Introduction to statistical inference III: antibiotic resistance in carriage versus invasive disease

In the previous two posts I discussed an example study designed to compare the frequency of antibiotic resistance in invasive S. aureus and carried S. aureus (Table 1). The broad aim of the study was to determine whether carried and invasive bacteria differed genetically, with a focus on resistance to the antibiotic ciprofloxacin. In this post I will discuss confidence intervals, their relationship to hypothesis testing, and how to construct them in order to quantify the uncertainty in estimating parameters such as the frequencies of ciprofloxacin resistance in invasive and carried isolates.

Introduction to statistical inference II: antibiotic resistance in carriage versus invasive disease

In the previous post I discussed an example study designed to compare the frequency of antibiotic resistance in invasive S. aureus and carried S. aureus (Table 1). The broad aim of the study was to determine whether carried and invasive bacteria differed genetically, with a focus on resistance to the antibiotic ciprofloxacin. In this post I will cover how to formally compare the frequencies to test for a difference between invasive and carried isolates.

	Susceptible	Resistant
Carried	89	11
Invasive	63	37

Table 1. Number of carried versus invasive S. aureus that are susceptible versus resistant to the antibiotic ciprofloxacin.

Introduction to statistical inference: antibiotic resistance in carriage versus invasive disease

Pathogenic bacteria such as Staphylococcus aureus, Streptococcus pneumoniae and Neisseria meningitidis are major causes of communicable disease, but more often than not, they are carried by people as part of their body's natural microbiota with no ill effect, to the point that they wouldn't even know they were carriers without being screened. Comparisons of asymptomatically carried bacteria to those that have caused invasive disease could reveal the underlying reasons why some people suffer illness, while others do not. Invasive bacteria may differ genetically from those carried asymptomatically - for example they may contain virulence genes or genes that confer resistance to antimicrobial medicines. How do we go about testing for these differences, and if we detect a difference, how do we quantify whether it is meaningful?

To test for a difference in the frequency of a characteristic, such as antibiotic resistance, between different groups, first it is necessary to understand how frequency is estimated - in a rigorous statistical sense - in a single population. Here I will use this example to talk about formal approaches to statistical inference in a simple setting.