Background: The health status of individuals is determined by multiple factors operating at both micro and macro levels and the interactive effects of them. Measures of health inequalities should reflect such determinants explicitly through sources of levels and combining mean differences at group levels and the variation of individuals, for the benefits of decision making and intervention planning. Measures derived recently from marginal models such as beta-binomial and frailty survival, address this issue to some extent, but are limited in handling data with complex structures. Betabinomial models were also limited in relation to measuring inequalities of life expectancy (LE) directly.