Avoiding blindness to health status in health achievement and health inequality measurement

•New class of health achievement indices.•New class of socioeconomic health inequality indices.•These indices account for pure and socioeconomic health inequality.

The concentration index, being focused on the socioeconomic dimension of health inequality and overlooking aversion to pure health inequality, can produce ethically contestable rankings of health distributions. A health transfer from a sicker but richer individual to healthier but poorer individual will decrease the concentration index. This paper presents a new class of health inequality indices that avoid this limitation by trading off socioeconomic-related health inequality against pure health inequality.