What the evidence says
One study uses an instrumental-variable design — a distance-from-target instrument — to identify the causal effect of secondary-care (hospital) expenditure on mortality. In its preferred model, a 1% increase in secondary-care expenditure reduces all-age mortality by approximately 0.92% (95% CI -1.47% to -0.37%). The confidence interval spans more than a fourfold range, so while the direction of the effect (more expenditure, less mortality) is rated high confidence, the exact magnitude is rated only medium confidence.
The same study then decomposes this mortality gain by deprivation group and finds no simple pro-poor pattern. Across all 12 model variants tested, there is no sign of a significant pro-poor gradient — more deprived populations do not gain disproportionately more mortality benefit from the same marginal increase in secondary-care expenditure. This finding is rated high confidence on both direction and magnitude, given its consistency across specifications and sensitivity analyses.
Instead of a monotonic gradient, the distributional pattern is inverted U-shaped: the middle deprivation quintile group gains significantly more mortality benefit than all other groups. This shape holds across all 12 variants, though it reaches statistical significance in only 10 of the 12, and the size of the middle group's advantage varies by specification.
When the comparison is narrowed to the two most-deprived groups versus the two least-deprived groups, the evidence is mixed. In 7 of 12 model variants, the study cannot reject the null hypothesis that the two groups received the same mortality gain. In the remaining 5 of 12 variants, the pattern reverses: less-deprived groups gain significantly more than more-deprived groups, a "pro-rich" result.
All of the above comes from a single source studying secondary-care expenditure, not personal or household income. No claim in the current sources measures a causal effect of income itself on mortality via an IV or natural-experiment design — that is a gap in what this page currently covers, not a finding.