Table 1.

Exposure metrics

	X(c(t);a)
	Continuous		Discrete
Metric	Average	Total	Average		Total
(i)Moving recent exposure	$\frac{{\int }_{t-a}^{t}c(s)ds}{a}$	${\int }_{t-a}^{t}c(s)ds$	$\frac{{\sum }_{s=t-a}^{t}I(s)c(s)}{{\sum }_{s=t-a}^{t}I(s)}$ or $\frac{{\sum }_{s=t-a}^t\tilde{c}(s)}{a+1}$		${\sum }_{s=t-a}^t\tilde{c}(s)$
(ii)mid- or later-life-related susceptibility window	$\frac{{\int }_{t-a}^{t}c(s)ds}{t-a}$	${\int }_a^{t}c(s)ds$	$\frac{{\sum }_{s=a}^{t}I(s)c(s)}{{\sum }_{s=a}^{t}I(s)}$ or $\frac{{\sum }_{s=a}^t\tilde{c}(s)}{t-a+1}$		${\sum }_{s=a}^t\tilde{c}(s)$
(iii)Exposure during critical	1. $\frac{{\int }_{t_0}^{a}c(s)ds}{a-t_0}$	${\int }_{t_0}^{a}c(s)ds$	$\frac{{\sum }_{s=t_0}^{a}I(s)c(s)}{{\sum }_{s=t_0}^{a}I(s)}$ or $\frac{{\sum }_{s=t_0}^a\tilde{c}(s)}{a-t_0+1}$		${\sum }_{s=t_0}^a\tilde{c}(s)$
period of susceptibility	2. $\frac{{\int }_{a_1}^{a_2}c(s)ds}{a_2-a_1}$	${\int }_{a_1}^{a_2}c(s)ds$	$\frac{{\sum }_{s=a_1}^{a_2}I(s)c(s)}{{\sum }_{s=a_1}^{a_2}I(s)}$ or $\frac{{\sum }_{s=a_1}^{a_2}\tilde{c}(s)}{a_2-a_1+1}$		${\sum }_{s=a_1}^{a_2}\tilde{c}(s)$
(iv)Age- or time related moving	1. $\frac{{\int }_{t_0}^{t-a}c(s)ds}{t-a-t_0}$	${\int }_{t_0}^{t-a}c(s)ds$	$\frac{{\sum }_{s=t_0}^{t-a}I(s)c(s)}{{\sum }_{s=t_0}^{t-a}I(s)}$ or $\frac{{\sum }_{s=t_0}^{t-a}\tilde{c}(s)}{t-a-t_0+1}$		${\sum }_{s=t_0}^{t-a}\tilde{c}(s)$
exposure with a lag	2. $\frac{{\int }_{a_1}^{t-a_2}c(s)ds}{t-a_2-a_1}$	${\int }_{a_1}^{t-a_2}c(s)ds$	$\frac{{\sum }_{s=a_1}^{t-a_2}I(s)c(s)}{{\sum }_{s=a_1}^{t-a_2}I(s)}$ or $\frac{{\sum }_{s=a_1}^{t-a_2}\tilde{c}(s)}{t-a_2-a_1+1}$		${\sum }_{s=a_1}^{t-a_2}\tilde{c}(s)$
	3. $\frac{{\int }_{t-a_1}^{t-a_2}c(s)ds}{a_1-a_2}$	${\int }_{t-a_1}^{t-a_2}c(s)ds$	$\frac{{\sum }_{s=t-a_1}^{t-a_2}I(s)c(s)}{{\sum }_{s=t-a_1}^{t-a_2}I(s)}$ or $\frac{{\sum }_{s=t-a_1}^{t-a_2}\tilde{c}(s)}{a_1-a_2+1}$		${\sum }_{s=t-a_1}^{t-a_2}\tilde{c}(s)$
(v)One time exposure effect			c(a)
(vi)A lag type model			c(t − a)

I (s) is a missing indicator; it is 1 if c(s) is available and 0 otherwise. c̃(s) is c(s) when c(s) is available, and is the exposure value c(s (carrying backward imputation) or c(s − Δ_b) (carrying forward imputation) if c(s) is not available and the closest time points when exposure is available is s − Δ_f and s + Δ_b in the forward and backward directions, respectively. Assumes missingness is random. There are the following restrictions: for (i), a ≥ 0; for (ii), 0 ≤ a ≤ t ; for (iii.1), a ≥ t₀; for (iii.2), a₂ ≥ a₁ ≥ 0; for (iv.1), t ≥ a + t₀; for (iv.2), t ≥ a₁ + a₂; for (iv.3), a₂ ≤ a₁; for (v) and (vi), a ≥ 0.