Table 1

Process of estimation of the AF: equations, bias sources and bias model parameters

Process of estimation of the AF	Equations	Key bias sources	Bias model parameter for MCSA (suffices 0, t indicate chosen and unknown true values, respectively)
(1) Point estimate of the numbers exposed	n₀ = p_wk(E)*n_employed	Biases acting on point estimate of numbers exposed (n₀) 1. Inadequate data for numbers employed (n_employed) 2. Unknown proportion exposed [p_wk(E)] 3. High/low exposure level split inaccurate	C_n=n₀/n_t
(2) Number ever exposed accounting for turnover and latency*	N_e(REP)=n₀ + {n₀ * TO * t}	4. Unknown or inaccurate latency and thus the length of the REP (t)	C_l=t₀/t_t
	N_e(REP)=n₀ + {n₀ * TO * t}	5. Inaccurate staff turnover (TO)	C_t= TO₀/TO_t
(3) Proportion of the population exposed	p(E) = N_e(REP) / N_p(REP)
(4) AF: Levin’s equation	AF = p(E)(RR–1)/{1+p(E)(RR–1)}, extended to AF = {Σ_jp(E_j)(RR_j-1)}/{1+{Σ_j p(E_j)(RR-1)} summed over j separate exposure level/industry sector/time period combinations	6. Random error affecting RR
		7. Bias affecting RR chosen from an inappropriate published study regarding distribution of confounders	C_r= RR₀/RR_t
		8. Bias affecting RR chosen from a published study that is inaccurately matched to GB exposure situation, or is subject to exposure misclassification or publication bias	C_m= RR₀/RR_t
		9. Bias from using adjusted estimate of RR (RR_a) incorrectly instead of unadjusted (RR_u) in Levin’s equation16	C_u= RR_a/RR_u
(5) Estimating attributable numbers	AN=AF*∑_jD_j summed over the j age-groups of the REP exposed population in the target year	10. Bias due to not estimating age-specific AFs

*This equation is modified when estimating AF to account for recruitment and retirement ages and survival of exposed workers by the target year.6
AF, attributable fraction; AN, attributable numbers; D, deaths /registrations; MCSA, Monte Carlo sensitivity analysis; n₀,numbers exposed at a particular year in the REP; n_employed, total numbers employed; p_wk(E), proportion in the workplace exposed; TO, staff turnover per year; t, latent period, ie, number of years in the REP; N_e(REP), numbers ever exposed during the REP; N_p(REP), numbers ever of working age during the REP; p(E), proportion of the population exposed; REP, risk exposure period; RR, relative risk.