The determined fits of the biphasic curves for different days of transition (days 2–7, Y-axis) from quick to slow phase.

The box-whisker plots represent the results from groupings from dividing the range of PK values into 10–40 equal intervals. (TIF)</p

Mechanisms that can result in a slowdown in bacterial decline: persistence and heteroresistance.

In both cases, X-axis is the time and the Y axis is the number of bacteria. Fig 1A illustrates persistence where bacteria switch back and forth between a susceptible and non-susceptible state over time only the non-susceptible ones remain. These are only killed when they exit a non-susceptible state. Fig 1B illustrates heteroresistance that is defined by a diversity within the susceptibility on antibiotics within the population of bacteria, some subpopulations will end up being killed at a slower pace.</p

Overview of the fitting process and the relationship between the decline rates of bacteria and pharmacokinetic measures.

We have grouped participants (Fig 2A) by forming equal groups within the pharmacokinetic measures. For each group, we pooled the bacterial count measurements (Y-axis) of all participants (dots, here one colour corresponds to one participant) and fitted biphasic curves to them (solid line) (Fig 2B). Next, we analysed the relationship between the groups’ median pharmacokinetic measurements (X axis) and the properties of the fitted curves (Y axis) (Fig 2C). Fig 2D summarizes the dependence of the decline rates in the quick and slow phases on and . Here, we have normalized the values (by dividing with the maximum), in order to be able to show that both measures produce the same result but with different errors. Fig 2E demonstrates how this affects the bacterial count measurements (X-axis) over time (Y-axis). The curves were made with Eq (1), starting at 106 CFU/ml bacteria, using day 4 as the day of transition, with the obtained fits for decline rates (see Table 1), and Cmax values of 10, 20, 30…80 [mg/l] (in the dataset the Cmax values range from 7.7 to 85.6 mg/ml).</p

Adjusted R squared values for the fits on the quick and slow phases’ dependence on PK values.

The different box-whisker plots in each figure correspond to a different set day of transition. These plots both show that values are consistently better predictors for the slope of the slow phase (based on adjusted R-squared values), as well as that we achieve the best fits for days 3 and 4. (TIF)</p

Comparison of the smoothed averages of the clinical trial and model predictions on sputum bacterial counts over time.

This figure compares the smoothed averages of the clinical trial (Fig 5A, this is the same plot as in Fig 2E), the predicted decline of bacteria in cavity walls if the slowdown is caused by heteroresistance (Fig 5B) or persistence (Fig 5C). We generated these plots using pharmacokinetic models in the cavity wall with the same Cmax values as in Fig 5A (10…80 mg/l). Finally, Fig 5D shows the difference between the curves on Fig 5A and 5B: on all days and Cmax values combined, the X axis shows the model predictions and the Y axis shows the smoothed averages of the clinical trial ().</p

Difference of corrected AIC values for the fits on the slow and quick phases for different days of transition.

Here, the positive values indicate that Cmax is a better predictor, while negative values would indicate that AUC is a better predictor for the given phase. (TIF)</p

Estimating the sensitivity distribution of bacteria.

This figure shows the method we used to estimate the sensitivity distribution of bacteria when the slowdown is caused by heteroresistance. Fig 4A (illustration) shows that different parts of the time-kill curves (bacterial count (Y-axis) over time (X-axis)) represent the decline of subpopulations with different MICs (different colours) [28]. In these cases, even after fitting biphasic curves on a multi-phasic time-kill curves (Fig 4B (illustration)), the slow phase will represent a subset of subpopulations which can be identified based on the decline rates at the given antibiotic concentration (Cmax or AUC in case of PK based models). Fig 4C shows the parameters used obtained from clinical trial dataset: decline rates in the slow phase and the corresponding “subpopulation sizes” at each Cmax. Fig 4D shows the value pairs from Fig 4C: the obtained sensitivity distribution and a fitted (assumed) normal distribution to it. Fig 4E shows the distribution of Cmax values in each dosing group and how they compare to the pharmacodynamic parameters of MIC (1.3mg/l) and EC50 (5.6mg/l, concentration at which bactericidal activity is 50%) [35]. These values are marked for both a drug sensitive subpopulations and a less susceptible subpopulation (8x MIC) to illustrate how the sensitivity of bacterial subpopulations in Fig 4D relate to the pharmacodynamic parameters. Here, we assume that the EC50 values of the less susceptible (8x MIC) subpopulations are 8x the original EC50 values. However, the correct relationship between MIC and EC50 in different subpopulations is unknown as resistance mutations have a chance of affecting the slope of the PD curves not just the effective antibiotic concentration [46], therefore this figure is for illustrative purposes.</p

Summary of the median fitted values to the dataset across all groupings, when assuming a monophasic killing (fitting a straight line though the data).

All the P values reported are corrected for multiple testing with the Benjamini-Hochberg method. (DOCX)</p

Estimated TSCC based on the statistical analysis, and comparison to measured TSCCs in a multi arm multi stage (MAMS) clinical trial (NCT01785186, [30]).

Note: this the left and right columns of this figure are the same as Fig 6. but extended with the standard dosing group for comparison. There, estimates relied on extrapolation outside the range of PK values of the EBA trials (see S7A and S7D Fig). On all of the plots the green curves show estimates based on biphasic curves (i.e taking the slowdown in decline into account), while red shows estimation based on monophasic curves (i.e. neglecting the possibility of a slowdown in decline). Blue always corresponds to data from the MAMS clinical trial. S7A and S7D Fig show the dependence of the predicted TSCC on the pharmacokinetic parameters (Cmax and AUC respectively), as well as the measured pharmacokinetic ranges for the HRZE and HR35ZE treatment arms in the MAMS clinical trial used for comparison (blue boxes). Here, the area around the estimates signify the 95% confidence interval around our estimates. The estimates are only shown within the parameter ranges of the EBA clinical trial. S7B, S7C, S7E, and S7FF Fig show the cumulative probability (Y-axis) of TSCC (X-axis) based on the estimates within the PK ranges of the MAMS trial as well as the data from the MAMS trial itself. This is shown for both Cmax and AUC, as well as the HRZE, and HR35ZE treatment arms. (TIF)</p

P-values for the fitted data with different day of transition (days 2–7, Y-axis) from quick to slow phase.

The box-whisker plots represent the results from groupings from dividing the range of PK values into 10–40 equal intervals. These plots show that if we get the best fits if the days of transition are set to day 3 or 4. Furthermore these also show that Cmax is consistently a better predictor for the slope of the slow phase than the AUC. (TIF)</p