Dependent Happenings: A Recent Methodological Review

One hundred years ago Sir Ronald Ross published his treatise on a general Theory of Happenings. Dependent happenings are those in which the frequency depends on the number already affected. When there is dependency of events, interventions can have different types of effects. Interventions such as vaccination can have direct protective effects for the person receiving the treatment, as well as indirect/spillover effects for others in the population. Causal inference is a framework for carefully defining the causal effect of a treatment, exposure, or policy, and then determining conditions under which such effects can be estimated from the observed data. We consider here scenarios in which the potential outcomes of an individual can depend on the treatment of other individuals in the population, known as causal inference with interference. Much of the research so far has assumed the population is divided into groups or clusters, and individuals can interfere with others within their clusters but not across clusters. Recent developments have assumed more general forms of interference. We review some of the different types of effects that have been defined for dependent happenings, particularly using the methods of causal inference with interference. Many of the methods are applicable across disciplines, such as infectious diseases, social sciences, and economics.