Smoothing a discrete hazard function for the number of patients colonized with Methicillin‐resistant Staphylococcus Aureus in an intensive care unit

Abstract

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.

Daily Hazard of Acquisition of Methicillin-Resistant Staphylococcus aureus Infection in the Intensive Care Unit

“…Ismail and Pettitt, 6 using a nonparametric Bayesian smoothing technique, also showed an increasing hazard for MRSA acquisition up to day 13, then an approximate leveling of hazard. These findings are consistent with those of the current study, with one main difference.…”

“…These findings are consistent with those of the current study, with one main difference. The hazard on the first day of admission was 0 in the study of Ismail and Pettitt, 6 and it increased over the next few days. In the current study, the hazard at day 1 was approximately 0.01, less than one-half that of the peak hazard seen after day 12.…”

“…In other words, it is not known whether the risk is the same on each day of hospital stay and that prolonged length of stay merely exposes a patient for longer and therefore increases the risk of acquisition or whether there is genuinely a difference in risk, depending on the point in a patient's hospital stay. Although 2 studies have examined these questions through use of different methodologies, 6 ' 7 ours is the first study, to our knowledge, that both adjusts for patient cofactors and analyzes the hazard continually from the time of admission.…”

Bayesian statistics in medicine: a 25 year review

“…Prediction of meningococcal disease outbreaks in structured populations was used to inform information collection in the event of an actual outbreak [583]. Time to colonization of MRSA in an intensive care unit was modelled using priors on the first or second difference to smooth the hazard function [584]. Transmission of influenza was modelled within households [585], and transmission of gastroenteritis within schools [586].…”