Table 1.

Assumptions of the simulation methods

Method	Variable simulated	Modelling assumptions	Population assumptions	Estimation of the C
MC	$2{\mathit{\sigma }}_R^2\frac{y_g}{y}$	$2{\mathit{\sigma }}_{\text{R}}^2\frac{y_g}{y}\sim N\left({\mathit{\mu }}_g,{\mathit{\sigma }}_g^2\right)$	μ g is the observed value of $2{\mathit{\sigma }}_R^2\frac{y_g}{y}$	The regression method (2)
			σ 2g is the observed value of $\left(2{\mathit{\sigma }}_g^2\frac{y_g}{y\sqrt{n_g}}\right)$
			n g is the number of events in the income group
MC rate	y g	$y_g\sim N\left(y_g,\frac{y_g^2}{n_g}\right)$	y g is the observed rate of the event	The arithmetic method (1) or the regression method (2)
BIN	d ig	d ig ∼ B(D i, ρ ig)	D t is the observed number of events in age group i:∑ Gg=1 d ig = D i	Method (1) or (2)
		The population size in group ig is held fixed	ρ ig = d ig/D i
		The number of events is allowed to vary between income groups within the age group
POIS	d ig	d ig ∼ Pois(λ ig)	λ ig is the observed number of events in group ig	Method (1) or (2)
MN	d ig	d ig follows a multinomial distribution with parameters D, and ρ and mean E{X ig} = D i ρ ig with the constraint that ∑ Gg=1 X ig = D i	The probabilities ${\mathit{\rho }}_i=\left\{{\mathit{\rho }}_{i1},\dots ,{\mathit{\rho }}_{ig}\right\}$ (with constraints ∑ Gg=1 ρ ig = 1 and 0 < ρig ≤ 1) are estimated from the observed data: ρ ig = d ig/D i	Method (1) or (2)
		The number of events within age group D i is held fixed
		The number of deaths is allowed to vary between income groups within each age group