Staphylococcus aureus: Dose Response Models

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Staphylococcus aureus

Author: Sushil Tamrakar

General overview of Staphylococcus aureus

Staphylococcus aureus is a spherical bacterium which on microscopic examination appears in pairs, short chains, or bunched, grape-like clusters. These organisms are gram-positive. Some strains are capable of producing a highly heat-stable protein toxin that causes illness in humans (Anonymous 2012).

S. aureus can cause a range of illnesses, from minor skin infections to life-threatening diseases such as pneumonia, meningitis, osteomyelitis, endocarditis, toxic shock syndrome (TSS), bacteremia, and sepsis. It is still one of the five most common causes of nosocomial infections and is often the cause of postsurgical wound infections. Each year, some 500,000 patients in American hospitals contract a staphylococcal infection (Anonymous 1999).

Summary Data

Singh et al (1971) inoculated the forearm skin of volunteers with known initial doses of S. aureus and measured the infection and bacterial growth kinetic over 6 days. Rose and Haas in 1999 recalculated the initial doses as there was an increase in density of S. aureus after inoculation. The doses inoculated by Singh, Marples et al. in 1971 represent the initial loading of the organism on volunteers' forearms. Over the course of the time there was microbial growth that led to infection (Rose and Haas 1999).The initial loading of the organism on volunteers is given in the table:

Initial loading data/Staphylococcus aureus [1]
Dose Infected Non-infected Total
40 4 16 20
220 8 12 20
2000 13 7 20
105000 14 6 20
1600000 19 1 20
10000000 20 0 20

Because there was an increase in density of S. aureus after inoculation, the initial inoculum can not be used as a dose parameter in dose-response modeling. To modify the dose, an assumption was made to take into account the effect of contact time using following equation:

Where d is dose metric and C is density in number per square centimeter of organisms on the skin at time t

A quasimechanistic model of the growth curve was developed to to define the modified dose. Following differential equation was used to estimate the revised doses of infection.

N=microorganism density (numbers/cm sq.), Nmax=maximum organism density, k1=initial inactivation rate, k2=rate constant for the decrease in activation, k3= growth rate constant

The dose-response analysis was based on the modified doses. (Singh, Marples et al. 1971; Rose and Haas 1999).

Experiment serial number Reference Host type Agent strain Route # of doses Dose units Response Best fit model Optimized parameter(s) LD50/ID50
278* [2] human subcutaneous 6 CFU/cm2 infection exponential k = 7.64E-08 9.08E+06
*This model is preferred in most circumstances. However, consider all available models to decide which one is most appropriate for your analysis.

Exponential and betapoisson model.jpg

Optimization Output for experiment 278

Human/Staphylococcus aureus [2]
Dose Infected Non-infected Total
2430000 4 16 20
6270000 8 12 20
1.27E+07 13 7 20
2.5E+07 14 6 20
3.34E+07 19 1 20
3.91E+07 20 0 20

Goodness of fit and model selection
Model Deviance Δ Degrees
of freedom
Exponential 5.52 5.36e-05 5 3.84
Beta Poisson 5.52 4 9.49
Exponential is preferred to beta-Poisson; cannot reject good fit for exponential.

Optimized k parameter for the exponential model, from 10000 bootstrap iterations
Parameter MLE estimate Percentiles
0.5% 2.5% 5% 95% 97.5% 99.5%
k 7.64E-08 5.67E-08 6.19E-08 6.41E-08 1.00E-07 1.02E-07 1.35E-06
ID50/LD50/ETC* 9.08E+06 2.70E+06 6.79E+06 6.93E+06 1.08E+07 1.12E+07 1.22E+07
*Not a parameter of the exponential model; however, it facilitates comparison with other models.

Parameter histogram for exponential model (uncertainty of the parameter)
Exponential model plot, with confidence bounds around optimized model


The data set used in this analysis was modified by Rose and Haas (1999).


  1. Singh, G., R. R. Marples, et al. (1971). "EXPERIMENTAL STAPHYLOCOCCUS AUREUS INFECTIONS IN HUMANS." J Investig Dermatol 57(3): 149-162.
  2. 2.0 2.1 Rose, J. B. and C. N. Haas (1999). "A risk assessment framework for the evaluation of skin infections and the potential impact of antibacterial soap washing." American Journal of Infection Control 27(6): S26-S33

Anonymous (1999) Experimental Staph Vaccine Broadly Protective in Animal Studies, National Institute of Allergy and Infectious Diseases ,U.S. Department of Health and Human Services.

Anonymous (2012) Foodborne Pathogenic Microorganisms and Natural Toxins Handbook Staphylococcus aureus, U.S. Food and Drug Administration.

Rose JB, Haas CN (1999) A risk assessment framework for the evaluation of skin infections and the potential impact of antibacterial soap washing. American Journal of Infection Control 27(6): S26-S33.

Singh G, Marples RR, et al. (1971) EXPERIMENTAL STAPHYLOCOCCUS AUREUS INFECTIONS IN HUMANS. J Investig Dermatol 57(3): 149-162.