STOCHASTIC MODELING OF ANTIMICROBIAL RESISTANCE
Background: Continuous variables, along with proportions and rates, are often encountered in lots of regions of statistical practice such as proportion of hours spent on a weekly work, fraction of income spent on a household expenses and rate of antimicrobial resistance (AMR). Currently, there is a great need for the stochastic modeling of AMR identifying a suitable distribution for the variable of interest which is continuous and restricted to the interval (0, 1). Present article aims to identify a suitable probability distribution to a proportion data of E.coli in blood resistant to gentamicin antibiotic with the support in the interval (0, 1).
Data: An AMR data on E.coli in blood, resistant to gentamicin has been collected from clinical microbiology lab of tertiary care hospital, Udupi district, Karnataka during 2008 - 2019. The data with total of 144 time points includes information of the number of isolates of E.coli in blood and the total number of resistance for each month for the antibiotic gentamicin. The proportion of resistance has been calculated for each month which lies in the interval (0, 1).
Methods: Goodness of fit (GOF) test has been carried out for different probability distributions using Kolmogorov-Smirnov, Anderson-Darling and the Chi-Square tests. Method of maximum likelihood estimation (MLE) has been used to estimate the parameters of the distribution. Akaike information criterion (AIC) and Bayesian information criterion (BIC) have been computed to select the best model for the data.
Result: The average proportion of resistance of E.coli in blood to the antibiotic gentamicin is 0.46 ± 0.14. Three probability distributions namely: Beta distribution, Kumaraswamy distribution and Johnson SB distribution fitted to the data and the corresponding Akaike information criterion (AIC) and Bayesian information criterion (BIC) were: Beta distribution (-156.90, -156.59), Kumaraswamy distribution (-149.09, -148.77) and Johnson SB distribution (-156.85, -156.54). The Beta distribution is identified as the best fit probability model for the proportion data followed by Johnson SB distribution.
Conclusion: In the statistical analysis problems in which the researcher aims to identify the effect of different variables on the proportion of E.coli in blood resistant to gentamicin, one can employ regression or time-series modeling techniques by assuming the response data following a Beta or Johnson SB distribution.
stochastic modeling, antimicrobial resistance, Johnson SB distribution, Beta distribution, Kumaraswamy distribution.
Received: February 17, 2021; Accepted: March 25, 2021; Published: May 28, 2021
How to cite this article: Lobo Jevitha, N. Vipin, K. E. Vandana and Asha Kamath, Stochastic modeling of antimicrobial resistance, JP Journal of Biostatistics 18(2) (2021), 199-208. DOI: 10.17654/JB018020199
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
Reference:
[1] R. Wise, T. Hart, O. Cars, M. Streulens, R. Helmuth, P. Huovinen and M. Sprenger, Antimicrobial resistance. Is a major threat to public health, BMJ 317(7159) (1998), 609-610.[2] H. Von Baum and R. Marre, Antimicrobial resistance of Escherichia coli and therapeutic implications, International Journal of Medical Microbiology 295(6-7) (2005), 503-511.[3] R. S. Edson and C. L. Terrell, The aminoglycosides, Mayo Clinic Proceedings, Elsevier 74(5) (1999), 519-528. [4] J. Nocedal and S. Wright, Numerical Optimization, Springer Science and Business Media, 2006.[5] V. K. Rohatgi and A. M. Saleh, An Introduction to Probability and Statistics, John Wiley & Sons, 2015.[6] P. Kumaraswamy, A generalized probability density function for double-bounded random processes, Journal of Hydrology 46(1-2) (1980), 79-88.[7] N. L. Johnson, Systems of frequency curves generated by methods of translation, Biometrika 36(1/2) (1949), 149-176.[8] F. F. Gan and K. J. Koehler, Goodness-of-fit tests based on P-P probability plots, Technometrics 32(3) (1990), 289-303.[9] L. Jantschi and S. D. Bolboaca, Distribution Fitting 2. Pearson-Fisher, Kolmogorov-Smirnov, Anderson-Darling, Wilks-Shapiro, Cramer-von-Misses and Jarque-Bera statistics, 2009. arXiv preprint arXiv:0907.2832.[10] J. Kuha, AIC and BIC: Comparisons of assumptions and performance, Sociological Methods and Research 33(2) (2004), 188-229.
