An assessment of nurses’ sufficient immunity when treating infectious patients using bumped-up binomial model

Ramalingam Shanmugam


Background: In times of an outbreak of a contagious deadly epidemic1-4 such as severe acute respiratory syndrome (SARS), the patients are quarantined and rushed to an emergency department of a hospital for treatment. Paradoxically, the nurses who treat them to become healthy get infected in spite of the nurses’ precautionary defensive alertness. This is so unfortunate because the nurses might not have been in close contact with the virus otherwise in their life. The nurses’ sufficient immunity level is a key factor to avert hospital site infection. Is it possible to quantify informatics about the nurses’ immunity from the virus?

Methods: The above question is answered with a development of an appropriate new model and methodology. This new frequency trend is named Bumped-up Binomial Distribution (BBD). Several useful properties of the BBD are derived, applied, and explained using SARS data5 in the literature. Though SARS data are considered in the illustration, the contents of the article are versatile enough to analyze and interpret data from other contagious diseases.

Results: With the help of BBD (3) and the Toronto data in Table 1, we have identified the informatics about the attending nurses’ sufficient immunity level. There were 32 nurses providing 16 patient care services. Though the nurses were precautionary to avoid infection, not all of them were immune to infection in those activities. Using the new methodology of this article, their sufficient immunity level is estimated to be only 0.25 in a scale of zero to one with a p-value of 0.001. It suggests that the nurses’ sufficient immunity level is statistically significant. The power of accepting the true alternative hypothesis of 0.50 immunity level, if it occurs, is calculated to be 0.948 in a scale of zero to one. It suggests that the methodology is powerful.

Conclusions: The estimate of nurse’s sufficient immunity level is a helpful factor for the hospital administrators in the time of making work schedules and assignments of the nurses to highly contagious patients who come in to the emergency or regular wings of the hospital for treatment. When the approach and methodology of this article are applied, it would reduce if not a total elimination of the hospital site infections among the nurses and physicians.



Likelihood ratio, Conditional probability, Odds ratio, SARS epidemic, p-value, Statistical power, Prevalence, Hypothesis test, Nuisance parameter

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