Administrators at a small hospital are concerned with an outbreak of staph infections in one of their wards. The strain of bacteria is partially drug resistant and the first case appeared six weeks ago. Since then eight other patients have become infected, all on the same ward. The ward is staffed by 12 nurses in 3 eight hour shifts. Each nurse in a shift is assigned a set of hospital beds (patients). You hypothesize that one or more of the nurses is transmitting the infection from patient to patient, and decide to investigate using a designer statistic. You code the data to record the location of each patient’s bed along and a case identifier. The case identifier is "1" if the patient was infected, and 0 otherwise. You define a data metric which is the product of the case identifiers – hence the data metric for a patient pair is "1" if both patients are cases, and 0 otherwise. Your colleague suggests using the Euclidean distance between beds as the proximity metric.

Questions:

1. Is this appropriate? Why or why not?
2. You also have available the list of hospital beds assigned to each nurse. How might this be used as a proximity metric to explore the hypothesis that a specific nurse is spreading the infection?