Split bootstrap hierarchical modeling of antibiotics abuse in China

In the 1990s, China experienced a high degree of antibiotics abuse, which resulted in increased drug resistance. As a result, the World Health Organization introduced a program for children under the age of 5 years who had an acute respiratory tract infection. We analyze the data pertaining to the treatment provided by doctors in several hospitals in China in order to understand the relationships in the data. The data are nested in a three-level hierarchical structure with small cluster sizes ranging from 2 to 10. While large sample theory provides a mechanism to construct confidence intervals and test hypotheses about regression coefficients, the estimation algorithms often fail to converge when they are applied to small cluster sizes. This paper presents a combination of the cluster bootstrap and primary unit splitting methods, called split bootstrap, which is a novel combination that can be used as an alternative when analyzing data pertaining to the abuse of antibiotics in China with small cluster sizes. The split bootstrap method provides accurate estimations with a minimal reduction in precision.