Convergence in Pace, Not in Outcomes: A Multilevel Growth Curve Analysis of Child Mortality Across 179 Countries

Abstract Background The global decline in under-five mortality since 1990 is well documented in aggregate, but aggregate trends are silent about the distribution of national experience. Whether countries with the highest mortality caught up, and whether the gap between countries narrowed, are different questions, and the child-survival agenda from the fourth Millennium Development Goal to Sustainable Development Goal target 3.2 has been framed around aggregate targets that cannot distinguish them. Methods We modelled annual under-five mortality for 179 countries over 1990 to 2019 (5,370 country-years; World Bank series disseminated from UN IGME estimates) with a multilevel growth curve on the logarithmic scale: country-specific random intercepts and slopes, with standardized 1990 income as a country-level predictor. Convergence in pace, the association between initial level and subsequent proportional decline, was estimated from the random-effects covariance (with cluster-bootstrap confidence intervals) and from regressions of observed change on observed baselines, including a strictly non-overlapping baseline design; convergence in outcomes was assessed from the year-by-year cross-country standard deviation of log mortality, with a within- and between-region decomposition. Robustness analyses covered piecewise and random-quadratic trends, autoregressive residuals, population-averaged estimators, and sensitivity to the time origin, baseline definition, and added measurement error. Results Mortality fell by 30.7% per decade on average (95% CI 28.9 to 32.4). South Asia declined fastest and sub-Saharan Africa combined the highest burden with a near-average pace. Countries with higher 1990 mortality declined proportionally faster: the intercept-slope correlation was − 0.24 (bootstrap 95% CI − 0.37 to − 0.11), essentially unchanged without income adjustment, and the non-overlapping baseline regression gave − 0.034 per decade (95% CI − 0.054 to − 0.013). Yet the cross-country dispersion of log mortality showed no net reduction, rising from 1.05 to a 1999 peak of 1.14 before receding to 1.09 in 2019; dispersion within regions fell while dispersion between regions rose. The direction and approximate magnitude of the average decline were robust across error structures, while the random-effects decomposition was sensitive to the residual specification and inference on the income-by-time interaction varied across estimators. The weak income gradient in rates of decline is consistent with, but does not directly demonstrate, the diffusion of broadly accessible health interventions. Conclusions Progress in child survival over 1990 to 2019 was convergent in pace but not, on net, in outcomes, and the missing narrowing lies between world regions rather than within them. Monitoring frameworks that track only aggregate averages will not register this distributional shortfall.