A multicategory logit model detecting temporal changes in antimicrobial resistance

Abstract

Monitoring and investigating temporal trends in antimicrobial data is a high priority for human and animal health authorities. Timely detection of temporal changes in antimicrobial resistance (AMR) can rely not only on monitoring and analyzing the proportion of resistant isolates based on the use of a clinical or epidemiological cut-off value, but also on more subtle changes and trends in the full distribution of minimum inhibitory concentration (MIC) values. The nature of the MIC distribution is categorical and ordinal (discrete). In this contribution, we developed a particular family of multicategory logit models for estimating and modelling MIC distributions over time. It allows the detection of a multitude of temporal trends in the full discrete distribution, without any assumption on the underlying continuous distribution for the MIC values. The experimental ranges of the serial dilution experiments may vary across laboratories and over time. The proposed categorical model allows to estimate the MIC distribution over the maximal range of the observed experiments, and allows the observed ranges to vary across labs and over time. The use and performance of the model is illustrated with two datasets on AMR in Salmonella.

Fig 1. The family of models.

Illustration of particular models using the identity, sign and null function, with reference to the setting of the CIPR data analysis (Table 2). The red curve refers to the MIC distribution at year x, the other curves refer to the distribution at year x + 1, according to different models: model 7 (solid, black) is the model with f_s(x) = 0 and f_r(x) = x with β_r > 0; model 8 (dashed, black) is the model with f_s(x) = 0 and f_r(x) = sign(x) with β_r > 0; model 12 (solid, blue) is the model with f_s(x) = x with β_s > 0, and f_r(x) = x with β_r > 0. The vertical red line refers to the ECOFF category. The upper panel shows the MIC distribution P(y = j), j = −7, …, 0 (corresponding to MIC values 2^j). The lower panel shows the logits $\text{log}\frac{P(y=j)}{P(y=J_{\text{E}})}$. The short vertical lines at the horizontal axis in the lower panel show how these logits have changed after one year (LOR’s) according to model 7, model 8 and model 12, in their respective line types and colors.

Fig 2. The CIPR data.

Jittered MIC values in blue; the red lines show the experimental ranges.

Fig 3. Barplots of the CIPR data.

Barplots with observed relative frequencies for each year in the period 2002–2013, with barwidth proportional to the sample size of the respective year. The dotted vertical lines indicate: the smallest lower bound -7 and the highest upper bound 5 across all years (in red); the lower and upper bound of the experiments of the corresponding year (in green), the ECOFF (in black).

Fig 4. The CIPR data with fitted model.

Scatterplot of observed proportions of resistant isolates by year, with bubble size proportional to the number of isolates. Solid line is the fitted model for the probability for an isolate to be resistant, as a function of time, and based on the final model 7.

Fig 5. The ISU VDL data.

Upper 2 rows: the observed and fitted trend over time using the best fitting model 7, for the probability for each of the 7 MIC values (on log2-scale), and, in the right lower panel, for the proportion resistant > 1 (1 being the threshold). Lower 2 rows: the observed and fitted MIC distribution using the best fitting model 7, for each year. The vertical red line refers to the threshold category.

Fig 6. MIC distribution for the ISU VDL data.

The observed and fitted MIC distribution, using the best fitting model 7, for each year. The vertical red line refers to the threshold category.