RESUMEN
We offer a natural and extensible measure-theoretic treatment of missingness at random. Within the standard missing-data framework, we give a novel characterization of the observed data as a stopping-set sigma algebra. We demonstrate that the usual missingness-at-random conditions are equivalent to requiring particular stochastic processes to be adapted to a set-indexed filtration. These measurability conditions ensure the usual factorization of likelihood ratios. We illustrate how the theory can be extended easily to incorporate explanatory variables, to describe longitudinal data in continuous time, and to admit more general coarsening of observations.
RESUMEN
INTRODUCTION: Excessive alcohol consumption has adverse effects on health and there is a recognised need for the longitudinal analysis of population data to improve our understanding of the patterns of alcohol use, harms to consumers and those in their immediate environment. The UK has a number of linkable, longitudinal databases that if assembled properly could support valuable research on this topic. AIMS AND OBJECTIVES: This paper describes the development of a broad set of cross-linked cohorts, e-cohorts, surveys and linked electronic healthcare records (EHRs) to construct an alcohol-specific analytical platform in the United Kingdom using datasets on the population of Wales.The objective of this paper is to provide a description of existing key datasets integrated with existing, routinely collected electronic health data on a secure platform, and relevant derived variables to enable population-based research on alcohol-related harm in Wales. We illustrate our use of these data with some exemplar research questions that are currently under investigation. METHODS: Record-linkage of routine and observational datasets. Routine data includes hospital admissions, general practice, and cohorts specific to children. Two observational studies were included. Routine socioeconomic descriptors and mortality data were also linked. CONCLUSION: We described a record-linked, population-based research protocol for alcohol related harm on a secure platform. As the datasets used here are available in many countries, ELAStiC provides a template for setting up similar initiatives in other countries. We have also defined a number of alcohol specific variables using routinely-collected available data that can be used in other epidemiological studies into alcohol related outcomes. With over 10 years of longitudinal data, it will help to understand alcohol-related disease and health trajectories across the lifespan.
RESUMEN
Likelihood factors that can be disregarded for inference are termed ignorable. We demonstrate that close ties exist between ignorability and identification of causal effects by covariate adjustment. A graphical condition, stability, plays a role analogous to that of missingness at random, but is applicable to general longitudinal data. Our formulation of ignorability does not depend on any notion of missing data, so is appealing in situations where missing data may not actually exist. Several examples illustrate how stability may be assessed.
