TABLE 1.
Statistical comparison of various parameters for S/R and AR models
| Parametera | Model results [estimate and relative standard errorb (%)] for strain: |
|||||||
|---|---|---|---|---|---|---|---|---|
| KP_WT |
KP_MCR-1 |
|||||||
| 1 TK |
Sequential TK |
1 TK |
Sequential TK |
|||||
| S/R | AR | S/R | AR | S/R | AR | S/R | AR | |
| BIC | 23.4 | 39.5 | 35.1 | 208.8 | 14.1 | 47.1 | 163.7 | 86.5 |
| INOC (log10 CFU/ml) | 5.60 (2.1) | 5.52 (2.5) | 5.63 (2.0) | 5.55 (4.1) | 5.78 (1.8) | 5.9 (2.5) | 5.64 (2.9) | 5.56 (2.2) |
| INOC2 (log10 CFU/ml) | 5.93 (0.9) | 5.03 (3.2) | 5.3 (2.6) | 5.85 (1.9) | ||||
| Bmax (log10 CFU/ml) | 9.29 (1.2) | 9.32 (1.1) | 9.24 (1.3) | 9.19 (2.0) | 9.34 (1.6) | 9.24 (1.4) | 9.1 (1.6) | 9.13 (1.0) |
| mutf (log10 CFU/ml) | −3.69 (9.0) | −3.49 (10.4) | −4.46 (8.9) | −10.5 (7.8) | ||||
| Kg (h−1) | 1.54 (8.1) | 1.15 (15.2) | 1.42 (10.4) | 0.935 (20.1) | (S), 1.03 (12.8); (R), 0.568 (8.0)c | 0.959 (15.9) | (S), 1.64 (20.0); (R), 1.19 (8.4)c | 1.58 (7.9) |
| Emax (h−1) | 4.40 (5.9) | 4.36 (4.8) | 3.24 (6.4) | 5.41 (10.3) | ||||
| Emax(0) (h−1) | 5.18 (8.2) | 4.92 (13.7) | 5.28 (10.8) | 7.43 (7.0) | ||||
| EC50 (mg/liter) | 0.121 (5.7) | 0.371 (14.3) | 1.85 (23.3) | 6.98 (14.6) | ||||
| EC50,S (mg/liter) | 0.0631 (2.2) | 0.065 (15.6) | 0.932 (7.2) | 1.87 (31.0) | ||||
| EC50,R (mg/liter) | 0.141 (1.3) | 0.162 (4.5) | 3.9 (13.8) | 31.1 (18.1) | ||||
| γ | 10 (fixed)d | 2.39 (15.1) | 5.01 (15.3) | 3.33 (33.4) | 3.8 (18.7) | 1 (fixed)e | 1 (fixed)e | 1 (fixed)e |
| Kon (h−1) | 0.0956 (17.5)f | 0.001 (1.2)f | 0.0856 (17.2)f | 0.0547 (7.5)g | ||||
| Kon50 (mg/liter) | 2.89 (7.4) | |||||||
| δ | 3.63 (9.8) | |||||||
| σ (log10 CFU/ml) | 0.255 (19.3) | 0.382 (20.4) | 0.29 (10.7) | 1.97 (14.9) | 0.226 (17.0) | 0.498 (18.1) | 0.825 (13.3) | 0.469 (8.4) |
INOC, bacterial count at time 0 (before the start of the 1st TK); INOC2, bacterial count at 30 h (before the start of the 2nd TK); Bmax, maximum bacterial population size supported by the system; mutf, fraction of resistant bacteria (R) at time 0; Kg, apparent growth rate constant; Emax, maximum kill rate constant; Emax(0), maximum kill rate constant when no adaptive resistance has developed; EC50, PMB concentration that produces 50% of Emax(0); EC50,S and EC50,R, PMB concentrations that produce 50% of Emax for the (S) and (R) subpopulations, respectively; γ, Hill coefficient in PMB effect relationship; Kon, rate constant for development of adaptive resistance to PMB; Kon50, PMB concentration yielding 50% of Kon; δ, Hill coefficient for rate constant for development of AR; σ, additive residual error on log10 scale for total bacteria count.
Relative standard error obtained by sampling importance resampling.
The sensitive (S) and resistant (R) subpopulations were assumed to grow at different rates, with the estimation of 2 different Kg for (S) and (R) resulting in a significant decrease in the objective function value given by NONMEM.
The Hill coefficient for this relationship, initially estimated to fall between 10 and 20, was fixed to 10 to improve model stability (13).
PMB bactericidal effect was modeled using an ordinary Emax model, with the estimation of Hill coefficient resulting in a nonsignificant decrease in the objective function value given by NONMEM.
Kon was estimated in the presence of PMB but was not dependent on its concentration.
The resistance onset rate was determined by the PMB concentration through a sigmoid Emax model. Kon corresponds to the maximal rate constant for development of AR in this case.