Statistical Methods for Geospatial Modeling with Stratified Cluster Survey Data

Abstract

The production of fine-scale, pixel level maps have become increasingly common in the current era of precision public health. This has led to the use of cluster level spatial models by major organizations such as WorldPop and the Institute for Health and Metrics Evaluation. However, many of these models were originally developed in the context of environmental applications, and, when estimating health and demographic indicators in low and middle income countries, they are frequently applied to demographic data from complex, multi-stage household surveys, leaving the potential for both biased and anticonservative estimates unless adjustment for the design is carried out. We highlight three potential problems. First, survey stratification and cluster level variation are often not accounted for. Second, the cluster level models either do not fully account for the population census frame, or completely ignore this aspect. This is made more problematic by confusion between the terms `prevalence' and `risk'. Third, even if stratification is accounted for in the cluster level spatial model, if that model is continuously indexed in space, then it often becomes necessary to infer what stratification level is associated with each spatial location or enumeration area (EA) when aggregating predictions, which is inevitably inexact. However, little work has been done to identify how stratification misclassification can impact predictions and how to produce predictions that are more robust to this problem. In this thesis, we investigate a variety of issues relevant to the use of cluster level data for estimating demographic outcomes continuously through space, and also as aggregates over administrative areas. We focus on the three problems mentioned above when estimating the neonatal mortality rate and secondary education completion for women aged 20--29 in Kenya using the 2014 Kenya Demographic Health Survey (DHS). First, we explore methods in small area estimation that can account for survey stratification, proposing models that include stratum level fixed effects for cluster-indexed spatial models. Second, we propose a general framework capable of accounting for cluster level, population denominator, and population-level variation as well as some aspects of EA location uncertainty. We call a model in this framework a combined population aggregation model (CPAM) since they are formed by combining standard cluster level risk models with an aggregation model for producing areal estimates. We propose a CPAM that, for Admin2 level areal estimates, produces estimates with substantially more uncertainty in the resulting neonatal mortality population aggregates of prevalence, total deaths, and relative prevalence between urban and rural areas, and at only moderately increased computational expense. The proposed CPAM is the first continuous spatial model accounting for the population census frame, cluster level variation, and population numerator and denominator variation when estimating prevalence, total counts, and relative prevalence in urban versus rural parts of an area. Lastly, we develop a Bayesian extension to the popular LatticeKrig model, which we call extended LatticeKrig (ELK). ELK allows for flexible, multiscale spatial dependence and non-Gaussian responses. We show this model holds particular promise for predicting areal aggregates due to its ability to flexibly model the covariance structure, and is more robust than traditional stochastic partial differential equation methods when accounting for confounding factors such as urbanicity.