time-varying exposure outside of this time period must be unaffected by the instrument or have no effect on the outcome.c	If all relevant exposure time points have been measured and there are a sufficient number of instruments, no additional assumptions are needed. If only a subset of relevant exposure time points have been measured, the instrument-exposure association during unmeasured time points must be the same as the instrument-exposure association for at least one of the measured time points.

^aFrom Swanson and colleagues (2017)⁵, and VanderWeele and colleagues (2014)¹⁰

^bWhen $m-p=0$ represents conception, this is often referred to as the lifetime effect

^cFrom Labrecque and Swanson (2018)⁹