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Accurate estimates of the under-five mortality rate in a developing world context are a key barometer of the health of a nation. This paper describes a new model to analyze survey data on mortality in this context. We are interested in both spatial and temporal description, that is wishing to estimate under-five mortality rate across regions and years and to investigate the association between the under-five mortality rate and spatially varying covariate surfaces. We illustrate the methodology by producing yearly estimates for subnational areas in Kenya over the period 1980-2014 using data from the Demographic and Health Surveys, which use stratified cluster sampling. We use a binomial likelihood with fixed effects for the urban/rural strata and random effects for the clustering to account for the complex survey design. Smoothing is carried out using Bayesian hierarchical models with continuous spatial and temporally discrete components. A key component of the model is an offset to adjust for bias due to the effects of HIV epidemics. Substantively, there has been a sharp decline in Kenya in the under-five mortality rate in the period 1980-2014, but large variability in estimated subnational rates remains. A priority for future research is understanding this variability. In exploratory work, we examine whether a variety of spatial covariate surfaces can explain the variability in under-five mortality rate. Temperature, precipitation, a measure of malaria infection prevalence, and a measure of nearness to cities were candidates for inclusion in the covariate model, but the interplay between space, time, and covariates is complex. [ABSTRACT FROM AUTHOR]

Age-period-cohort (APC) models are used to analyse data from disease registers given by age and time. When data are stratified by one further variable, for example geographical location, multivariate APC (MAPC) models can be applied to identify and estimate heterogeneous time trends across the different strata. In such models, outcomes share a set of parameters, typically the age effects, while the remaining parameters may differ across strata. In this article, we propose a conditional approach for inference to directly model relative time trends. We show that in certain situations the conditional approach can handle unmeasured confounding so that relative risks might be estimated with higher precision. Furthermore, we propose an extension for data with more stratification levels. Maximum likelihood estimation is performed using software for multinomial logistic regression. The usage of smoothing splines is suggested to stabilise estimates of relative time trends, if necessary. We apply the methodology to chronic obstructive pulmonary disease mortality data in England & Wales, stratified by three different areas and gender. [ABSTRACT FROM PUBLISHER]