Statistical characterisation of bacterial wild-type MIC value distributions and the determination of epidemiological cut-off values

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MIC distribution data were obtained from a variety of international sources, and pooled after selection by a defined criterion. Sixty-seven of these datasets were subjected to a range of statistical goodness-of-fit tests. The log-normal distribution was selected for subsequent modelling. Cumulative counts of MIC distribution data were fitted to the cumulative log-normal distribution using non-linear least squares regression for a range of data subsets from each antibiotic–bacterium combination. Estimated parameters in the regression were the number of isolates in the subset, and (the log2 values of) the mean and standard deviation. Optimum fits for the cumulative log-normal curve were then used to determine the wild-type MIC range, determined by calculating the MICs associated with the lower and upper 0.1% of the distribution, rounding to the nearest two-fold dilution, and calculating the probabilities of values higher and lower than these values. When plotted logarithmically, histograms of MIC frequencies appeared normal (Gaussian), but standard goodness-of-fit tests showed that the two-fold dilution grouping of MICs fits poorly to a log-normal distribution, whereas non-linear regression gave good fits to population (histogram) log-normal distributions of log2 MIC frequencies, and even better fits to log-normal cumulative distributions. Optimum fits were found when the difference between the estimated and true number of isolates in the fitted subset was minimal. Sixteen antibiotic–bacterium datasets were fitted using this technique, and the log2 values of the means and standard deviations were used to determine the 0.1% and 99.9% wild-type cut-off values. When rounded to the nearest two-fold dilution, ≥ 98.5% of MIC values fall within the cut-off value range. Non-linear regression fitting to a cumulative log-normal distribution is a novel and effective method for modelling MIC distributions and quantifying wild-type MIC ranges.

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